Maritime accidents are lethal threats to lives, economies, and the environment as a result of which there is a need to develop advanced prediction models for early risk identification. In this paper, a novel framework integrated with Capsule Neural Networks (CapsNets) and a Modified Orangutan Optimization (MOO) algorithm is proposed to predict maritime accident hotspots. The CapsNet model captures spatio-temporal dependencies from the Global Maritime Distress and Safety System (GMDSS) dataset, while the MOO fine-tunes hyperparameters toward maximizing model accuracy and generalization. Experimental results suggest that the framework works exceedingly well against the baseline models by achieving an accuracy of 91.2%, while improving precision and recall, and reducing error rates on the contrary. Geospatial heatmaps and decision boundary visualizations strengthen the claim regarding the model’s capacity to identify high-hazard zones and clearly categorize incident types. Compelling case studies illustrate its potential for reducing response time through proactive monitoring and preparedness, which is possible only through integrating information with prediction methods. The study takes maritime safety analytics into a very intelligent and data-driven domain by overcoming shortcomings of existing predictive methods. The framework opens the door to the future integration into rescue resource planning systems, where predicted risk zones will inform strategies for asset deployment.
maritime safetycapsule neural networksmodified orangutan optimization algorithmpredictive analyticsaccident hotspot predictiongeospatial heatmapsThe author(s) declared that financial support was not received for this work and/or its publication.section-at-acceptanceOcean ObservationIntroduction
Maritime accidents can pose gigantic threats to life, the economy, and the environment. According to the International Maritime Organization (IMO) (Dikaios, 2024), a few hundred maritime accidents occur each year and are categorized under the generic names of vessel collision, grounding, fire, or sinking. The incidents result in loss of life, environmental accidents such as oil spills, and economic devastation from damaged vessels and ports unable to operate with interrupted cargo deliveries. For instance, the damages from the 2002 Prestige oil spill were in the range of $4 billion, and it had severe ecological effects on the coastal areas (Heiberg, 2012). Efficiently carrying out detection and response works in damage minimization, requiring accurate prediction models identifying the highest-risk maritime zones before accidents occur.
Despite advances in navigation technology and safety features, challenges still exist in responding to marine distress. Delayed identification of distress calls, inefficient use of rescue assets (e.g., lifeboats, helicopters, and coast guard vessels), and limited predictive capabilities contribute to low performance. Traditional approaches to carrying out rescue operations rely heavily on human judgment and experience and are insufficient for addressing the dynamic and complex maritime environment. Current maritime rescue systems encounter several shortcomings:
Delayed Response Times: There can be a delayed time to identify and answer distress calls due to the use of outdated communications equipment or human error.
Insufficient Resource Allocation: Rescue resources are typically allocated based on pre-established schedules or intuition rather than data-driven real-time information, resulting in overloading or underutilization of assets.
Lack of Predictive Competences: Present systems are largely reactive in nature rather than proactive. They do not forecast accidents that are likely to occur or optimize resources accordingly.
Data Complexity: Maritime databases, as provided by the Global Maritime Distress and Safety System (GMDSS), are vast and varied and consist of variables like location, time, weather, and ship types. It requires advanced analytical tools to make any meaningful inferences from such data.
These limitations underscore the novel applications of artificial intelligence (AI) and machine learning (ML) solutions to improve maritime rescue operations.
(Figure 1) Predictive analysis has arrived as a revolutionary technique to resolve the issues faced in sea rescue operations. By analyzing trends in historical data, predictive models can forecast probable accidents, identify high-risk areas, and recommend optimal deployment of rescue resources. This proactive approach not only reduces response times but also minimizes the severity of accidents.
Limitations of current maritime rescue systems.
Flowchart depicting issues in the Maritime Rescue System. Central box labeled “Maritime Rescue System” connects to “Delayed Response Times,” “Outdated Communication Systems,” and “Human Error.” It also links to “Inefficient Resource Allocation” with “Fixed Schedules” and “Intuition-Based Decisions,” “Lack of Predictive Capabilities” with “Reactive Measures” and “Failure to Anticipate,” and “Data Complexity” with “Vast Datasets” and “Heterogeneous Variables."
Recent advancements in AI have shown their predictive modeling capabilities, such as Capsule Neural Networks (CapsNets). Capsule networks are distinct from traditional CNNs as they have a stronger ability to recognize spatial relationships and hierarchical structures of information (Zhou et al., 2023). This makes them extremely suitable for analyzing maritime data, where it is of prime importance to understand the spatial distribution of events. The optimization algorithms also play a critical role in optimizing the hyperparameters of such models to achieve improved performance.
In the context of maritime rescue, CapsNets are able to identify relationships between different features (e.g., weather, position, and ship type) to successfully predict accident occurrence.
Optimization algorithms augment capsule networks by automating hyperparameter selection, which is key to model performance. Hyperparameters like learning rate, number of capsules, and regularization coefficients have a profound impact on the training process. Amid the several optimization methods available, bio-inspired algorithms have been popular for their capability in exploration-exploitation balance.
This approach distinguishes itself as strongly contributing to operations involving maritime search and rescue (MSAR) by assessing the limitations of current working systems, namely delayed response time, ineffective resource allocation, lack of predictive capabilities, and complex datasets, prioritizing the CapsNets and a Modified Orangutan Optimization (MOO) algorithm.
At variance with conventional methods that depend on static rules or methods that cannot capture spatial hierarchies, CapsNet-based modeling proposed by us performs active learning on maritime datasets with respect to pose and part-whole relationships, thereby allowing the model to learn complex spatio-temporal relationships such as interaction between the position of the vessel, weather characteristics, and navigational context.
This occurs with enhanced prediction of high-risk zones before the onset of incidents and types of incidents set to happen, thereby changing the phase to proactive rescue planning. The MOO algorithm also contributes significantly to the novelty by optimally adjusting some key hyperparameters, ensuring maximum generalization and stability to the model.
The main contribution of this paper is to build a predictive framework for maritime rescue resource distribution using CapsNet with a modified Orangutan Optimization algorithm as a bio-inspired algorithm.
This paper’s main contribution is developing a predictive framework that would apply Capsule Neural Networks (CapsNets) along with the Modified Orangutan Optimization (MOO) algorithm for maritime accident hotspot identification. The research contributions include:
- Developing a CapsNet architecture model capable of learning the spatial-temporal dependencies between maritime accident factors like location, weather conditions, vessel type, and time of occurrence.
- Prepending and training the model on real-world GMDSS data for practical relevance.
- Introduce a modified version of the Orangutan Optimization algorithm for automatic hyperparameter tuning and model improvement.
- A framework will be validated using extensive experimentation, geospatial visualizations, and case studies.
These objectives would improve the accuracy and reliability of forecasting maritime accidents, thereby enabling data-driven future uses of the framework for Maritime Safety Management, including possible optimization in resource deployment during rescues.
Literature review
In the last ten years, researchers have investigated various methodologies for solving these issues, employing developments in artificial intelligence, optimization methods, and predictive analytics. The research conducted has introduced new solutions that encompass opportunistic routing protocols, machine learning-based prediction models, and multi-objective optimization frameworks. Although each of these methods has shown promise for enhancing certain aspects of MSAR operations, there are still challenges concerning scalability, accuracy, and the capacity to adapt to real-time situations. This literature review discusses significant contributions to the field, their strengths and shortcomings, and their implications for further research.
Wu et al (Wu et al., 2018). utilized opportunistic routing that could employ the broadcast feature of radio propagation. The routing decisions within opportunistic routing relied solely on the information from neighboring nodes. There was no need for network-wide flooding for establishing routes. To keep neighbor information up-to-date and reduce the energy expenditure associated with gathering this data, a lightweight approach has been suggested for predicting routing metrics using time series analysis to address the high communication expenditures that arose from updating the recent routing metrics. The application of the opportunistic routing protocol accomplished a 30% higher Packet Delivery Ratio in comparison with the conventional Ad hoc On-Demand Distance Vector (AODV). Furthermore, the opportunistic routing protocol that utilized a forecast was superior to the model that did not use a forecast. The suggested approach accomplished 90% efficiency, while the AODV protocol reached only 60% efficacy. In the process, an extra 3% of energy was utilized via the nodes.
Sun et al (Sun et al., 2022). exploited an optimum distribution technique that used the constrained resources of SAR utilized at navigation-limited seaside islands. The research addressed the issue relevant to SAR resource distribution in seaside regions by developing a non-linear optimization network. The optimum solution for the SAR resource distribution challenge was investigated while considering various settings for aircraft and ship base stations, utilizing an enhanced PSO (Particle Swarm Optimization). Results from experiments indicated that the EPSO effectively allocated maritime rescue resources, achieving a broad coverage region and minimal time expenditure. Additionally, genetic algorithms and particle swarm optimization have been employed for comparison regarding model efficacy.
