Huang et al. (Huang et al., 2020) developed a hybrid optimization approach for residential energy management systems. The main aim of the approach is to solve the non-convex mixed-integer non-linear problems (H-MINLP) in management systems. MINLP consumes more energy ratio, which causes severe damage to the management systems. The developed approach increases the feasibility and functionality range of the systems.

Habib et al. (Hab et al., 2020) proposed a combined heat and power (CHP) unit for optimization in residential buildings. An artificial bee colony (ABC) algorithm is used here to identify the heat loads that are presented in the buildings. A cost–benefit analysis technique is also used in the system, which analyzes the beneficial level of energy consumption process. The CHP unit enhances the efficiency level of residential buildings.

Foroozandeh et al. (Foroozandeh et al., 2022) designed a goal programming (GP) approach for the energy management process in smart buildings. The designed GP approach predicts the exact necessity level of electricity, which reduces the complexity of the energy scheduling process. The GP approach also predicts the energy computational cost that produces optimal information for further processes. The designed GP approach minimizes the energy consumption level in smart buildings.

Nizami et al. (Nizami et al., 2019) introduced a multi-agent-based Transactive Energy Management Framework (TEMF) for residential buildings. The actual goal of the framework is to identify the optimization and grid overloading ratio of the buildings. The multi-agent architecture provides necessary services to the users, reducing the inconvenience level in performing tasks. The introduced framework increases the flexibility and effectiveness level of residential buildings.

Rezaei and Dagdougui (Rezaei and Dagdougui, 2020) proposed an efficient real-time optimization approach for residential buildings. The proposed approach uses a heating, ventilation, and air conditioning (HVAC) system that produces optimal control measures for the users. The proposed approach increases the accuracy in decision-making, which reduces the energy consumption level in computation. The proposed optimization approach improves the efficiency and performance range in multitasking.

Iturriaga et al. (Iturriaga et al.) developed a mixer-integer linear programming (MILP) optimization method for residential buildings in urban areas. The main aim of the method is to analyze the energy consumption ratio in buildings. MILP calculates the zero-energy district (ZED), which is presented in urban areas. The ZED produces relevant information for energy-saving measures. The developed MINP method enhances the significance and feasibility range of residential buildings.

Haider et al. (Haider et al., 2022) designed a new approach for multi-objective cost-peak optimization in smart buildings. The designed approach is mostly used for a multi-criteria decision-making process. It is also used to identify smart buildings’ peak energy consumption levels. The exact consumption ratio and task capacity are detected using an optimization scheme. The designed approach improves the overall performance and successful ratio in smart buildings. Table 1 summarizes the references from (Zhu et al., 2021) to (Du et al., 2022).

Energy-saving optimization methods (Hab et al., 2020; Rezaei and Dagdougui, 2020; Rezaei and Dagdougui, 2020; Haider et al., 2022) are designed to improve the state of analysis and precise decisions for multiple constraints. The constraints are identified using the existing drawbacks identified from the previous outcomes. In the constraint mitigation process, multi-objective optimization is impeded in any spiking complex process. Therefore, constraint modification and optimization for differential problems are to be jointly addressed to prevent chained downfalls. This feature is best suited for energy saving and carbon control across different objectives for constraint mitigation. This feature is adapted in the proposed method for balancing energy saving and carbon emission control.

To enhance the remuneration of residential buildings and to eliminate the gratuitous energy impoverishment, energy saving is essential for the process. This energy saving can be enhanced by using the lower amount of carbon emissions power, which helps with the future optimization procedures in determining the objectives. The ideal energy-preserving methods are executed from the low-carbon-emitting origins and renewable energy origins. Contemplating these characteristics in this article, a Multi-Objective Energy-Saving Optimization Method (MOESOM) is introduced. This optimization method helps in the usage of less energy by fulfilling the requirements of the residential buildings with prompt needs. In this process, the Osprey Optimization algorithm is used for the progression identification operation. This is the meta-heuristic algorithm, which is widely used in the solvation of the optimization process. Here, the Osprey agents are helping in the optimization process, which aids in the adaption of the circumstances by producing effective outcomes in all kinds of problems and situations in residential buildings’ energy-saving processes. From the residential buildings, energy savings and low-carbon emissions are extracted for the optimization process. This method executes the perceptions into the energy-saving operation by using green energy resources and then circumscribing energy implementations. Now, the optimization process takes place with the help of Osprey agents. The vital objective of the optimization algorithm is determined by using the multiple objectives defined. The processes included in the proposed method are illustrated in Figure 1.

