Multi-objective arithmetic optimization algorithm with random searching strategies to solve combined economic emission dispatch problem

Given the escalating environmental problems, the significance of combined economic emission dispatch (CEED) in electricity generation is progressively growing. To solve the CEED problem more effectively and achieve reduced fuel costs and pollutant emissions, a multi-objective arithmetic optimization algorithm (AOA) with random searching strategies was proposed. The math optimizer probability (MOP) is a parameter that governs the individual position update of the AOA algorithm. The proposed algorithm uses four random search strategies, namely tangent flight, Levy flight, Brownian motion and lognormal flight, to replace the MOP parameter in AOA. This modification significantly enhances the algorithm's global search capability. The math optimizer accelerated (MOA) function is a crucial parameter for controlling the search mode selection in AOA. By incorporating hyperbolic tangent fluctuation into the variation trend of MOA, the exploration ability of the algorithm is enhanced. To achieve the Pareto optimal solution with extensive coverage, the non-dominated solutions are initially stored in a repository. Subsequently, the roulette mechanism is employed to select a leader from the repository for position update. Ultimately, this process yields a set of Pareto optimal solutions with relatively uniform distribution. The effectiveness of the proposed algorithm is verified through simulation experiments with 20 multi-objective benchmark functions, and the optimal improved strategy is selected among four improvement methods. It is also the best in comparison with other multi-objective algorithms. Subsequently, simulation experiments are conducted by using three CEED cases with varying sizes (6 units 1200 MW, 10 units 2000 MW and 40 units 10500 MW), wherein the objectives of fuel cost and pollutant emission are compared with methodologies employed in existing literature. The results show that the proposed algorithm is superior to other algorithms in solving CEED problems, and can get smaller fuel cost and pollutant emission, and can obtain more evenly distributed Pareto optimal solution set.