The researches on improved types of particle swarm optimization (PSO) to solve all kinds of optimization problems in real life have become hot topics. Chaos PSO is an important one of all improved types of PSO. In this paper, the definition of chaos PSO is given, and the chaos PSO algorithms are classified, and the characteristics of chaos PSO algorithms are analyzed. In all of chaos PSO algorithms, PSO with chaotic local search is the most effective method. Nowadays, although many chaotic local search algorithms are proposed, these proposed algorithms have the same characteristic, namely, each dimension of the specified solution vector is changed during one search. However, this way can’t perform refine search when the dimensions of the specified solution vector are many, a single dimensional chaotic local search is proposed to solve this problem. Based on the single dimensional chaotic local search, PSO and some other strategies, the following four algorithms are proposed to solve different types of optimization problems.1) A kind of chaos PSO with single dimensional chaotic local search and diversity maintenance strategy is proposed to solve single objective continuous function optimization problems without constraints, where single dimensional chaotic local search is employed to increase the local search ability of PSO, and chaotic sequences are used to substitute some parameters of PSO to improve the global search ability of PSO. In addition, the diversity maintenance strategy is introduced into the proposed algorithm to prevent from premature convergence. Ten dimensions and thirty dimensions of eight benchmark functions are solved by the proposed algorithm and the other three chaos PSO algorithms in50times, respectively. The simulation results show that for each function, the average error accuracy and standard deviation of the optimal solutions obtained by proposed algorithm in both cases are better than by the other three algorithms.2) A new algorithm which hybrids PSO with chaotic global and local searches is proposed to solve integer programming problems (which belong to single objective function optimization problems with constraints, where all the decision variables are discrete) and mixed integer programming problems (which belong to single objective function optimization problems with constraints, where some decision variables are discrete, and others are continuous). In the new algorithm, the chaotic global search is applied to increase the global search ability of PSO, and the chaotic local search is used to improve the local search ability of PSO. The most important difference between the chaotic local search in the proposed algorithm and other chaotic local search algorithms is that the former can simultaneously perform multi-dimensional and single dimensional chaotic local search, but the latter can only perform multi-dimensional chaotic local search. The simulation results indicate that among fourteen problems, the proposed algorithm can obtain100%success in solving integer problems, but can’t obtain100%success in solving mixed integer problems.3) Because the proposed algorithm, PSO combined with chaotic global and local searches, can’t obtain100%success in solving mixed integer problems, a novel algorithm is proposed to solve a class of mixed integer programming problems, namely, reliability-redundancy allocation problem. The novel algorithm is a combination of differential evolution, chaotic local search and PSO, where differential evolution is used to indirectly increase global search ability of PSO, and the chaotic local search is a combination of a multi-dimensional one and a single dimensional one. The experiments compared the novel algorithm with the other six improved meta-heuristic algorithms in solving four typical system reliability-redundancy allocation problems, and the results show that the novel algorithm can obtain the best system reliabilities or the same system reliabilities as the best one of six algorithms. In addition, considering the deficiency of the performance evaluation index MPI, a new performance evaluation index SR is proposed. The new algorithm and the other six algorithms are evaluated by SR, and the results show that the new algorithm is the best one of all compared algorithms.4) A multi-objective PSO algorithm based on chaotic local search is proposed to solve the multi-objective continuous function optimization problems without constraints, where individual archive and global archive save individual non-dominated solutions and global non-dominated solutions, respectively. In order to make non-dominated solutions uniformly distribute in the solutions space, when the individual or global archive exceeds the maximum capacity, excessive non-dominated solutions will be deleted by the smallest value of the sum of the adjacent individuals distances. Also, in order to find more or closer to the Pareto optimal solutions, dominated solutions (with respect to non-dominated solutions in global archive) generated by all particles and all non-dominated solutions in global archive are performed by chaotic local search in each generation. The proposed algorithm was compared with the other two multi-objective PSO algorithms in solving nine basic multi-objective function optimization problems, and the results indicate that for each problem, the proposed algorithm is better than the other two algorithms using two performance evaluation indexes (final generational distance and spacing). |