The progression and the difference are determined by using the Osprey agents in the optimization procedure, and then the objectives are identified. Based on the progression detection outcome of energy saving identified by the Osprey agents and low-carbon emission, the total number of repetitions for enlarging the Osprey agents is resolved. This progression checks whether there is consistency during the energy-saving procedure with renewable energy resources. Then, it verifies, depending on the progression, whether the objectives are satisfying the energy carbon and energy-saving operations. The difference is determined if there is a lack of progress during the energy-saving process, and then, based on the progression results, the agents are augmented for prompt progression for the determination of the objectives. The number of decreased progression results in the same number of differences during the optimization process. Based on the progression, the objectives are determined, and based on the different agents, the augmentation process takes place. It also checks whether the newly added agents help in the progression process for the estimation of the objectives. This Osprey agent-based optimization is accomplished if any of the lagging progression is satisfied by the newly added agent. Contemplating the difference between new and old agent progression, the carbon emission control level and energy-saving factors are calculated. This entire process helps in determining the different objectives that satisfy the given criteria with the prompt progression level and energy-saving factors.

The data from (Kaggle, 2023) are explored in this article for validating the energy-saving and carbon emission control factors. The data used for validation are represented in Figure 2.

The power is utilized, as is the energy drain from the outcome and saving. In this consideration, the unnecessary drain is optimized for energy saving and efficient utilization. The carbon emission is geared up from the final consumed for power generation that includes wastage and DF, as presented in the above data source. The OOA is allocated using the B   _ I D for augmenting progression and reducing the differences. Such reductions are used for objective satisfaction with low-carbon emission recommendations (Figure 2).

The energy-saving resources are extracted from the residential buildings for the optimization process. Renewable resources are used for the elimination of unwanted energy loss and high-carbon emissions. It is necessary to save energy to protect the surroundings from the highly polluted carbon during the construction of residential buildings. Energy is also saved by using low-carbon powers, which help to keep the environment wholesome during residential building development. The process of energy saving from residential buildings is explained by Eq. 1: A = A 1 ⋮ A i ⋮ A n i × n = a 1,1 ⋯ a 1 , j ⋯ a 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ a i , 1 ⋮ a n , 1 ⋯ ⋱ ⋯ a i , j ⋮ a n , j ⋯ ⋱ ⋯ a i , n ⋮ a n , n n × n a i , j = b j + A i j ⊙ n b j + i b j i = 1,2 , . . , n j = 1,2 , . . , n (1)

Where A is the operation of the energy saving in the residential buildings, b is the aid of the renewable sources, i is the outcome of the energy-saving procedure, and j is the enhancement of the lucrativeness of the residential buildings. Therefore, this energy-saving process mainly helps in eliminating unnecessary energy loss in residential buildings. This energy saving also helps in the enhancement of the worth of the building by enhancing energy preservation. The energy saving from the residential buildings is extracted along with the low-carbon emission powers, which are utilized in energy preservation operations. Based on this, the optimization process takes place by determining the objectives and the agent augmentation procedures. The process of avoiding the energy drain during the energy-saving process for the future optimization process is explained by Eq. 2: Z = Z 1 ⋮ Z i ⋮ Z n n × 1 = Z A 1 ⋮ Z A i ⋮ Z A n n × 1 Z b i = A n n ∈ 1,2 , … , N ∆ Z n < Z i ∪ X n A n = A n 1 ⋮ A n 2 ⋮ A n n × Z 1 ⋮ Z i ⋮ Z n = A n 1 Z 1 ⋮ A n 2 Z i ⋮ A n n Z n (2)

Where Z is the elimination of the unnecessary energy drains in the procedures, and X is the development of the building by energy saving. Now, the low-carbon emissions are contemplated from the residential buildings for the purpose of helping the Osprey agents in the optimization algorithm. Based on Eq. 2, the energy drain estimation and saving development from the explored data are presented in Figure 3.

