Research On Niching Multi-modal Multi-objective Optimization Algorithms

There are a large number of multi-objective optimization problems in real life,and the optimization objectives are often in conflict and restrict each other,there is no unique solution to make all objectives optimal at the same time.In recent years,the field of multi-objective optimization has been developed rapidly.In solving unconstrained multi-objective optimization problems,the classical objective decomposition method is sensitive to the shape of Pareto Front surface.Without knowing the shape of Pareto Front,it is difficult to approximate a set of evenly distributed Pareto optimal solutions.Therefore,the diversity of solution set should be improved as much as possible.In many practical projects,the problem of multiple Pareto solutions corresponding to the same Pareto Front is called a multi-modal multi-objective optimization problem.The traditional multi-objective optimization algorithm often ignores the distribution of solutions in the decision space when solving such problems,which leads to the poor diversity of Pareto solution set,and can not solve the multi-modal multi-objective optimization problems well.Therefore,it is necessary to improve the distribution of Pareto solutions in decision space and provide more choices for decision makers.Therefore,this paper designs and implements multi-modal and multi-objective optimization algorithm,the main research contents are as follows:(1)A multi-objective differential evolution algorithm with elite-archive and oppositionbased learning is designed and implemented.This algorithm establishes an external file to store the non-dominated solutions in the evolution process to improve the convergence speed of the algorithm.Using opposition-based learning to expand the search range of solutions and enhance the diversity of the population.The grid system is used to determine the coordinates of the solution,and Differential Evolution(DE)algorithm is used to generate new individuals.The next generation population is selected by grid constrained decomposition sorting to improve the diversity of solution distribution.(2)A multi-modal multi-objective optimization algorithm with two topology structures is designed and implemented.This algorithm is based on particle swarm optimization algorithm and combines the advantages and disadvantages of the two topology structures.In the early stage of the search,it searches in the global range,and in the later stage,the population searches within a certain range,thus forming a stable niching and making the population search for more and better decision space optimal solutions in the decision space.(3)A multi-modal multi-objective algorithm with neighborhood mutation is designed and implemented.This algorithm is based on differential evolution algorithm,uses niching based on neighborhood constraints in the decision space,uses an index-based selection mechanism to select the parent individuals in the mating pool.Using the distribution of solutions in the decision space,a reasonable environment selection mechanism is designed in the decision space,and the longest distance mechanism is used instead of the crowding distance mechanism to make the distribution of Pareto optimal solution more uniform.