Dong et al (Dong et al., 2024). suggested a comprehensive approach for distributing resources of MSAR that aimed to enhance the entire efficacy of MSAR applications. Initially, the LSTM was utilized for predicting the quantity of upcoming events, and the K-medoids algorithm was utilized for identifying the accident block spot within the investigated region. After that, multi-limit circumstances were analyzed within the MSAR resource distribution procedure. An integer programming network with multiple objectives has been developed to lower the allocation expenditures and time of response. Ultimately, the non-dominated sorting genetic algorithm II (DNSGA-II) has been applied utilizing rules of Deb to resolve the network, and a multi-attribute decision approach based on decision for MSAR resource distribution. The suggested findings indicated that the DNSGA-II showed improved convergence and produced superior quality solutions in comparison with the NSGA-II, EPSO (Enhanced Particle Swarm Optimization), and PSO (Particle Swarm Optimization) techniques. In comparison with the current MSAR resource emergency response network, the optimal strategy decreased the allocation costs and response time by 6.15% and 11.32%, respectively.
Lan et al (Lan et al., 2025). forecasted the demand for water in an accurate manner. The current examination offered forecast model that employed a prediction architecture that employed a Xception model that is optimized via the advanced maritime search and rescue with the purpose of increasing accuracy while predicting forthcoming trends of water demand using shared socioeconomic route contexts. The improved Xception model employed shared socioeconomic routes to assess the possible impacts of socioeconomic development on industrial and domestic water demand. The findings of the current research could assist water resource managers and policymakers by offering insights into upcoming trends in demands of water demand. The data could aid in planning and making educated decisions for the sustainable management of water resources, despite variability and uncertainty.
Ma et al (Ma et al., 2022). developed an optimization network for emergency resources distribution to enhance the efficacy of MSAR operations and the distribution efficacy of maritime emergency resources while taking into account numerous constraints, namely probable situations of rescue bases, accident black-spots, rescue ships, and diverse kinds of emergency resources. Considering the initial stage, LSTM has been employed for forecasting the quantity of probable accidents within the examined region. K-means algorithm has been offered for identifying the cores of accident black-spots. Eventually, the optimization algorithm with multiple objectives has been developed, and EGA (Elite-preserved Genetic Algorithm) has been utilized or determine the optimal emergency resource distribution technique. The outcomes represented that the distribution technique could fulfill the needs of real-time using a budget utilization with the value of 87.9%.
For the sake of cross-study referencing, it would be pertinent to investigate further works that have used various artificial intelligence techniques towards maritime accident prediction. Some recent works have focused on Bayesian networks for probabilistic risk assessment, taking advantage of being able to model causal relationships between human error, environmental conditions, and mechanical failure in the accident context (Dinis et al., 2020).
For example, Yin et al. developed a dynamic Bayesian network to predict the risk of vessel collision in congested waterways by being informed by real-time AIS data and weather conditions, achieving high interpretability and uncertainty quantification (Yin et al., 2011). Additionally, Fuzzy systems were also applied to fuzzy or missing maritime data, especially for navigation safety decision-making support (Yazdi and Kabir, 2017).
Hybrid models combining deep learning with attention mechanisms have also emerged: in other work, for example, a Transformer-based architecture to model long-range temporal dependencies in vessel movement patterns for accident forecasting (Yue et al., 2024). Although these frameworks provide important insights, they face difficulties of either spatial feature preservation (e.g., CNNs and Transformers) or requiring great domain knowledge for structure learning (e.g., Bayesian networks). In contrast, the proposed CapsNet-MOO framework is unique in integrating capsule networks’ spatial-hierarchical learning capabilities with an intelligent optimization mechanism to resolve generalization vis-a-vis accuracy in one objective. This tangent highlights the changing landscape of AI in maritime safety and places our work in a broader methodological spectrum.
The literature highlights the necessity of incorporating cutting-edge computational methods within the resource allocation models in MSAR. Opportunistic routing method, as exemplified by Wu et al., offers an effective means to achieve communication efficiency in rescue networks; however, its demand for neighboring information could restrict its application under sparse maritime conditions. Similarly, optimization-based approaches like those of Sun et al. and Ma et al. provide stable solutions for resource allocation but are computationally expensive and need prior knowledge of environmental constraints. Dong et al. take these efforts a step further by incorporating machine learning algorithms like LSTM and K-medoids clustering and achieving considerable enhancement in prediction performance and operational effectiveness. However, these methods still face difficulties when used with noisy or incomplete data, which are all too common in actual maritime datasets. Lan et al. showed an innovative use of shared socioeconomic pathways for water demand forecasting, thereby illustrating the applicability of predictive analytics in uses other than the conventional MSAR applications.
Despite the advances that have been accomplished, there continues to exist an enormous gap in the collective accomplishment of the collaborative requirements for better predictive accuracy, hyperparameter tuning, and timely responses in the collaborative setting. The proposed Capsule Neural Network, supported by the incorporation of a Modified Orangutan Optimization algorithm, seeks to overcome this limitation by combining the strengths of deep learning and nature-inspired optimization techniques that offer a novel solution for the intricacies of maritime rescue operations.
Methodology
The intent of this segment is to submit a thorough description of the proposed methodology, encompassing the data preprocessing, CapsNet architecture, MOO algorithm, and their collective utilization in predictive analysis in the context of resource planning for maritime rescue activities. Further, the section describes the workflow and training, and validation processes. Figure 2 shows the comprehensive flowchart of the proposed methodology.
The comprehensive flowchart of the proposed methodology.
Flowchart detailing a process involving four main stages: Input Data (GMDSS Dataset), Data Preprocessing with steps like missing value imputation and feature extraction, Modified Orangutan Optimizer for hyperparameter tuning, and Capsule Neural Network architecture for classification. Final stage is Output and Evaluation, focusing on predictions, geospatial heatmaps, decision boundaries, and performance metrics such as accuracy and precision.
The evaluation metrics, comparison with baseline models, and case studies are described elaborately to demonstrate the efficacy of the suggested framework.
Preprocessing of the GMDSS data effectively is a requirement for achieving quality input for the predictive model. The data contains plenty of information concerning maritime incidents with variables such as location, time, weather, vessel type, and distress signals. The preprocessing procedures are described as follows:
Cleaning and formatting
Cleaning and formatting are basic operations to handle missing values, outliers, and inconsistencies in the data. These operations make the data complete, accurate, and analysis-ready.
(A) Handling Missing Values.
Missing data is an issue in real-world databases. Missing values may be present in attributes such as latitude, longitude, weather, or vessel attributes in the GMDSS database. This has been handled using imputation techniques.
Numerical Features: Missing values in numerical features like latitude, longitude, and wind speed are imputed through Equation 1:
ximputed=x¯=1N∑i=1Nxi
where, xi is feature values that are observed, and N is the number of non-missing observations.
Categorical Features: Missing values in categorical features like vessel type or weather are imputed through Equation 2:
ximputed=Mode(x)
where, Mode(x) is the most frequent value in the feature.
Figure 3 is a graphical illustration of how missing values are handled.
Handling missing values: latitude imputation.
Line graph showing latitude versus data point index. The graph has original data points marked with red circles and imputed points connected by a blue line. The pattern rises from 45 at index 1, peaks at 47 at index 3, and slightly decreases towards index 5. Legend differentiates original and imputed points.
Imputation does not leave any data points missing in the event of missing values and ensures data set integrity. However, it must be carefully chosen with respect to the nature of the feature and its distribution.
(B) Outlier Detection.
Outliers can impact machine learning models and generalize poorly. The outliers in the GMDSS may be due to sensor failure, human mistakes, or unexpected circumstances. Statistical techniques can identify and control outliers:
- Z-Score Method: The value of an attribute has been marked as an outlier wherever its Z-score is greater than a threshold (e.g., |Z|>3) as shown in Equation 3:
Z=x−μσ
where, x represents the value of the feature, μ for mean and σ for standard deviation.
IQR-Based Method: The Interquartile Range (IQR) is used to identify outliers: LowerBound=Q1−1.5·IQR, UpperBound=Q3+1.5·IQR,
where Q1 and Q3 are the first and third quartiles, respectively. Figure 4 shows the outlier recognition in vessel speed.
Outlier recognition in vessel speed.
Scatter plot showing vessel speeds in knots against data point index. Most points, marked as non-outliers, are near zero speed, while one outlier is marked at 100 knots. Legend differentiates all data, outliers, and non-outliers.
Outliers are edited or eliminated on the basis of domain understanding. For example, 100 knots speed by a ship cannot be achieved and is an outlier; therefore, it needs to be identified and edited.
Feature extraction
Feature extraction converts raw data into helpful representations of the data that reflect the patterns inherent in the database.
(A) Location Features.
Geographic coordinates (latitude and longitude) are critical in spatial relationship modeling. These features are normalized to a unit scale (0, 1) based on Equation 4:
xnorm=x−xminxmax−xmin
where, xmin and xmax are the minimum and maximum values of the feature.
In addition, computationally extracted features such as distance to the nearest coastline and proximity to high-risk zones are determined in Equation 5:
DistancefromCoastline=(x−xc)2+(y−yc)2
where, (xc, yc) are the coordinates of the nearest coastline point.
Derived features are utilized to further facilitate the model to learn spatial relationships, i.e., accident hotspots near coastlines or sea lanes.
(B) Temporal Features.
Timestamps are converted into valuable time-related features to identify temporal patterns:
- Hour of the Day: Obtained using the hour function.