The observed data are split based on b ′ s outcome and j based on the procedure pursued. The fluctuations and unnecessary energy drain/wastage are considered in this analysis for rectifying the defects. The peaks in power utilization are observed due to Z n < Z i ∀ X n , such that X is required. The low-carbon emissions are determined when renewable resources are used in the energy-saving process (Figure 3). Those are the sources that emit lesser power to the environment without harming the surroundings. The process of executing the low-carbon emissions from the energy-saving process is explained by Eq. 3: A i , j C 1 = A i , j + d i , j ⊙ B z i , j − I i , j ⊙ a i , j A i , j C 1 = a i , j C 1 , b j ≤ a i , j C 1 ≤ c b j   ; b j , a i , j C 1 < C i , j ; Z b j , a i , j C 1 > Z b j A i = A i , j C 1 , Z 1 C 1 < Z i   ; A i e l s e I i , j = I 11 ⋯ I 1 n I 21 ⋯ I 2 m (3)

Along with the energy saving, low-carbon emissions are derived from the residential buildings to identify the progression and the difference by using the Osprey agents in the optimization algorithm. Where C is the low-carbon emission sources, d is the usage of low-carbon emission sources in the energy-saving procedures. The useful energy-saving approaches are enhanced by the low-carbon emissions and the energy resources that are used in the energy-saving process. The multi-objective gyrates closely to the energy-saving and sources implementation for decreasing the costs of the utilization and countering the high-carbon emissions. The process of enhancing the energy-saving approach from the low-carbon emissions is explained by Eq. 4: A i , j C 2 = a i j d b j + U ⊙ b j − d b j t i = 1,2 , … , n j = 1,2 … , n , t = 1,2 , . . , T A i , j C 2 = a i , j C 1 , b j ≤ a i , j C 1 ≤ c b j   ; b j , a i , j C 1 < C i , j ; Z b j , a i , j C 1 > Z b j T i j = T 1,1 ⋯ T 1 , j ⋯ T 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ T i , 1 ⋮ T n , 1 ⋯ ⋱ ⋯ T i , j ⋮ T n , j ⋯ ⋱ ⋯ T i , n ⋮ T n , n (4)

Where U is the enhancements of the energy-saving methods, and T is the implementation of the resources. Based on Eqs. 3 and (4), the average C and its associated d are illustrated in Figure 4.

The C and d for the varying energy demands are explored in the above Figure 4. Based on the available A i , j C u and T i j , the enhancements are pursued, for which the Z is pursued. The need for agent deployment relies on the C and d , pursued over different intervals and building demands. The explored outcomes in Figure 3 and Figure 4 are discussed after the optimization process discussed below.

Now, the Osprey agents are helpful in the optimization process where the progression and the difference are determined. These Osprey agents are also used in the estimation of the wholesome low-carbon emission and the energy-saving process for the optimization algorithm. They help in the identification of the prompt objectives for the process of energy preservation. Due to the estimation of the energy saving and the low-carbon emission process, the optimization process takes place effectively, which aids in the objective determination operation. The outcome of the optimization in calculating the progression helps in augmenting the new agents for the satisfaction of the given conventionalities. The multiple objectives that are found are also helpful in making the optimization procedure efficacious for energy saving in the residential building operation. The process of Osprey agents in the optimization process is explained by Eq. 5: a i , j C 1 ← a i j + u i j ⊙ Z i j − I i j . a i j P C 1 = A n n ∈ 1,2 , … , N ∆ Z n < Z i ∪ X n a i , j C 1 ← a i , j C 2 , b j ≤ a i , j C 2 ≤ u b j   ; b j , a i , j C 1 < b j ; U b j , a i , j C 2 > U b j A i ← A i , j C 2 , Z 1 C 2 < Z i   ; A i e l s e a i , j C 1 ← a i , j C 1 , b j ≤ a i , j C 1 ≤ u b j   ; b j , a i , j C 1 < b j ; U b j , a i , j C 1 > U b j (5)

