Hybrid Multi-objective Optimizations Based On EDA And AIS

As meta-heuristic search algorithms, evolutionary algorithms have been applied to multi-objective optimization successfully. Evolutionary multi-objective optimization has become a hot topic. Recently, some new evolutionary paradigms have been introduced into EMO community, such as artificial immune system, estimation distribution algorithms, and co-evolutionary algorithms. This paper proposed two improved algorithms based on these representative algorithms. The main research work of this paper includes the following:1、A Regularity Model-Based Multi-objective Estimation of Distribution Algorithm (RMMEDA) samples new solutions from a probability model which characterizes the distribution of promising solutions in the search space at each generation. However, it does not directly use the location information of the locally optimal solutions found so far for generating new trial solutions. Immune Clonal Selection Algorithm (ICSA) uses cloning、crossover and mutation operators as mechanisms to create new individuals from the best individuals of the previous generation, but it ignores the intrinsic character of the population. To overcome their shortcomings and combine their advantages, this paper proposed Hybrid Immune Algorithm with EDA for Multi-objective Optimization(HIAEDA) in which some offspring are generated by cloning、crossover and mutation operators while the others by EDA operators. HIAEDA firstly selects minority isolated non-dominated individuals in the population to guide the local search. Secondly, it simulates the distribution of the population in decision space to built probability model which capture the structure of variable interactions, so HIAEDA efficiently solves hard optimization and search problems with interactions among the variables. From the simulation results on a number of test problems, we find that HIAEDA outperforms two other contemporary MOEAs:RMMEDA and improved version of non-dominated sorting genetic algorithm (NSGAII) in terms of finding a diverse set of solutions and in converging near the true Pareto-optimal set.2、Based on HIAEDA, this paper proposed Hybrid Immune Algorithm with EDA for Multi-objective Optimization Based on Decomposition(HIAEDA/D).HIAEDA/D is a hybrid algorithm based on co-evolution of several subpopulations which can reduce the computational complexity significantly and get better performance than HIAEDA on some test problems. This algorithm divides the population into several subpopulation based on decomposition instead of clustering in HIAEDA which needs extra time for running Local PCA to cluster at each generation. Every subpopulation corresponds to a subspace in the decision space and simulates a portion of Pareto Set (PS) to built model. Several populations cooperate to solve the problems. Experimental studies have shown that HIAEDA/D performs better than RMMEDA, NSGAII, and HIAEDA on a set of test instances with nonlinear variable linkages and five ZDT problems.