Abstract
Many-objective optimization problems (MaOPs) are vital and challenging in real-world applications. Existing evolutionary algorithms mostly produce an approximate Pareto-optimal set using new dominance relations, dimensionality reduction, objective decomposition, and set-based evolution. In this paper, we propose a mutation operator guided by preferred regions to improve an existing set-based evolutionary many-objective optimization algorithm that integrates preferences. In the proposed mutation operator, optimal solutions in a preferred region are first chosen to form a reference set; then for each solution within the individual to be mutated, an optimal solution from the reference set is specified as its reference point; finally, the solution is mutated towards the preferred region via an adaptive Gaussian disturbance to accelerate the evolution, and thus an approximate Pareto-optimal set with high performances is obtained. We apply the proposed method to 21 instances of seven benchmark MaOPs, and the experimental results empirically demonstrate its superiority.
Highlights
Various optimization problems involving multiple objectives exist in real-world situations, such as the automated design of analog and mixed-signal circuits [1] and power system dispatch [2]
The proposed adaptive Gaussian mutation operator is related to a reference point in the decision space, which makes the individual mutate towards the preferred region; on the other hand, the random number in the operator is connected with the achievement function value in the objective space, suggesting that the operator is closer to the preferred region
The first one verifies the effectiveness of the proposed mutation operator via distribution of a set-based individual before and after mutation in the objective space; the second one compares the values of the H indicator of Pareto fronts produced by different mutation operators with respect to the number of generations in order to demonstrate that the proposed mutation operator can accelerate the convergence of the algorithm; the last one contrasts the statistical results of the H and D indicators obtained by different methods to validate the superiority of PSEA-m
Summary
Various optimization problems involving multiple objectives exist in real-world situations, such as the automated design of analog and mixed-signal circuits [1] and power system dispatch [2]. In this paper we develop a new mutation operator guided by preferred regions based on the study of Gong et al [27]. A preferredregion-based adaptive Gaussian mutation operator is designed to guide the set-based individuals to evolve towards the preferred region, accelerating the evolution and enhancing the performances of Pareto-optimal solutions. The main contribution of this paper is that evolutionary information of a population is fully utilized to develop a mutation operator to guide its evolution towards its preferred region. The proposed adaptive Gaussian mutation operator is related to a reference point in the decision space, which makes the individual mutate towards the preferred region; on the other hand, the random number in the operator is connected with the achievement function value in the objective space, suggesting that the operator is closer to the preferred region. The final section concludes the main work of this paper and highlights several topics to be researched in the future
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