Where P is the operation of the Osprey agents in the optimization algorithm procedures. These Osprey agents help in the determination of the efficiency of the energy-saving method in residential buildings. The outcome of this optimization operation helps in the detection of the lagging of the progression. The usage of the Osprey agents in the optimization process is explained by Eq. 6: M = M 1 M 2 ⋮ M n = m 1,1 m 1,2 ⋯ m 1 , n m 2,1 m 2,2 ⋯ m 2 , n ⋮ m n , 1 ⋯ m n , 2 ⋯ ⋯ ⋮ m n , n a i , j = b i , j + x n ° u b j − b j , 1 ≤ i ≤ n ; 1 ≤ j ≤ n a 1 = A C i = 1,2 , … , n   ; m = 1,2 , … , n − 1 (6)

Where M is the optimization algorithm procedure. Now, depending on the energy saving and the low-carbon emission, the progression and difference in the progression are estimated. The progression must be either in the energy-saving or low-carbon emission process. Here, it checks whether the progression is present in the energy-saving process or the low-carbon emission resource identification process. The Osprey optimization flow for the progression estimation is presented in Figure 5.

The optimization process allocates P for Z -generating intervals, such that the energy-saving condition X = j is analyzed before M . Therefore, if K is observed between successive Z intervals, then termination occurs. Contrarily, if the condition fails, then new P is augmented until X = j is satisfied. This condition is updated for α i , j = b i , j + x n ° provided J ≤ n is obtained (Figure 5). Along with the progression, the difference in the progression is also determined for the identification of the objectives for the energy-saving process. The Osprey agents help in the consistency of the progression during the energy-saving process without any lags and time issues. Based on the outcome of the energy saving and the low-carbon emissions, the progression and then the difference are estimated simultaneously. The process of identifying the progression is explained by Eq. 7: M i C = M i + u b j − I A i , C u i < C A i M i C = M i + u b j − A i , C u i ≥ C A i , I = 0,1 , M = 0,1,2 K i = M i C , U A i C ≤ C A i , K i = M i , U A i C ≤ C A i M i C = A i + d 2 U − 1 A i (7)

Where K is the progression in the process. The progression also helps in the determination of the difference between them, and it takes further steps to enhance the progression. The efficaciousness of the Osprey agents is determined in the progression estimation process, and thus, it is explained by Eq. 8: φ A = a 0 + a 1 M + a 2 M 2 φ A i = a 0 + a 1 M i + a 2 M i 2 φ A i + 1 = a 0 + a 1 M i + 1 + a 2 M i + 1 2 φ A i + 2 = a 0 + a 1 M i + 2 + a 2 M i + 2 2 a 0 = φ A i a 1 = φ A i + 1 a 2 = φ A i + 2 (8)

Where φ is represented a the outcome of the progression in the energy-saving process of the residential buildings. Now, the difference in the progression is determined based on the results of the energy-saving operation and the low-carbon emission resources. Here, the difference occurs when there is a reduction of the progression in the process. Figure 6 presents the Z and X following the operation time after the conditional OOA process.

The conditional validation pursued by the OOA augments agents for reducing Z wastage. Hence, it is eliminated using varying time intervals for improving the saving feasibility. In this process, the optimization condition for α M and ψ A i are concurrent such that any of the operation times include conditional satisfaction. Therefore, X that is improved is pursued for the rest of the intervals such that Z is improved (Figure 6). The total amount of difference indicates the total reduction of the progression in the process. The new Osprey agents are added in the difference solvation process for the reduction of the lags in the progression. The process of determining the difference in the progression is explained by Eqs. 9, 10: L * = 1 2 × A i + 1 2 − A i + 2 2 C A i + A i + 1 2 − A i 2 ∪ A i + 1 + A i 2 − A i + 1 2 C A i + 2 A i + 1 − A i + 2 C A i + A i + 2 − A i C A i + 1 + A i − A i + 1 C A i + 2 L i = L i 1 L i 2 ⋯ L i n L i n 1 L i n 2 ⋯ L i n n ⋮ L i j 1 ⋮ L i j 2 ⋱ ⋯ ⋮ L i j n L i = L * , U A * < U L i L i = L i , U A * ≥ U L i (9) L i ∼ = L B + U B − A i L i ¯ = ∑ n = 1 L B + U B 2 , L B + U B − M i L i ¯ = ∑ n = 1 L B + U B 2 , A i A → = A 1 , A 2 , A 3 , A 4 = T a , T b , T c , T d Z A → = 1 2 − a 1 a 2 a 3 a 4 (10)

Where L is the difference in the progression. Now, the objectives are determined from the progression. The Osprey optimization process for difference identification is illustrated in Figure 7.

