Improved Multi-objective Immune Algorithm And Particle Swarm Algorithm

Multi-objective optimization problems exist widely in science and engineer-ing field.Different from a single objective problem,the multi-objective optimiza-tion problem has a set of solutions representing the optimal balance between each goal.The traditional optimization methods are limited because one solu-tion can be obtained at each run.Therefore,evolutionary algorithms are widely concerned and applied due to the simple principle,easy implementation,inher-ent parallelism,high robustness and low requirements.Although some classi-cal multi-objective evolutionary algorithms,such as NSGA-?,MOEA/D,SPEA2 and so on,can solve multi-objective optimization problems well,there are sev-eral shortcomings such as the diversity and poor distribution of solutions.The multi-objective immune algorithm and multi-objective particle swarm optimiza-tion algorithm have the advantages of high search efficiency,group optimiza-tion and self-adaptation in solving multi-objective optimization problems.Com-bined with excellent characteristics of the differential evolution operator,this the-sis presents an individual strength-based multi-objective immune algorithm with adaptive differential evolution and a clustering multi-objective particle swarm al-gorithm with hierarchical Maximin selection.The main contents are as follows:1.An individual strength-based multi-objective immune algorithm with adaptive differential evolution is proposed by considering that some informa-tion contained in the dominant solution may be helpful to search for the optimal solution.In the clone phase,some non-dominated individuals and dominat-ed individual are selected to enhance the diversity of population and avoid the premature.In the evolutionary phase,crossover and mutation are excuted by an adaptive differential evolution operator and population is perturbed by the polynomial mutation operator to balance effectively global and local search of the algorithm.An archive is built based on individual strength to store a number of good solutions,which are evolved and updated at each iteration.The final archive is used as the optimal solution set of the algorithm2.A clustering multi-objective particle swarm algorithm with hierarchical Maximin selection is proposed.To avoid the population towards the same di-rection,the K-means clustering method is used to divide the population into several sub-populations and individuals at sub-populations are updated by par-ticle swarm formula.Sub-populations are then merged and evolved by using adaptive differential evolution operator.Finally,an improved Maximin selection strategy is presented to choose a certain number of better solutions from the par-ent and offspring population to the next evolution.An archive is built to store a number of good solutions chosen by this,which are evolved and updated at each iteration.The results of numerical experiments show that the proposed algorithms are superior in both convergence and distribution...