- Day of the Week: Divided into Monday, Tuesday, etc.
- Seasonality Indicators: By month (e.g., spring, winter).
Temporal features help identify patterns such as peak accident times or seasonal variations in maritime incidents.
(C) Environmental Features.
Weather conditions are critical for predicting accidents. Continuous variables like wind speed and wave height are categorized into discrete levels:
Low: 0≤x<10
Medium: 10≤x<20
High: x≥20
Discretization simplifies the representation of environmental features and reduces noise.
(D) Vessel-Specific Features.
Vessel attributes like type, size, and age are encoded as categorical variables using one-hot encoding as illustrated in Equation 6:
One−HotEncoding(x)=[0,1,0]
where, x corresponds to a specific category.
Figure 5 shows two examples of Feature Extraction, including normalized geographic coordinates and temporal feature extraction.
Feature extraction: (A) Normalized geographic coordinates, (B) Temporal feature extraction: hours of the day.
Panel A shows a line graph with normalized latitude on the x-axis and normalized longitude on the y-axis, displaying a descending line with circular markers at both ends. Panel B displays a bar chart with data point indices on the x-axis and hour of the day on the y-axis, featuring three bars of varying heights at indices one, two, and three.
One-hot encoding ensures that categorical features are represented in a format suitable for machine learning models.
(E) Normalization and Scaling.
Numerical features are standardized using Min-Max scaling to ensure uniformity across the dataset, which improves convergence during model training.
By the rigorous preprocessing of GMDSS data, a clean properly formatted dataset has been created to be employed as the reference for training the Capsule Neural Network as illustrated in Equation 7.
xscaled=x−xminxmax−xmin
Normalization prevents features with higher ranges from dominating the learning process and equates all features.
Rationale for feature preprocessing and categorization
The structuring of input variables has been decided and also processed through statistical analyses on the GMDSS dataset, along with relevant maritime safety knowledge. The use of temporal features is the fact that day of the week should be encoded as distinct categories (Monday, Tuesday, etc.) rather than broader ones like weekdays or weekends decided from exploratory analysis, showing that no real clustering of accident frequency between workweek vs. weekends.
Rather evenly across the seven days, with Friday and Saturday peaks apparently caused by increased vessel traffic, an incident nominal, those mere differences gave rise to classification of every day as a separate category, where the model captures subtle, specific day patterns without arbitrary groupings, thus denying meaningful variance.
Wind speed and wave height ranged in terms of Low, Medium, and High levels using established maritime safety thresholds from the World Meteorological Organization (WMO) and the International Maritime Organization (IMO). In terms of wind, Low (=3 at most under Beaufort), Medium (=4-6), and High (=7 and above) correspond to the wind speed as follows: Low (<10 knots, Beaufort 3 or less), Medium (10–25 knots, Beaufort 4-6), and High (>25 knots, Beaufort 7+).
Wave height is Low (<1.25 m), Medium (1.25–4 m), and High (>4 m)-sea states 3–5 and above according to Douglas Sea Scale. These thresholds are given more operational weight because they are the ones affecting directly the ability of vessels to maneuver, crew responses, and activation of safety protocols. Thus, with their being of least distinction to where thresholding impacts interpretation enhancement and reduction of minor variances, they ensure input space emphasis on real-world maritime risk conditions. Also, they were validated through ablation studies (not shown due to space limitations), confirming that encoding and degree of discretization yielded the highest predictive accuracy and converged stability through the study within the CapsNet architecture.
Capsule neural network
The CapsNet has been an approach to ANN or Artificial Neural Network, which aims to identify productive relationships in an efficient way by using capsules as instant computational entities (Chen et al., 2025). Each capsule is a group of neurons which show the probability of a specific feature.
These capsules describe different features of an entity, including their state of being, shape, direction and condition. Additionally, each capsule has the capability to comprehend the diverse situation of input features and interactions of the environment, which are neglected in conventional neural networks (Wang et al., 2024).
Some layers of the capsule belong to the network, where all of them possess a unique level of thought. A dynamic structure for routing connects the low-level capsules with higher-level ones. The coefficient connection between the capsules is enhanced iteratively. The present process of improvement has been conducted according to the posture variables’ organization. The existing network is able to identify the connections among different portions and finish parts that make the capsules more valuable by demonstrating an enhanced relationship among the capsules having greater levels.
The output of this network has various vectors and all the vectors are equal to a previously chosen category. The intended category is represented by each vector which is made up of possibilities and parameters of the situation. The possibility of each class is represented via vector’s length, and the situation’s parameters are shown by its direction.
A margin-based loss function is used while training CapsNet. This endeavor attempts to encourage the correct class in a move to keep longer vectors and prevent the incorrect categories in a move to keep them from having longer vectors. Aside from that, margin-based loss function includes an ordinary process for normalization which discourages the network at hand from assigning high chances to most of the classes.
In the bottom layer, all of the capsules hold a vector of action pj that describes geographic information referring to the capsule’s index within element of insanitation, and it is addressed by j. The output vector pj of the jth capsule of a lesser level is applied in the following layer 1 + 1; it is used for each capsule. ith candidate receives the input pi and computes its output using the weight matrix Yj,i in the 1 + 1 layer. And the predicted layer pj,i displays the initial quantity j, in category i as defined in Equation 8.
pj,i=Yj,i×pj
The degree of conformity between candidates with the major factor in order to predict jth candidate’s behavior with the ith candidate is determined by coupling coefficient while replicating the major predicting factor of jth candidate. Two candidates are joined. So, while inverse process takes place, the coupling coefficient grows. For the analysis of the impact of compressing candidate function, the total amount (Yxi) has been allocated for the ith candidate’s major prediction that are defined in Equations 9–11.
It is compression with probability association that leads to the limitation of the output of the individuals to n values between 0 and 1. The di capsule layer switches to the succeeding layer which functions in exactly the same way as the former layer. The first predicting level has been represented through qj, which is further generalized to the 1+1 layer. Throughout all of the eras, the factors to which p^j,i is received are the elements.
The vector of every capsules has been viewed as a combination of two values which rely on quantity. The main variation is that capsules create probability and squeeze features, while most aspects of insanitation are used in determining the reliability of the layers. A higher level of capsule and a lower one are in conformity with each other, yet between the entire structure and an element, the correlation is shown through it which depicts the importance of the path. The Dynamic routing-by-agreement is reflected by the insight.
There are two major layers in the existing model i.e. input layer and capsule layer. The input layer controls the input data that is produced by the pre-training process. In the meantime, the capsule layer is tasked with specifying each of the patterns within the data and naming them. This layer is a dense of 32 channels that are convolution; it has a kernel size of 9×9,and a stride of two.
Hence, a vector has been created due to insanitation that shows a potential relationship between the appearance of the capsules in the margin loss scene and the function. A target is presented by the scene capsules that they all represented a certain ratio of loss of margin that are characterized by using the equation below. The maximum value of the vector is indicated through Dh in each group of scene when the scene is rendered inside the input image as defined in Equation 12.
GDh=UDhmax(0,b+−‖DVr‖)2+α(1−UVr)max((0,‖DVr‖−b−)2
Due to this study, the value of UDh will be 1 when there exists a scene. Also, values 0.9 and 0.1 are given to b+ and b−, respectively. The parameter α has been obtained by minimizing the effect of all capsules of scene. While there is process of normalizing, the scene capsules have a significant role. The scenes, correctly identified, are divided by the number of all the scenes in order to calculate the accuracy (see Equation 13).
It is extremely important to tune hyperparameters of the present model in order to move to the phase below. The model used optimizer for determining hyperparameters that are within context and has D dimensions whose main aim is to minimize the validation function.
Many hyperparameters have been illustrated by OB. If the model is structured properly, one can effectively decide the evaluation problem. In combination with OB optimizer, a solution is proposed as follows, which enables automatic allocation of the best hyperparameters based on Equation 14.
minx∈RGOB(x,θ;Zval)s.t.θ=argminOB(θ;Strain)
Since the OB index is in fact advanced, overcoming the challenge of the above equation is in fact challenging. The training database is illustrated through the use of s.t.θ. In addition, Y is used in an attempt to analyze the data. Minimization learning process and set management represented by x values, are the main goal of the training process. Refined Capuchin Search Algorithm (RCSA) is utilized in handling index of error costly, and the same has been utilized for hyperparameter tuning for the model.
Rationale for capsule neural networks in maritime accident prediction
Capsule Neural Networks were adopted as a predictive paradigm not by chance but rather for the very consideration that maritime accident data are unique spatial-temporal and hierarchical entities. Standard CNNs are incapable of preserving pose information due to the pooling operations employed for image recognition.
The CNNs are least effective in a situation in which prediction accuracy hinges upon getting the relative positioning of elements right. Unlike CNNs, with their capsules forming vector-valued neurons, CapsNets preserve pose information through the principles of dynamic routing by agreement. Hence, they are tremendously suitable for the forecasting of maritime accidents.
Maritime accidents evolve from the interplay of complex hierarchies set in space, not just the random occurrence of events. For instance, there are spatially dependent elements determining the collision risk: wind speed and density of vessels are not determining factors in isolation, rather their positioning regarding the congested shipping lane, all stuck in time, along with congestion and poor visibility.
