A Many-Objective Evolutionary Algorithm Based on Decomposition and Local Dominance

Many-objective evolutionary algorithms (MOEAs), especially the decomposition-based MOEAs, have attracted wide attention in recent years. Recent studies show that a well designed combination of the decomposition method and the domination method can improve the performance ,i.e., convergence and diversity, of a MOEA. In this paper, a novel way of combining the decomposition method and the domination method is proposed. More precisely, a set of weight vectors is employed to decompose a given many-objective optimization problem(MaOP), and a hybrid method of the penalty-based boundary intersection function and dominance is proposed to compare local solutions within a subpopulation defined by a weight vector. A MOEA based on the hybrid method is implemented and tested on problems chosen from two famous test suites, i.e., DTLZ and WFG. The experimental results show that our algorithm is very competitive in dealing with MaOPs. Subsequently, our algorithm is extended to solve constraint MaOPs, and the constrained version of our algorithm also shows good performance in terms of convergence and diversity. These reveals that using dominance locally and combining it with the decomposition method can effectively improve the performance of a MOEA.

A Decomposition-Based Many-Objective Evolutionary Algorithm with Local Iterative Update

Existing studies have shown that the conventional multi-objective evolutionary algorithms (MOEAs) based on decomposition may lose the population diversity when solving some many-objective optimization problems. In this paper, a simple decomposition-based MOEA with local iterative update (LIU) is proposed. The LIU strategy has two features that are expected to drive the population to approximate the Pareto Front with good distribution. One is that only the worst solution in the current neighborhood is swapped out by the newly generated offspring, preventing the population from being occupied by copies of a few individuals. The other is that its iterative process helps to assign better solutions to subproblems, which is beneficial to make full use of the similarity of solutions to neighboring subproblems and explore local areas in the search space. In addition, the time complexity of the proposed algorithm is the same as that of MOEA/D, and lower than that of other known MOEAs, since it considers only individuals within the current neighborhood at each update. The algorithm is compared with several of the best MOEAs on problems chosen from two famous test suites DTLZ and WFG. Experimental results demonstrate that only a handful of running instances of the algorithm on DTLZ4 lose their population diversity. What's more, the algorithm wins in most of the test instances in terms of both running time and solution quality, indicating that it is very effective in solving MaOPs.

A mullti- or many- objective evolutionary algorithm with global loop update

Multi- or many-objective evolutionary algorithm- s(MOEAs), especially the decomposition-based MOEAs have been widely concerned in recent years. The decomposition-based MOEAs emphasize convergence and diversity in a simple model and have made a great success in dealing with theoretical and practical multi- or many-objective optimization problems. In this paper, we focus on update strategies of the decomposition- based MOEAs, and their criteria for comparing solutions. Three disadvantages of the decomposition-based MOEAs with local update strategies and several existing criteria for comparing solutions are analyzed and discussed. And a global loop update strategy and two hybrid criteria are suggested. Subsequently, an evolutionary algorithm with the global loop update is implement- ed and compared to several of the best multi- or many-objective optimization algorithms on two famous unconstraint test suites with up to 15 objectives. Experimental results demonstrate that unlike evolutionary algorithms with local update strategies, the population of our algorithm does not degenerate at any generation of its evolution, which guarantees the diversity of the resulting population. In addition, our algorithm wins in most instances of the two test suites, indicating that it is very compet- itive in terms of convergence and diversity. Running results of our algorithm with different criteria for comparing solutions are also compared. Their differences are very significant, indicating that the performance of our algorithm is affected by the criterion it adopts.