Manta ray foraging optimization algorithm with mathematical spiral foraging strategies for solving economic load dispatching problems in power systems

Economic Load Dispatch (ELD) is an effective dispatch strategy to improve economic efficiency while ensuring the safety and stability of the power system. It minimizes production costs by rationally allocating the power generated by each power system unit. In this paper, an Manta Ray Foraging Optimization (MRFO) algorithm based on the mathematical spiral foraging strategy is proposed to solve the ELD problem in power systems considering transmission losses. Eight different mathematical spirals were introduced into the MRFO algorithm's foraging strategy, including the Rose spiral, Archimedes spiral, Fermat spiral, Cycloid spiral, Hypotrochoid spiral, Epitrochoid spiral, Inverse spiral and Lituus spiral. The mathematical spiral foraging strategy can enhance the global search ability of the MRFO algorithm and improves its convergence velocity. To verify the performance of the proposed improved MRFO algorithm, 30 benchmark functions are tested and the optimization performances are compared with BOA, AOA, SCA, HHO, WOA, RSA, and GWO. The simulation experimental results show that the performance and application of the manta ray foraging optimization algorithm based on the mathematical spiral foraging strategy outperform other intelligent optimization algorithms tested on 30 benchmark functions. Finally, two ELD cases with total demands of 2500 MW and 10500 MW are selected and solved using the improved manta ray foraging optimization algorithm. Comparing the simulation results with other optimization algorithms, it is shown that the proposed improved algorithm obtains the best fuel cost and smaller transmission loss in almost every test case, which canl help to improve the economic efficiency of the power system and achieve the goal of economic load dispatch.