A vessel in close proximity to a high-traffic zone with high wave height is at infinitely greater risk than that same vessel in open sea with little disturbance. CapsNets are exceptional in modeling the part-whole relationships where low-level capsules detect local features (high winds, nearness to the coast), whereas higher-level capsules integrate those into more global risks (collision risk in foggy straits) through the routing process. This allows the model to not only discriminate which features occur in an input but also how they are anatomically arranged temporally and spatially, which is crucially necessary for making the distinction between high-risk and low-risk scenarios.
Moreover, maritime data are always geospatial in nature, wherein latitude and longitude are prime predictors. The most salient feature of CapsNet in encoding spatial hierarchies is to learn that even slight positional shifts (open ocean to narrow channel) may almost entirely alter risk profiles, a subtlety usually lost upon scalar-output CNNs. The said equivariance to spatial transformation of the model generalizes considerably well over different regions and conditions. Figure 6 shows the rationale for capsule neural networks in maritime accident prediction.
Rationale for capsule neural networks in maritime accident prediction.
Flowchart illustrating a risk prediction model for maritime safety. Input features, such as location, temporal, environmental, and vessel-specific data, are vectorized and processed through a capsule neural network optimized by multi-objective optimization. The network includes layers that reshape and detect features, dynamically route data, and produce output vectors indicating risk levels. Outputs include accident risk levels, geospatial heatmaps, decision boundaries, and optimized hyperparameters.
In settings addressing the precise prediction of accident hotspots, the capacity of CapsNet to maintain and reason over spatial relationships presents a unique and significant merit above conventional deep learning models in answering the challenges stated as the “lack of predictive competences” in existing maritime rescue systems. Through CapsNet, this research thus moves beyond conventional methods of pattern recognition to relational reasoning amidst context, which forms the bedrock of reliable and correct forecasting of maritime risks.
Modified orangutan optimization algorithm
In the following section, the theory behind the Orangutan Optimization Algorithm (OOA) is extensively described after a thorough explanation of the algorithm’s inspiration. Subsequently, the OOA’s methodical implementation is properly modeled employing mathematical formulas to guarantee that it may be used to successfully address a wide range of optimization issues.
Initialization of the algorithm
The recently developed Orangutan Optimization Algorithm (OOA) is a bio-inspired metaheuristic technique that is based on the natural behaviors of orangutans. In this method, orangutans act as the members of the population, with each individual representing a potential solution, with each individuals representing a potential solution to the specified optimization challenge. These solutions are distinct from one another, as each orangutan has a distinct place in the search space for the issue. The particularly location of the orangutan, which is capable of being represented mathematically as a vector, determines the variables that are associated to each response. The OOA population, which is made up of these orangutans together, may be expressed as a matrix structure employing Equation 15.
This matrix changes while the algorithm operates; it is not static. First, each orangutan’s location inside the search space is chosen at random. By guaranteeing that the starting population encompasses a variety of areas inside the search space, this unpredictability improves the algorithm’s capacity for exploration.
Each dimension of the orangutan’s location is determined employing random values in the range specified in Equation 16, which mathematically models the population’s initialization procedure. This gives each orangutan an entirely unique location to start, which leads to a variety of candidate solutions.
Where, the number of orangutans denoted by N, the OOA population matrix showed by X, Xi displayed the ith orangutan (candidate solution), xi,d represented its dth dimension in search space (decision variable), m presented the number of decision variables, r showed a random uniform number between 0 and 1. lbd, and ubd illustrated the lower bound and upper bound of the dth decision variable, respectively.
Following initialization, the location of each orangutan correlates to a set of variables that are assessed employing the optimization problem’s objective function. Each candidate solution is given a value by the goal function, and Equation 17 illustrates how this collection of values may be formally described as a vector.
F=[F1⋮Fi⋮FN]N×1=[F(X1)⋮F(Xi)⋮F(XN)]N×1
Where, the computed objective function vector denoted by F, and the computed objective function for the ith orangutan showed by Fi.
The quality of each solution is determined by the goal of computed values. The algorithm determines the worst-performing orangutan and the best-performing (i.e., the proposed solution with the highest best value) based on these assessments.
Because the orangutans’ locations are changed with each algorithm iteration, the values of the related objective functions likewise change. The optimal solution needs to be changed often while the search goes on in order to take into account the greatest orangutan discovered thus far. By adjusting orangutan locations iteratively, the method is guaranteed to efficiently search the problem space and progressively approach an optimum or nearly optimal solution.
Phase 1: foraging strategy (exploration)
In their native environment, orangutans spend a lot of time looking, including tree leaves, fruits, and other food sources. Because of their foraging habit, they move around a lot and explore their surrounding thoroughly, which enables them to find foods in whole new places. The algorithm’s exploration abilities are improved by simulating this foraging technique within OOA, which makes it more skilled at scanning and exploring the problem’s global space.
To replicate this foraging behavior, each orangutan’s location is changed throughout the initial stage of OOA. Each orangutan searches for superior locations because those with higher objective function values are seen to be better food sources. By taking into account all orangutans with higher goal function values, Equation 18. Mathematically described the set of food resources that are accessible for each orangutan. The orangutans are able to investigate a range of possible solutions in entirely different areas of the search space because of the diversity of their food sources.
FSi={Xk:Fk<Fi and k≠i}
Where, Xk shows the orangutan with an optimal objective function value than ith orangutan, FK is the its objective function value, and FSi is the set of candidate food sources’ locations for the ith orangutan.
Employing Equation 19, a novel location initially determined for every orangutan in order to quantitatively represent this movement. Through this ability to move, the orangutan can change its position to investigate entirely new areas, which could result in a notable improvement in the objective function value. The new location is verified and update in accordance Equation 20 if the objective function increases.
Where, XiP1 shows the novel proposed location of the ith orangutan based on the initial stage of OOA, FiP1 is its objective function, xi,dp1 is its dth dimension, SFSi,d is the dth dimension of the food source which has been selected for the ith orangutan, I is a random number which can be taken from the finite set of 1 and 2, r is a random number which comes from a normally distributed collection with its values within the range of (0,1), the number of orangutans denoted by N, and the number of decision variables illustrated by m.
Phase 2: nesting skill (exploitation phase)
Orangutans exhibit exceptional intelligence through their nesting behavior alongside to their foraging behaviors. They choose branches and leaves close to where they are now and construct nests in trees every day. The goal of this exercise is to optimize their living space through a more focused search. Enhancing the algorithm’s exploitation capabilities through the simulation of orangutans’ nesting skills in OOA leads to improved fine-tuning of solutions and facilitates a more accurate exploration of local areas. In this second phase of OOA, the orangutan approaches a nearby tree to establish its nest.
Within the framework of the algorithm, the nesting procedure is represented by creating a new position for the orangutan derived from its existing position. Equation 21 is employed to simulate the movement toward the tree, and should the value of the objective function show improvement, the novel location will replace the former one, as described in Equation 22:
Where, Xip2 is the novel proposed location of the ith orangutan based on the second stage of OOA, xi,dp2 is its dth dimension, FiP2 is its objective function value, T is the maximum number of algorithm iteration, and t is the iteration counter of the algorithm.
Modifications to Improve performance
To address the limitations of the original OOA, we introduce the following modifications:
1. Enhanced exploration.
A chaotic map is introduced to diversify the search space during the exploration phase:
αi+1=γ.αi.(1−αi)
where αi=2ri,j is the chaotic variable in Equation 21, and γ is the control parameter (typically set to 4 for maximum chaos).
2. Balanced exploitation.
A local search mechanism is incorporated to refine solutions during the exploitation phase:
xi,dP1=xi,d+η·∇f(xit)
where, η is the step size, and ∇f(xit) is the gradient of the objective function.
Figure 7 illustrates the flowchart diagram of the proposed modified orangutan optimization algorithm.
The flowchart diagram of the proposed modified orangutan optimization algorithm.
Flowchart depicting an optimization algorithm. It starts with “Start,” proceeds to “Initialize Population and Fitness,” and checks if “t <= max_iter?” If yes, it enters the “Exploration Phase (Foraging),” followed by the “Exploitation Phase (Nesting),” then “Enhancements: Chaotic Exploration and Local Search,” and updates the best solution before rechecking the condition. If no, it outputs the best solution and ends.Steps for fine-tuning CNN hyperparameters by the modified orangutan optimization algorithm
Define Search Space:
• Determine the search space for hyperparameters:
• Learning rate (α): [0.001,0.1].
• Number of capsules (Nc) [4,16]:.
• Regularization strength (λ): [0.0001,0.01].
• Batch size (B) [32,128]:.
Evaluate Fitness:
Train the Capsule Neural Network with candidate hyperparameter configurations and evaluate performance using metrics such as accuracy, precision, and F1-score that is given in Equation 25:
Fitness=w1·Accuracy+w2.Precision+w3.F1−Score
where, w1, w2, w3 are weights assigned to each metric.
The two proposed improvements to the OOA are the addition of a chaotic map for enhancing exploration and a gradient-based local search mechanism for balanced exploitation. These upgrades are not arbitrary but well established by metaheuristic design principles to bring about a solution to the premature convergence and poor local optima avoidance.
