The multi-objective optimization problem refers to the fact that there are often conflicts among optimization objectives,and it is impossible to find the solution that makes all objectives optimal at the same time.Optimizing one class of objectives will degrade the rest of the objectives,and the Pareto optimal solution set is obtained to make multiple objectives Pareto optimal;the multi-modal multi-objective optimization problem is based on satisfying the definition of multi-objective optimization problem,there are multiple Pareto optimal solution sets correspond to the same Pareto frontier,and multiple Pareto-optimal solution sets are distributed in the decision space.The swarm intelligence algorithm is widely used to deal with nonlinear and nonconvex multi-objective optimization problems due to its strong search ability,and it can effectively solve the problem of scattered distribution of Pareto optimal solution sets in multimodal multi-objective optimization problems due to its flexible diversity maintenance strategy.The existing swarm intelligence algorithms cannot control the iterative process when solving multi-objective optimization problems,and often easily fall into local optimum;they ignore the distribution of solution sets in decision space when dealing with multimodal multi-objective optimization problems,and their ability to find multiple PSs is weak.Therefore,this paper designs a multi-objective optimization algorithm and a multimodal multi-objective optimization algorithm based on the swarm intelligence algorithm,whose main research contents are as follows:(1)NSGAⅡ algorithm based on Sobol initialization population and time-varying factor with dual strategy selection operator is designed and implemented.This algorithm uses the NSGAⅡ algorithm as a framework to generate uniform and null-free solutions in the decision space using Sobol low-difference sequences to provide a good solution basis for population evolution;using a dual-strategy binary tournament selection operator based on a time-varying factor,the time-varying factor can adaptively control the convergence ability of the population and improve the diversity and convergence of the population,while the dual-strategy selection operator can be used in the tournament selection process.The dual-strategy selection operator can dynamically select the strategy during the tournament selection process and reduce the chance of duplicate individuals entering the offspring increasing the diversity of progeny solutions.Comparison with various improved NSGAⅡ algorithms on the twoobjective ZDT,three-objective DTLZ test functions verifies the superiority of the algorithms in terms of convergence ability,convergence speed.(2)A multimodal multi-objective whale optimization algorithm based on indexed niching is designed and implemented.This algorithm uses the whale algorithm as a framework and chooses an index niching strategy to divide the population into multiple Nichings,control the information transfer rate in the population,and help the algorithm find multiple PSs;uses opposite-Latin hypercube sampling to initialize the population so that particles are uniformly distributed in the decision space to provide a good solution for evolution;uses a fast non-dominated ranking based on special crowding distances to incorporate decision space crowding distance dynamically into the environment selection,which increases the diversity of the population decision space.The proposed algorithm is compared with four optimization algorithms on 11 benchmark test functions,and the experiments show that the proposed algorithm finds multiple PSs significantly better than the remaining four algorithms,and the optimal neighborhood radius for Niching is calculated experimentally. |