In the actual functioning of power systems, economic load dispatch (ELD) is a crucial problem to solve. The role of the power system is to deliver continuous power to the consumers at an affordable price which is its main feature (Panigrahi et al., 2006), (Jadoun et al., 2015). The objective is to reduce energy-generating costs while fulfilling load needs and ensuring equality and in-quality constraints. This fact results in a higher degree of pollution awareness in thermal plants and a lower cost of diagnosing the problem. Because they operate in conjunction with a collection of viable alternatives, evolutionary methods are now perfectly suited for discovering answers to optimization problems. All optimization approaches, including evolutionary ones, are known to be influenced by constraints (Salcedo-Sanz, 2009). Since the traditional procedure of an evolutionary approach, employing operators for individuals in a population may violate the constraint rules. The way evolutionary approaches deal with constraint rules of challenges is a significant aspect that is directly connected to the quality of solutions created for such problems. By converting the present solution that opposes the constraints into a viable one, a redesigned method eliminates unattainable solutions.

Wind, solar, thermal, nuclear, renewable, hydro, and other power-producing facilities are used in most power generation systems. In the case of renewable energy systems, the operational cost will not change as much as the production. In thermal systems, however, the running cost varies with the total power output. As a result, the ELD issue, which includes the use of thermal systems as generators, is considered a critical optimization issue in electric power systems. Maintaining an economical operation is a difficult challenge for both traditional and smart grid systems. When power systems are exposed to operational and a transmission imperative, the ELD limits the optimal outcome for an electric power generation to sustain the load demand with a minimum generation price. The ELD problem is usually solved by sophisticated computerized approaches that meet the operational and power system imperatives via minute-to-minute monitoring. A little increase in the ELD demonstrates its long-term reaction to the declining price of the total power output. As a result, a variety of optimization methods have been developed to address cost-effective load dispatch issues while producing high-quality results. Traditional optimization approaches were the sole option to address ELD concerns for many years. Because of the limitations of conventional methods, system operators have a chance to fail to notice the realistic and technological imperatives of the system’s units. There are two types of simplifications in this category: first, combined with the accuracy of the generating unit’s pricing model, particularly for different types of fuels or taking the valve-point loading impact into account (Cai et al., 2012; Zhong et al., 2013). Multi-valve steam turbines are widely seen in real-world generating units. The valve point of the generating unit is drawn when the steam turbine’s intake valve opens abruptly, pushing the energy consumption curve upward.

The economic load dispatch problem is a major concern for the cost-effective operation of electric power systems as it concentrates on basically assembling the power outputs of the units by establishing time intervals to decrease generating costs while still meeting other system requirements. In general, the traditional ELD problem is reduced to solve the convex quadratic programming problem (Reid and Hasdorff, 1973), which may now be handled effectively using MOSEK (Babonneau et al., 2019). Furthermore, the system becomes non-smoothed, non-convex, and non-continuous when the valve-point loading effect, transmission loss, and prohibited operating zones are considered. The objective function arises as multiples of the local minimum because of these features, making global minima exceedingly difficult to attain. Aside from that, the non-smooth nature of the function makes the derivate-based mathematical programming technique challenging to apply directly.

Traditional optimization techniques often look at linear, piece-wise linear, and price functions of generators in quadratic functions, with just network loss being considered. These classic techniques include lambda iteration (Zhan et al., 2014), gradient descent method (Dibangoye et al., 2015), linear programming (Torreglosa et al., 2016), Newton’s technique (Wang et al., 2014), dynamic programming (Al-Kalaani, 2009), gradient search (Subathra et al., 2015), and the Lagrangian relaxation algorithm (Li et al., 2013; Mohammadi-Ivatloo et al., 2013). Because of the persistence of severe non-linear characteristics in real-world practical networks, while dealing with high-dimensional economic dispatch difficulties, these suffer disadvantages such as failure to meet imperatives and lengthy time calculations.

This time-consuming calculation in optimization methods prompted researchers to develop meta-heuristic optimization strategies to solve large-scale problems. The meta-heuristic method (Gjorgiev and Čepin, 2013) takes into consideration non-convex pricing functions and non-smooth operating functions as well as other imperatives. This includes techniques such as synergic predator–prey optimization (SPPO) (Singh et al., 2016), seeker optimization algorithm (SOA) (Shaw et al., 2012), genetic algorithm (GA) (Amjady and Nasiri-Rad, 2010), (Elsayed et al., 2014), evolutionary programming (EP) (Sinha et al., 2003), firefly algorithm (FA) (Yang et al., 2012), particle swarm optimization (PSO) (Neyestani et al., 2010), (Safari and Shayeghi, 2011), (Wang and Singh, 2009), artificial bee colony (ABC) (Aydın and Özyön, 2013), colonial competitive differential algorithm (CCDE) (Ghasemi et al., 2016), bacterial foraging algorithm (BFA) (Farhat and El-Hawary, 2010), improved Tabu search algorithm (ITS) (Whei-Min Lin et al., 2002), ant colony optimization (ACO) (Pothiya et al., 2010), group search optimizer (GSO) (Zare et al., 2012), harmony search algorithm (HAS) (Jeddi and Vahidinasab, 2014), biogeography-based optimization (BBO) (Bhattacharya and Chattopadhyay, 2010), and differential evolution (DE) (Jiang et al., 2013). Many researchers used slime mould algorithm to bring better results and few such algorithms are Dispersed Foraging Slime Mould Algorithm (DFSMA) (Hu et al., 2022), Chaos-opposition-enhanced slime mould algorithm (CO-SMA) (Rizk, 2022), Opposition based learning slime mould algorithm (OBLSMA) (Houssein et al., 2022), Multi-objective slime mould algorithm (MOSMA) (Houssein et al., 115870), Equilibrium optimizer slime mould algorithm (EOSMA) (Yin et al., 2022). In this work, SMA is used to identify solutions to economic load dispatch problems on a variety of test systems. Other new and popular approaches outcomes are compared to analyze the results.

The goal of the ELD problem is to lower the entire fuel cost of power systems by finding the optimum combination of power outputs from all generating units while congregating load demand and operational constraints (Dubey et al., 2013).

It is known that the behavior of the organism can be imitated and molded to tackle the mathematics of unconstrained and non-convex characteristics. Researchers have framed to imitate the guiding principles to develop computations and algorithms. The slime molds have received significant courteousness for the past few years. Scientifically, slime mold is titled as Physarum polycephalum (Howard, 1931). The slime mold undergoes few changes in its structure, that is, it repositions its front position into a fan-shaped model, and its interconnected venous network allows the cytoplasm to flow inside at some level in relocation series. This stretchable venous network helps in searching for food in multiple places and grabs the food from food points. The slime mold has the ability to creep up to 900 sq.m if it finds rich food points in the environment.

In this section of the article, the IEEE bus systems in small size test systems were considered, and comparison was done with other methods, to see how well the slime mold optimization algorithm performed on the ELD issue.

In this study, the slime mold optimization approach was used to solve economic load dispatch problems in electric power networks. This method’s effectiveness was tested on conventional IEEE bus systems with 3 and 5 producing units in small, medium, and large power systems. According to the statistics, the slime mold optimizer was clearly the best choice for dealing with economic load dispatch issues since it contributes reduced fuel costs and less transmission loss. It has a higher rate of convergence than other well-known optimizers. By establishing a balance between exploration and exploitation, the slime mold optimizer achieved maximal avoidance in the local optimum. As a result, this algorithm provided improved solutions for load dispatch difficulties that were cost-effective.