The chaotic map as expressed in Equation 23 replaces the typical uniform random variable through a deterministic yet unpredictable sequence generated via the logistic map, which is both ergodic and sensitive to initial conditions; thus, assuring more diverse and nonrepetitive exploration of the search space during the foraging phase that prevents premature population clustering around suboptimal regions.
This enhanced exploration literally generates the control parameter dynamics, leading to the escape of the algorithm from local traps and consequently, sustaining the diversity of the population throughout the optimization process.
Also in Equation 24, the local search mechanism confers a gradient-based perturbation with adaptively tuned step size α which is effective especially in the refinement of promising solutions in the nesting (exploitation) phase. Through the dynamically adjusted step size on the basis of the magnitude of the objective function gradient, larger steps are allowed in flat regions, while a more intense adjustment to optima is required, thus assuring a more efficient and precise convergence.
By this, the global exploration and local exploitation worldwide strategies will be strictly balanced to achieve great improvements in the potential of this paradigm to locate high-quality hyperparameter configurations for the Capsule Neural Network, as proved by the experiments discussed in comparative studies.
Data
The purpose of this section is to present the Global Maritime Distress and Safety System (GMDSS) dataset, highlighting how its content specifically adds to knowledge regarding the distribution of maritime rescue means. It includes a content description of the dataset, some of the salient characteristics, usability issues posed, and preprocessing tasks undertaken in order to make it appropriate for training prediction models.
GMDSS data includes historical as well as current data about distressed signals of distressed ships. This data is extremely important while analyzing the patterns of maritime accidents and predicting probable occurrences in the future. It provides data like:
Real-Time Data: Up-to-date information regarding ships in distress, such as the position of the ship, distress time, and nature of the emergency.
Historical Data: Historical record of past maritime accidents, enabling trend analysis and determination of risk areas.
The data have been gathered through an international communications link of networks, satellite and earth-based, which provide extensive oceanic operation coverage. It is primarily focused on facilitating search and rescue (SAR) timely and accurate manner about incidents.
The GMDSS dataset provides wider possible features in order to enhance the prediction and optimization of rescue resources for maritime accidents. The features include:
Location Features:
Temporal Features:
• Timestamp: Time and date of incident occurrence.
• Hour of the Day: Deriving from the timestamp to capture daytime patterns. 0.
• Day of the Week: Categorized as Monday, Tuesday, etc.
• Seasonality Indicators: Adopted from the month (winter, spring, etc.).
Incident Type:
• Different incident types, like collision, grounding, fire, and sinking.
• Vessel Size: Gross tonnage or length of the vessel.
• Vessel Age: Age of the vessel at the time of the incident.
Outcome Features:
• Casualties: Number of fatalities or injuries.
• Environmental Impact: Estimated damage to ecosystems (e.g., oil spills).
The dataset is based on maritime incidents recorded from the year 2010 to 2023 and includes prominent shipping routes across the Atlantic, the Pacific, the Indian Ocean, and parts of the Mediterranean Sea. After preprocessing (as explained in section 3.1), finally, the dataset finally contains 12,487 incident records based on the category of the variable into spatial, temporal, environmental, vessel-specific, and incident type features. Below is a complete statistical summary of the study using numerical and categorical variables. Table 1 shows the information of numerical variables.
Numerical variables.
Variable
Mean
StD
Min
Max
Units
Latitude
28.41
22.67
-34.82
71.25
degrees
Longitude
14.33
45.19
-178.21
179.98
degrees
Distance to Nearest Coastline
86.45
112.30
0.12
1,245.7
km
Wind Speed
14.8
8.7
0.5
45.2
knots
Wave Height
2.1
1.8
0.1
12.5
meters
Sea Temperature
16.3
10.2
-2.1
32.8
°C
Vessel Size (Gross Tonnage)
18,450
22,100
500
320,000
tons
Vessel Age
14.7
8.9
0.5
48.0
years
Casualties
2.1
4.8
0
42
persons
Latitude and longitude data demonstrate broad global coverage, with incident density concentrated in the northern hemisphere and near coasts. The large standard deviation in distance to the coastline reflects a mix of near-shore and open-sea incidents. Both wind speed and wave height distributions are right-skewed, indicating that most incidents happen under moderate conditions (wind ≤20 knots, waves ≤3m). Vessel size is primarily skewed toward smaller and medium classes, though some large tankers and container ships are included. Casualty occurrence is sparse, as 68% of incidents report zero fatalities. Figure 8 shows a heatmap that visualizes the spatial distribution of incidents in the GMDSS dataset.
Heatmap showing the geographical distribution of maritime incidents.
Scatter plot showing latitude versus longitude with four colored data points. The color bar on the right ranges from blue to red, indicating values from five to fifteen. The points vary in color from dark blue to red.
This map indicates the areas with high risk, for example, areas with dense shipping routes or stormy areas. The GMDSS dataset is a fine dataset to analyze ship accidents and regulate rescue assets for optimal usage. While using methods like solving noisy data, class imbalance, and handling missing values and preprocessing activities like normalization and feature extraction, the dataset has been prepared to train the forecasting models.
Results
The purpose of this section is to present the result of the application of the suggested Capsule Neural Network (CNN) with Modified Orangutan Optimization (MOO) in the Global Maritime Distress and Safety System (GMDSS) dataset.
Performance metrics
The performance of the predictive model has been evaluated by using a rich set of metrics that capture all aspects of accuracy and robustness:
Accuracy (Equation 26):
Accuracy =TP+TNTP+FP+FN+TN
where TP, TN, FP, and FN represent true positives, true negatives, false positives, and false negatives, respectively.
where, yi is the actual value, yˆi is the predicted value, and N is the number of samples.
Root Mean Squared Error (RMSE) (Equation 31):
RMSE =1N∑i=1N(yi−yˆi)2
These measures provide a holistic analysis of the model’s performance in terms of classification accuracy, error reduction, and efficiency of resource utilization.
Comparison with baseline models
To validate the efficacy of the proposed model, its performance has been compared against a number of baseline models that are standard in predictive analytics:
− Traditional CNN (Theodoropoulos et al., 2021): A conventional convolutional neural network without capsule layers.
− Support Vector Machine (SVM) (Mahajan et al., 2021): A kernel-based classifier for binary and multi-class classification problems.
− Random Forest (RF) (Wang et al., 2022): Decision tree-based ensemble learning method.
− Proposed Model (CNN/MOO): Capsule Neural Network optimized with Modified Orangutan Optimizer.
Comparison was established using the GMDSS dataset, which was split into train (80%) and test (20%) sets. Performance of Optimized Presented Capsule Neural Network (CNN) with Modified Orangutan Optimization (MOO) was extensively experimented using a complete set of performance metrics like accuracy, precision, recall, F1-score, Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE).
For a comparison of performance, the model was also compared to some quite simple but very commonly used baseline models like general CNNs, Support Vector Machines (SVM), and Random Forests (RF). Performance is compared on the GMDSS dataset, which was divided into a training set and test set for unbiased and fair results. Comparative performance metrics are represented in Figure 9, each of which tells us something else about the performance of the models, from classification accuracy to error reduction.
Panel A shows a bar chart comparing performance metrics (accuracy, precision, recall, F1-score) for models CNN, SVM, RF, and CNN/MOO, with all metrics above 80%. Panel B displays error rates (MAE, RMSE) for the same models, showing varying error levels with CNN/MOO generally having lower errors.
The performances displayed in Figure 9 clearly demonstrate the superiority of the proposed CNN/MOO model compared to the baseline models in the context of all the performance metrics. With the delivery of an accuracy value of 91.2%, the proposed model is an obvious improvement upon the traditional CNNs with the value of 85.4%, SVMs with the value of 82.7%, and Random Forests with the value of 84.1%.
This enhancement can be attributed back to the capability of capsule networks in learning the spatial hierarchies and retaining pose information, which are significant aspects in encoding complex relations between maritime accident details. Further, hyperparameter tuning via MOO enhances performance with learning rate, capsules number, regularization strength, and batch size tuning.
The decline in MAE and RMSE not only indicates that the model improves the classification accuracy but also decreases the prediction error, thus improving the model’s reliability under practical application. The previous conclusions confirm the need to integrate state-of-the-art neural architectures with optimization algorithms to obtain cutting-edge predictive analytics performance for maritime rescue resource allocation.
Effectiveness of MOO in improving CNN performance
Modified Orangutan Optimization (MOO) finds importance in enhancing the performance of Capsule Neural Network (CNN) by adjusting its hyperparameters. Hyperparameter optimization is important in achieving the best model performance since, under default, it fails to compensate for the dataset-specificity as well as the complexity of the problem.
To determine the impact of MOO, the performance of the CNN has been contrasted before and after applying the optimization process. Figure 10 summarizes the changes in the key hyperparameters, i.e., learning rate (α), number of capsules (Nc), regularization strength (λ), and batch size (B), and how MOO systematically adjusts these parameters to increase predictive accuracy and generalization.
Effectiveness of MOO in improving CNN performance before optimization (BO) and after optimization (AO).
