Research And Application Of Multi-objective Optimization Algorithm Based On Grid Difference And Co-evolution

Multi-objective optimization problem(MOP)is an urgent problem to be solved in the field of scientific research and practical engineering.The traditional multi-objective optimization algorithm has some shortcomings in the optimal solution set,which unable to improve the convergence and diversity.In order to deal with this problem,the most important for MOP is looking for a method to enhance the effectiveness of the algorithm and protect the diversity.This paper presents an effective approach,based on doing research and improving the NSGA-?.And it utilizes the grid mechanism and the method of co-evolution to improve the efficiency of algorithm.The details are as follows:(1)Aiming at improving the MOP in convergence,this paper put forward a grid-based bidirectional local search algorithm.Firstly,in the process of algorithm matching,we select two potential individuals,which have better orientation,to mating pool.Then by establishing the grid mechanism to analysis the merits and demerits of the new individual.The experimental results show that the algorithm is improved in convergence.Finally,the optimal solution set of the improved algorithm is eloser to the true Pareto-optimal front.(2)Aiming at improving the MOP in diversity,this paper put forward a novel environment selection strategy by penalty mechanism.Through the different punishment degree in environmental selection process,the best solutions can be gotten form the previous population.Therefore,the algorithm can prevent the optimal solution set from distribution crowded.This algorithm is compared with three classical algorithms in test function.And the experimental results show that the improved algorithm's optimal solution set can be obtained rapidly and distributed uniformly in objective space.(3)This paper combines and improves the method of co-evolution to make full use of cooperation between individuals during the evolutionary.The population of the algorithm is divided into two sub-populations which using parallel evolutionary strategy.Two sub-populations exchange some individuals which belong to the first nondominated front.In this way,the improved algorithm can take full advantage of cooperation between individuals to enhance the accuracy and convergence.(4)We apply the improved algorithm to PID parameter tuning.Then this paper compares with other multi-objective optimization algorithms and traditional PID parameter tuning methods.The experimental results show that the improved algorithm,which compares with traditional PID parameter tuning methods,can obtain the optimal parameters under the control performance index.And the improved algorithm,which compares with other algorithms,can obtain the better optimal solution set.