Abstract:
In order to solve the multimodal multi-objective optimization problem and find all solutions equivalent to the Pareto optimal solution, this paper proposes a novel group search optimization algorithm (MMO_LTSGSO) based on spatial learning mechanism and emotion tracking behavior by introducing social behavior into the basic group search algorithm. Firstly, a spatial learning mechanism is established and the decision of the population distribution state (discrete state and concentrated state) is made according to the real-time information of the learned individual's own position and the best individual position. When the population is in a discrete state, the following and wandering way is adopted to enhance the space exploration ability of the algorithm. With the optimization process, individuals interact with each other, and the spatial distance gradually decreases. At this time, the population gradually aggregates, and the dynamic step search strategy is used to update the individual position, which can explore the solution around the optimal solution in real time and accelerate the convergence speed of the algorithm. Secondly, in order to prevent the algorithm from falling into stagnation and improve the accuracy of the algorithm, the emotion factor is introduced to make certain individuals track their moving behavior along their preferred direction. Then, special congestion distance calculation and guided evolution strategy are used to ensure the diversity of the algorithm in decision space and target space. Finally, the convergence of the algorithm is proved theoretically, and its performance is verified via 15 multimodal multi-objective optimization test benchmark functions, and is also compared with several existing multimodal multi-objective optimization algorithms. It is shown via the experiments results that the proposed algorithm can effectively solve multimodal multi-objective optimization problems.