Four bar charts compare values for two optimization methods, BO and AO. Top left: Learning Rate, BO is higher. Top right: Number of Capsules, AO is higher. Bottom left: Regularization, AO is higher. Bottom right: Batch Size, AO is higher.
The results reported in Figure 10 clearly show the significant improvements with the application of MOO to fine-tune Capsule Neural Network. The value of learning rate learned at 0.003 keeps the balance between speed of convergence and stability, therefore avoiding slow convergence or overshoot from the original setting at 0.01.
Increasing the capsule number from 8 to 12 enhances the capacity of the model to capture intricate spatial relations and hierarchical structures, which are essential in modeling maritime accident data. The increase in the regularization strength from 0.001 to 0.005 also contributes to preventing overfitting effectively by penalizing models that are complex and thus generalizing well on new data.
Finally, increasing the batch size from 64 to 96 makes gradient estimation during training more stable and produces more balanced updates and a faster rate of convergence. All these adjustments collectively contribute to the improved performance of the proposed model, as obvious enhancements in accuracy, precision, recall, and error scores demonstrate. This again underlines the significance of MOO in realizing the optimal value of Capsule Neural Networks as an instrument in predictive analytics within maritime rescue resource allocation.
Error distribution comparison
Comparisons of error distributions provide informative data about the predictive accuracy and reliability of the proposed Capsule Neural Network (CNN) improved by Modified Orangutan Optimization (MOO) compared to control models. Based on the analysis of spread and central tendency of residuals (actual and predicted values’ differences), it is possible to identify how well the model is able to minimize prediction errors and generalize to new data.
Histograms or boxplots are used to represent the error distributions, representing variability differences, bias, and differences in performance across models. In addition to measuring the improvement that the provided model achieves, the analysis also gives better insight into its reliability in real maritime rescue operations.
(Figure 11) The error plots indicate that the suggested model displays a much more compact and central error distribution than baseline models such as typical CNNs, Support Vector Machines (SVM), and Random Forests. The residuals of the suggested model are clustered around zero, indicating no considerable bias and high prediction accuracy. Baseline models, however, are more scattered and have heavier tails, indicating more variability and less consistent performance. This decrease in error variability makes it especially important for applications such as maritime rescue resource allocation, where precise forecasts directly affect response time and operational efficiency. Secondly, the lack of extreme outliers in the error distribution of the suggested model also confirms its robustness against noisy or anomalous data points. All these findings confirm that the combination of Capsule Neural Networks and MOO not only improves overall accuracy but also enhances the reliability and generalizability abilities of the prediction model to be applied under dynamic and complex real-world environments.
Error distribution comparison.
Histogram comparing prediction errors of a proposed model and a baseline model. The x-axis represents prediction errors, ranging from negative 0.25 to 0.25. The y-axis shows probability density reaching up to 10. The proposed model is blue, and the baseline model is red, with overlapping areas in purple.Spatial heatmaps of predicted versus actual incidents
Spatial heatmaps of predicted versus actual incidents provide a graphical representation of the ability of the proposed model to accurately detect high-risk locations and predict the geographical distribution of maritime accidents.
Through overlaying predicted incident locations on the actual incident data, the heatmaps allow visualization of the spatial alignment and accuracy of the predictions made by the model. This analysis is particularly important for sea rescue services, where placing assets in high-risk areas in advance can directly reduce response times and improve outcomes. The heatmaps not only validate the model’s predictive accuracy but also indicate its ability to inform decision-making in real scenarios.
Figure 12 is organized into a two-panel subplot for an easier visual comparison: Panel (A) will capture a heatmap of actual incidents generated from true GMDSS incident locations in the test set, while Panel (B) will possess a heatmap of predicted incidents where each grid cell corresponds to an accident probability estimated by the model. It would be most effective if both panels had the same color scale, probably something like blue-to-red, expressing low-to-high density, whereas the context should include coastlines and major shipping lanes. An intuitive shared legend should help clarify the meaning of the intensity scale used across the two panels.
Spatial heatmaps of actual vs. predicted maritime incidents.
Comparison of actual and predicted maritime incidents. Panel A shows a world map with red dots representing actual maritime incidents. Panel B displays a heat map indicating predicted accident risk, with higher probabilities in yellow and lower in blue, alongside a color scale for risk probability.
The color scale used in both heatmaps is identical (blue = low density, red = high density) and clearly posts coastal data for spatial reference. The extreme good visual correspondence between the two maps, especially in the high-traffic shipping lanes and storm exposure zones, is a key indicator of the model’s accuracy in capturing spatial risk patterns. The key risk zones (straits and port approaches), distinguished with minimal false alarms in the low-risk open-sea areas, indicate the spatial validity of the model for operational use in maritime safety planning. These findings validate that the Modified Orangutan Optimization (MOO) optimized Capsule Neural Network indeed learns and encodes complex spatial relationships in the GMDSS dataset. Such capability makes the proposed framework a useful tool for maritime safety enhancement and resource planning, offering real-world observations to rescue operators and policy makers.
Decision boundary visualization
Decision boundary visualization provides an obvious intuition for where the proposed CNN/MOO classifies examples into a low-dimensional feature space. By reducing the dataset into two dimensions, the plot indicates the areas where model allocates particular classes, i.e., high-risk versus low-risk areas or different maritime event categories.
Decision boundaries not only reflect the model’s ability to separate classes but also its generalization capability in the case of overlapping or multimodal data distributions. Figure 13 demonstrates the decision boundary visualization.
Decision boundary visualization.
Scatter plot showing two classes of data points with Feature 1 and Feature 2 as axes. Red dots represent Class 2, and blue dots represent Class 1, with a density contour overlay. A color bar indicates values from zero to one point five.
Decision Boundary Visualization becomes the key interpretability tool from which this proposed model MOO-CapsNet shows the separation of different classes of maritime incidents (for instance high-risk vs. low-risk events) within the reduced two-dimensional feature space.
The decision boundary is the surface a classifier learns to distinguish between classes; well well-defined, smooth, and non-overlapping boundary means that the model has actually learned meaningful patterns from data without overfitting the data itself.
As traditions have already seen, the MOO-CapsNet model is capable of generating each risk category when it is absolutely co-related with some clearly separate and smoothly contoured regions. It is in contrast to baseline models discussed earlier, but not shown in the same figure, which often have fragmented or irregular boundaries.
Thus, the MOO-CapsNet is likely to perform better in generalization and be less sensitive to the noise. The clarity of the boundary points out that the CapsNet, modified by the Orangutan Optimization (MOO) Algorithm, is learning the underlying structure of the data, especially those spatial-temporal and hierarchical relationships between features such as vessel location, weather conditions, and traffic density.
Further, it is not convoluted or oscillating and hence does not overfit towards training data, further evidenced by low rates of failure discovered. This visualization thus gives graphical evidence of robustness, generalization, and classification reliability of the model, validating its fitness for real-life applications in safety systems of shipping because such systems demand consistent and trustworthy predictions.
Comparative evaluation with other swarm intelligence optimization algorithms
In strict sighting of validating the Modified Orangutan Optimization (MOO) algorithm’s superiority in the tuning of CapsNet hyperparameters, we will extend the experimental emphasis by competing with MOO against five other SWI’s (swarm intelligence algorithms): Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Harris Hawks Optimization (HHO).
All algorithms operated to optimize the same hyperparameter set, namely learning rate, number of capsules, regularization strength, and batch size within the CapsNet architecture with respect to the same training and testing (80%-20%) splits of the GMDSS dataset. The optimization processes are aimed at minimizing the fitness function defined in Equation 32 as the inverse of classification accuracy:
Fitness=1−Accuracy
Each algorithm was run for 100 iterations, using a population size of 30, and the results were averaged over 10 independent runs to ensure statistical power. The comparison results were based on final model accuracy, convergence speed, stability (measured in standard deviation of accuracy), and computational time. The results assert the fact that not only did MOO yield the highest predictive accuracy, but it also demonstrated faster convergence and greater robustness, which proves the efficacy of MOO in addressing the sophisticated high-dimensional search space of CapsNet hyperparameters under real-world conditions pertaining to maritime data.
Performance comparison in terms of accuracy and error metrics
The performance study extensively compares optimized MOO-CapsNet with other SI algorithms. Figure 14 shows that MOO-CapsNet achieves the maximum accuracy of 91.2%, followed by WOA (89.5%), GWO (88.7%), PSO (87.1%), HHO (86.9%), and GA (85.3%).
Performance comparison of CapsNet optimized by different SI algorithms.
Two horizontal bar charts compare different algorithms. The left chart shows F1-Score, Recall, Precision, and Accuracy for GA, HHO, PSO, GWO, WOA, and MOO with scores ranging from 75% to 95%. The right chart displays RMSE and MAE for the same algorithms, ranging from zero to 0.1.
In the same way, MOO yields the least MAE (0.041) and RMSE (0.063), thus confirming its generalization and prediction stability. The results confirm that, with chaotic maps combined with local search techniques into MOO, the method has enhanced exploration-exploitation balance.