Different from the P ∀ X , the L detection and improvement are performed using the remaining P . That is, the U A < U L failure and U A < C A failures increase the chance of increasing P . If P is increased, then the chance for new M is high, provided that M is optimal. Therefore, X is achievable only if Z is satisfied. Therefore, the OOA as presented in Figure 5 pursues the above operation until L = 0 is obtained (Figure 7).

The agent checks whether the objectives satisfy the energy carbon and the energy-saving procedures based on the progression. These objectives also help in the reduction of the differences that occurred in the progression by enhancing energy saving in residential buildings. The process of obtaining the objectives based on the progression is explained by Eqs. 11, 12: V i t + 1 = C i t ± L i t 2 ∑ n = 1 1 φ , C i t = 1,2 , … , n , i = 1,2 , … , n C i t = φ C b i t + 1 − φ C m t φ = C 1 U 1 C 1 U 1 + C 2 U 2 C 1 , C 2 = 0,1 ∈ A n (11) F i n = Z t − a C i t + C i t + a C i t − C i t − a C i t   x n n = 1,2 , … n F i n = Z t − U a i x + Z t − C m i x φ A i + φ M i j − φ M i + φ A i j (12)

Where V is the objectives obtained based on the progression, and F is the verification operation of whether it satisfies the procedure. Now, if the difference occurs in the process, then the agent augmentation process takes place. Here, the new agents are added for the reduction of the progression difference. Moreover, it checks whether the new agents are helpful in the progression of the energy-saving process shown in Eq. 13: L i t + 1 = 2 γ t m − A i t m = ∑ n = 1 C U i n γ t = γ i j + T − t γ i − γ j T A i t + 1 = C i t + γ t m − A i t ∑ n = 1 1 n A n + 1 = φ m n 1 − A n x n ∈ ( 0,10 π = x n = m n ) (13)

By contemplating the difference between the new agent and old agents’ progression, the emission control level and energy-saving characteristics are evaluated. The process of agent augmentation is explained by the equation given above, where π is the agent augmentation procedure. This optimization algorithm helps in the enhancement of the energy-saving technique by eliminating unwanted energy loss. This approach also reduces the difference in the progression and then adds the new agents for the prompt energy-saving process with the low-carbon emission powers in the residential buildings. The objective verification is validated using Figures 8–10 for the two conditions: energy-saving and carbon control. In the three figures, the failure, successive achievement, and ratio of improvement are analyzed, respectively.

The conjoined points in the above representation are identified by satisfying V i t + 1 for i = 1,2 , . . n . In this satisfaction process, the C i t is analyzed based on C 1 , C 2 ∈ 0,1 . Therefore, the points below the conjoint θ positions satisfy the efficiency against energy-saving and carbon emission control (Figure 8). Based on this satisfaction (%), the successive achievements for varying operation intervals are analyzed in Figure 9.

The expected (from the data source) and the optimized successive intervals are presented in Figure 9. The condition X = j and U A < U L (or) U A < C A need not be satisfied at the same interval. Therefore, the operation time is induced with either U A and Z improvements. This is validated for providing better improvements across different operating intervals. Finally, the multi-objective improvement between the carbon control and energy-saving operation interval is presented in Figure 10.

The improvement in achieving Figure 9 and Figure 8 validations across 24-h time (operation) and weekdays is presented in Figure 10. The cumulative value of the buildings considered for 7 days of a week is analyzed. In the varying operation time, the successive intervals are by assigning different agents for K such that M is stabilized. The above representation is consolidated based on the utilization and peak demand for different days. This relies on the consumption based on people density, device utilization, and surges observed (Figure 10).