Traditional multiobjective evolutionary algorithms face a great challenge when dealing with many objectives. This is due to a high proportion of nondominated solutions in the population and low selection pressure toward the Pareto front. In order to tackle this issue, a series of indicator-based algorithms have been proposed to guide the search process toward the Pareto front. However, a single indicator might be biased and lead the population to converge to a subregion of the Pareto front. In this paper, a multi-indicator-based algorithm is proposed for many-objective optimization problems. The proposed algorithm, namely stochastic ranking-based multi-indicator Algorithm (SRA), adopts the stochastic ranking technique to balance the search biases of different indicators. Empirical studies on a large number (39 in total) of problem instances from two well-defined benchmark sets with 5, 10, and 15 objectives demonstrate that SRA performs well in terms of inverted generational distance and hypervolume metrics when compared with state-of-the-art algorithms. Empirical studies also reveal that, in the case a problem requires the algorithm to have strong convergence ability, the performance of SRA can be further improved by incorporating a direction-based archive to store well-converged solutions and maintain diversity. © 1997-2012 IEEE.
Bibliographical noteThis work was supported in part by the National Natural Science Foundation of China under Grant 61329302, Grant 61175065, and Grant 61573328; in part by the Program for New Century Excellent Talents in University under Grant NCET-12-0512; in part by the Engineering and Physical Sciences Research Council under Grant EP/K001523/1 and Grant EP/I010297/1; and in part by the Royal Society Newton Advanced Fellowship under Grant NA150123. The work of X. Yao was supported by the Royal Society Wolfson Research Merit Award.
- Archive method
- many-objective evolutionary algorithm
- multiobjective optimization
- stochastic ranking