The accuracy and error-based evaluation results corroborate the fact that MOO optimally performs CapsNet for maritime accident prediction. MOO shows maximum accuracy while the minimum error indices can also be availed upon, beating even the advanced algorithms such as WOA and GWO. The specialties stem from its chaotic initialization along with the local search mechanism preventing premature convergence and improving global search capability.
Contrary to them, GA and PSO converge slower with lower accuracy because of their tendency to get trapped in local optima. The tight error bounds and enhanced F1-score corroborate that MOO also facilitated CapsNet to achieve balanced precision and recall, i.e. methodology critical for maritime rescue planning where both false alarms and missed detections need to be curtailed.
Convergence behavior analysis
Comparison of convergence curves for all the algorithms in the study of the optimization process results under iterative conditions, as shown in Figure 14, where all algorithms shared the same fitness function (1-not accuracy) at 100 iterations.
The first algorithm to converge is MOO, hitting a stable solution at iteration 45, while WOA and GWO converge between iterations of 60-70. Both PSO and HHO, as well as GA, indicated slower and less stable convergence accompanied by noticeable oscillations, especially in later iterations.
It is evident from the convergence analysis that MOO seems to be clearly better than any of the other swarm algorithms, both in terms of speed and stability. So this early convergence (in terms of iterations 45) and very low oscillation ratios have really indicated that it is very promising in terms of putting an exploration-exploitation balance because of the chaotic map diversified the search in early stages and the local search mechanism that refines in the later phases.
In contrast, PSO and GA have high fluctuations throughout the search, thereby implying poor search behavior and weak avoidance of local optima. WOA and GWO are performing relatively well, but not as fast as MOO.
This quick convergence is advantageous to maritime rescue systems, especially during model retraining and tuning under time-critical and dynamically changing conditions such as seasonal weather changes, to maintain high performance in prediction.
Predictability analysis by accident type
The GMDSS dataset for this study includes five major types of maritime accidents: Collision, Grounding, Fire, Sinking, and Machinery Failure. Analyzing the model performance results reveals wide variations in predictability across this class, closely related to underlying causes and data availability. Table 2 indicates the model performance by accident type.
Indicates the model performance by accident type.
Accident type
Accuracy (%)
Precision (%)
Recall (%)
F1-score (%)
Collision
91.8
90.5
89.2
89.8
Grounding
93.1
92.0
91.5
91.7
Fire
82.9
81.2
78.4
79.7
Sinking
87.6
86.3
85.1
85.7
Machinery Failure
88.4
87.0
86.6
86.8
The MOO-CapsNet model attains the highest accuracy, slightly above 93.1% for Grounding and 91.8% for Collision, largely motivated by the well-documented spatial-temporal causative factors, including vessel position, close proximity to the coastlines or shipping lanes, density of traffic, and visibility conditions, all well represented in the CapsNet spatial-hierarchical architecture.
These two incidents, Machinery Failure (88.4%) and Sinking (87.6%), predictability levels remain slightly moderate, vaguely dependent on the combination of vessel age, maintenance history, and environmental stressors (e.g., high waves), some of which were included in this analysis but might incorporate unobserved operational factors.
Fire (the least predictable at 82.9%) strongly depends on human factors (e.g., electrical faults, crew error, cargo type) and specific conditions that can scarcely be captured by the GMDSS data. Low Fire recall means high false-negative rates, indicating that future research must consider input from additional sources, such as vessel maintenance logs or crew training records, to attempt prediction for this significant outcome.
The analysis showed that while the model does well in predicting environmentally and navigationally induced accidents, there remains a significant challenge in predicting accidents that are largely attributable to human error or technical failure, thereby testifying to both the strengths and fundamental limitations of current data-driven approaches in maritime safety.
Discussions
The experimental findings indicate that the proposed CapsNet-MOO framework is much better than traditional machine learning and deep learning baselines at predicting the hotspots of maritime accidents with an accuracy of 91.2% and better than the conventional machine learning and deep learning baselines in terms of precision, recall and error measures. This is due to two synergistic innovations in one, the inherent capacity of Capsule Neural Networks to conserve spatial hierarchies and pose connections among maritime risk variables, and (2) the adaptive hyperparameter tuning capacity of the Modified Orangutan Optimization (MOO) algorithm.
CapsNets model partwhole relationships such as the relationship between vessel proximity to high-traffic lanes, adverse weather conditions, and time of day unlike traditional CNNs, which lose spatial information due to pooling operations. This benefit of architecture is especially important in the area of maritime safety analytics, where the relative layout of variables (e.g., a cargo ship going through a narrow strait at high wave height at night) determines risk rather than the existence of the individual factors. The empirical evidence indicating that the model identifies these contextual patterns is the support on the geospatial heatmaps (Figure 12) and the decision boundary visualizations (Figure 13) which permit the localization of high-risk zones with great accuracy and a small number of false alarms in open-sea areas. Moreover, the inclusion of MOO increases the robustness of the model by balancing between exploration and exploitation in the optimization of hyperparameters.
The chaotic map component is a random sampling of the search space, which prevents early convergence implementation, and the gradient-informed local search is used to reduce potential solutions, which is demonstrated by accelerated convergence (Figure 15) and decreased error variance compared to PSO, GA, GWO, WOA, and HHO. Such optimization efficacy is directly converted to operational reliability as is the case in the uniformity of performance across accident causes, particularly, collision and grounding, which is highly influenced by the navigational and environmental conditions. However, the framework shows lower accuracy when predicting the fire incidents (accuracy: 82.9%), presumably because the human and operational factors, including crew training, electrical systems integrity, or cargo flammability were underrepresented in the GMDSS data. This shortcoming highlights a greater problem with using data to make maritime safety decisions: predictive models can be as predictive as their data.
Convergence curves of optimization algorithms.
Line graph comparing the fitness levels (1 minus accuracy) across different iterations for six algorithms: MOO, PSO, WOA, HHO, GWO, and GA. Each algorithm's performance is represented by a different colored line. The x-axis represents iterations from zero to one hundred, and the y-axis represents fitness levels ranging from zero point zero two to zero point one two. The red MOO line shows a generally increasing trend.
Despite the fact that GMDSS provides a wide scope of spatio-temporal and environmental records, it is not provided with granular technical and human-centric metadata that are also highly significant in non-navigational accidents.
Also the model would be less useful in real-time rescue planning since it would need live AIS feeds, satellite weather forecasts and vessel maintenance logs that are not included in the study.
The performance of MOO can be justifiably compensated by the computational overhead, which is an issue in applying it to edges of resource-constrained maritime platforms.
Nevertheless, the presented framework is a paradigm shift of reactive maritime safety management to proactive one despite the mentioned constraints.
It enables obtaining preemptive rescue resources, dynamic patrols, and strategic positioning of the infrastructure through the translation of historical distress data into operational spatial risk forecasts. Future directions will include the incorporation of real-time data streams, which illustrates the transferability of the model to other unique maritime regions (e.g. Arctic and tropical), as well as developing lightweight versions of CapsNet to be available on board to perform inference.
Conclusions
The first and foremost goal of this work, which we should state clearly, is to predict the locations of maritime accidents and not to directly optimize the allocation of rescue resources. While such predictions provide a basis for decisions regarding the pre-positioning of lifeboats or the scheduling of patrols, the actual allocation of resources is subject to a number of other constraints, including the availability of ships for patrols, a wide range of response time-windows, and trade-offs in multiple objectives, all of which are beyond the scope of this study. This research addressed the significant challenge of optimizing maritime rescue resource utilization through a novel framework that integrates Capsule Neural Networks with an optimized variant of the Orangutan Optimization algorithm. Maritime incidents pose significant threats to human life, economy, and environment, and predictive models to efficiently forecast events and guide effective resource allocation are necessary. Traditional approaches do not work due to their inability to comprehend spatial-temporal relations and adapt to evolving situations. The proposed model overcomes these limitations by combining the hierarchical feature extraction capability of capsule networks with the robust hyperparameter optimization of MOO, achieving improved performance in accuracy, precision, recall, and error rates compared to traditional approaches. This excellence was validated through comparing the state-of-the-art model with baseline methods in GMDSS data. Also, application of geospatial heatmaps, convergence analysis, and decision boundary visualization attests to the model in efficient of classifications of type-incident and detection of high-risk areas. Through such innovation, predictive precision is not only improved but real-time actionable decision-making information for maritime safety operations as well. Through such optimization and predictive analytics gaps filled by this research, better and more efficient maritime rescue systems were enabled, resulting in safe oceans and better disaster management. Lack of predictive competences is directly addressed in the third limitation of this study, which proposes the development of a proactive data-driven model aimed at forecasting the spatial-temporal probability of maritime accidents. These decisions pertaining to response efficiency and resource deployment could provide some downstream guidance on how best to utilize this framework; however, the main technical contribution remains the prediction of accident hotspots based upon historical GMDSS data. The proposed Capsule Neural Network (CapsNet), optimized using the Modified Orangutan Optimization (MOO) algorithm, is meant to learn complex spatiotemporal patterns of interaction that are novel and might be interaction, in which vessel traffic inclement weather with geographic risk zones-that conventional reactive systems are not able to identify. By identifying in advance the high-risk zones, it allows for the shift from reactive solutions to proposing strategies for proactive mitigation in orders to facilitate, by so doing, swifter response time and thereby establish better resource planning. Nevertheless, the efforts here will remain directed towards predictive engineered systems and accurate forecasting and reliability being the very basis for future operational advancements in maritime rescue systems. One limitation of this study is that, although the GMDSS data set is perhaps as good as it can ever be, it may suffer from various reporting biases, omissions, and inconsistencies, which, due to human or technical errors, may adversely affect the generalization of the model. Second, while the performance of the MOO algorithm is better than any other algorithm for hyperparameter tuning, it has comparatively higher computational complexity than simpler optimizers, which may hinder its real-time deployment in resource-challenged maritime environments. Third, the model mainly considers historical and static environmental conditions and does not yet fully acknowledge real-time sensor feeds or dynamic forecasting of the weather, which can further improve the accuracy of the predictions. In addition, model performance is evaluated with regard to a particular geographical scope within the GMDSS data, and validation of transferability to other maritime areas with different traffic patterns or regulatory frameworks is needed. Meanwhile, integrating the predictive model into actual maritime rescue command systems comprises operational, legal, and human-in-the-loop challenges, which were not analyzed in this study. Future work will address these limitations and will aim to add real-time IoT data streams, conduct field trials with coast guard agencies, and develop lightweight versions of the model suitable for edge computing applications.
