Research On Improvement And Application Of NSGA-? Multi-Objective Optimization Method

In real life,various problems are needed to be optimized for multiple goals at the same time.Such as customers want to buy superior goods at a cheaper price,this "contradiction" is a typical example of multi-objective optimization problem.Multi-objective optimization problem is playing an important role in many areas,including manufacturing industry,carrying trade,service industry,and telecommunications.Multi-objective optimization problems can be seen everywhere.In order to solve the "contradiction" of multiple targets,it is necessary to transform the related multiple sub-goals into corresponding functions and then optimize them frequently.This is the multi-objective optimization.Genetic algorithm(GA)has a unique advantage in multi-objective optimization methods.Especially the multi-objective optimization genetic algorithm(MOGA)and its related derivative algorithms,which are widely studied and applied in recent years.The non-dominated sorting genetic algorithm-?(NSGA-?)is the representative.However,the traditional NSGA-? is limited to the simulated binary crossover operator(SBX)and the polynomial mutation operator,so that the non-dominated individuals have weak global search ability and poor population diversity.Aiming at the problems existing in traditional NSGA-?,this paper proposes an improved NSGA-? multi-objective optimization algorithm,which obtains the satisfactory Pareto optimal solution set by simulation experiments,and validates the improved theoretical results by practical application,solves multi-objective optimization problems finally.In this paper,an improved NSGA-? multi-objective optimization algorithm is proposed,and the specific research contents are mainly reflected in the following aspects:(1)The mathematical model of the system is established for different multi-objective optimization problems.The experimental samples are obtained by orthogonal experiment,and the best optimized parameters are determined finally.So the efficiency of the algorithm is improved,and the operation time is saved.(2)The normal distribution crossover operator(NDX)is introduced in the evolution process,which effectively solves the problem that the search space is too narrow caused by the simulated binary cross operator(SBX)in the traditional NSGA-? algorithm,and easy to fall into the local optimum.It enhances the spatial search ability of the algorithm.(3)The improved adaptive adjustment of variation is proposed to improve the population optimization speed.For the complex nonlinear optimization problem,the traditional NSGA-? algorithm adopts the polynomial variation proposed by Deb,due to the presence of random parameters and subjective parameters,the randomness is large and the convergence rate is slow.The improved adaptive adjustment mutation can achieve better convergence effect through its mechanism,not only speed up the population convergence rate,but also maintain the diversity of the population,making the Pareto boundary distribution better.(4)The optimum reaction rate,reaction time,catalyst and its additives in the synthesis process of polysiloxane were optimized by the improved NSGA-? algorithm,and the maximum value of single molecule conversion and the expected value of viscosity molecular weight were obtained.In the experiment,the solution coverage and spatial distribution are defined to measure the performance of Pareto solution,and the optimal evolution parameters aredetermined by orthogonal experiment.The simulation results show that the improved NSGA-? algorithm is superior to the traditional MOGA and its derivative algorithms with quantitative standards.The Pareto optimal frontier further shows that the solution set distribution of the improved algorithm is more uniform and continuous,which verifies the correctness and rationality of the improved NSGA-? multi-objective optimization algorithm theory in polymerization optimization.