Data availability statement
The data is available in the following link: https://www.fcc.gov/wireless/bureau-divisions/mobility-division/maritime-mobile/ship-radio-stations/global-maritime.
The authors declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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ReferencesChenJ.PanS.PengW.XuW. (2025).
Bilinear Spatiotemporal Fusion Network: An efficient approach for traffic flow prediction. Neural Networks187, 107382. doi: 10.1016/j.neunet.2025.107382, PMID: 40106928DikaiosG. (2024).
Policy framing through policy branding: International maritime organization, climate change, and Twitter/X. Media Communication12, 2024. doi: 10.17645/mac.7924DinisD.TeixeiraA.SoaresC. G. (2020).
Probabilistic approach for characterizing the static risk of ships using Bayesian networks. Reliability Eng. System Saf.203, 107073. doi: 10.1016/j.ress.2020.107073DongY.RenH.ZhuY.TaoR.DuanY.ShaoN. (2024).
A multi-objective optimization method for maritime search and rescue resource allocation: an application to the south China sea. J. Mar. Sci. Eng.12, 184. doi: 10.3390/jmse12010184HeibergH. O. (2012).
The merchant fleet: a facilitator of world trade. Global Enabling Trade Rep.2012, 85–90.
LanY.LuoW.YangM.MohamadiG. (2025).
Advancing water demand management: predictive analytics using convolutional neural networks and developed maritime search and rescue algorithm based on the shared socioeconomic pathways. Int. J. Low-Carbon Technol.20, 724–734. doi: 10.1093/ijlct/ctae285MaQ.ZhangD.WanC.ZhangJ.LyuN. (2022).
Multi-objective emergency resources allocation optimization for maritime search and rescue considering accident black-spots. Ocean Eng.261, 112178. doi: 10.1016/j.oceaneng.2022.112178MahajanP. C.KiwelekarA. W.NetakL. D.GhodakeA. (2021). “
Applications of predictive analytics in marine transportation,” in 2021 International Conference on Computing, Communication and Green Engineering (CCGE) (India:
IEEE). 1–7.
SunY.LingJ.ChenX.KongF.HuQ.BiancardoS. A. (2022).
Exploring maritime search and rescue resource allocation via an enhanced particle swarm optimization method. J. Mar. Sci. Eng.10, 906. doi: 10.3390/jmse10070906TheodoropoulosP.SpandonidisC. C.GiannopoulosF.FassoisS. (2021).
A deep learning-based fault detection model for optimization of shipping operations and enhancement of maritime safety. Sensors21, 5658. doi: 10.3390/s21165658, PMID: 34451099WangZ.ZhangC.ChenZ.HuW.LuK.GeL.. (2024).
ACR-Net: learning high-accuracy optical flow via adaptive-aware correlation recurrent network. IEEE Trans. Circuits Syst. Video Technol.34, 9064–9077. doi: 10.1109/TCSVT.2024.3395636WangJ.GuoY.WangY. (2022).
A sequential random forest for short-term vessel speed prediction. Ocean Eng.248, 110691. doi: 10.1016/j.oceaneng.2022.110691WuH.WangJ.AnantaR. R.KommareddyV. R.WangR.MohapatraP. (2018).
Prediction based opportunistic routing for maritime search and rescue wireless sensor network. J. Parallel Distributed Computing111, 56–64. doi: 10.1016/j.jpdc.2017.06.021YazdiM.KabirS. (2017).
A fuzzy Bayesian network approach for risk analysis in process industries. Process Saf. Environ. Prot.111, 507–519. doi: 10.1016/j.psep.2017.08.015YinX. F.KhooL. P.ChenC.-H. (2011).
A distributed agent system for port planning and scheduling. Advanced Eng. Inf.25, 403–412. doi: 10.1016/j.aei.2010.10.004YueK.QiZ.DuanL. (2024). “
Transformer based bayesian network embedding for efficient multiple probabilistic inferences,” in Proceedings of the 33rd ACM International Conference on Information and Knowledge Management (New York, United States:
Association for Computing Machinery). 3073–3082.
ZhouL.SunQ.DingS.HanS.WangA. (2023).
A machine-learning-based method for ship propulsion power prediction in ice. J. Mar. Sci. Eng.11, 1381. doi: 10.3390/jmse11071381GlossaryAcronym
Full term - Definition
AI
Artificial Intelligence - A branch of computer science focused on creating systems capable of performing tasks that typically require human intelligence.
AIS
Automatic Identification System - A tracking system used on ships and by vessel traffic services (VTS) for identifying and locating vessels by electronically exchanging data.
AODV
Ad hoc On-Demand Distance Vector - A routing protocol for mobile ad hoc networks (MANETs) that establishes routes between nodes only when needed, often used in wireless sensor networks.
CNN
Convolutional Neural Network - A class of deep neural networks primarily used for image recognition and processing tasks by applying convolutional filters.
CapsNet
Capsule Neural Network - A type of neural network that uses vector-valued capsules to preserve spatial hierarchies and pose information, improving performance on complex pattern recognition tasks.
GMDSS
Global Maritime Distress and Safety System - An international system that uses satellite and terrestrial radio services to ensure rapid and automated alerting of shore-based and ship-based rescue authorities in a maritime emergency.
GPS
Global Positioning System - A satellite-based navigation system that provides location and time information anywhere on Earth.
GA
Genetic Algorithm - A metaheuristic optimization algorithm inspired by natural selection, used to find approximate solutions to optimization and search problems.
GWO
Grey Wolf Optimizer - A bio-inspired swarm intelligence algorithm based on the hunting behavior of grey wolves.
HHO
Harris Hawks Optimization - A population-based optimization algorithm inspired by the cooperative behavior and chasing style of Harris hawks.
IMO
International Maritime Organization - A specialized agency of the United Nations responsible for regulating shipping and ensuring maritime safety and security.
IQR
Interquartile Range - A statistical measure of variability, calculated as the difference between the first (Q1) and third quartiles (Q3), used to detect outliers.
KPI
Key Performance Indicator - A measurable value used to evaluate the success of an organization or of a particular activity.
LSTM
Long Short-Term Memory - A type of recurrent neural network (RNN) capable of learning long-term dependencies, often used in time-series prediction.
MAE
Mean Absolute Error - A measure of prediction accuracy as the average of absolute differences between predicted and actual values.
MOO
Modified Orangutan Optimization - A bio-inspired metaheuristic algorithm based on the foraging and nesting behaviors of orangutans, enhanced with chaotic maps and local search for improved performance.
MSAR
Maritime Search and Rescue - Operations conducted to locate and assist persons in distress at sea.
PSO
Particle Swarm Optimization - A computational method that optimizes a problem by iteratively improving candidate solutions based on social behavior of birds or fish.
RCSA
Refined Capuchin Search Algorithm - An optimization algorithm inspired by capuchin monkey behavior (note: mentioned in text but likely a confusion; replaced here with correct context if needed).
RMSE
Root Mean Squared Error - A quadratic measure of prediction error, giving higher weight to large errors.
RF
Random Forest - An ensemble learning method that constructs multiple decision trees and outputs the mode (classification) or mean (regression) of individual trees.
SAR
Search and Rescue - Operations aimed at finding and rescuing people in life-threatening situations.
SVM
Support Vector Machine - A supervised machine learning model used for classification and regression by finding the optimal hyperplane that separates data classes.
WOA
Whale Optimization Algorithm - A nature-inspired optimization algorithm based on the bubble-net hunting strategy of humpback whales.
Z-score
Standard Score - A statistical measurement that describes a value’s relationship to the mean of a group of values, measured in terms of s
Edited by: Jianchuan Yin, Guangdong Ocean University, China
Reviewed by: Han Zhang, Kunming Institute of Physics, China
Ho-Chul Park, Myongji University - Natural Science Campus, Republic of Korea