A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

TLDR

In evolutionary multiobjective optimization, balancing convergence and diversity is crucial, and incorporating user preferences becomes increasingly important as the number of objectives grows and population sizes are limited. This paper proposes a reference vector‑guided evolutionary algorithm for many‑objective optimization. The algorithm uses reference vectors to decompose the problem, applies an angle‑penalized distance scalarization to balance convergence and diversity, dynamically adapts vector distribution to objective scales, regenerates vectors for irregular Pareto fronts, and extends to constrained many‑objective problems. Experimental results show the algorithm outperforms five state‑of‑the‑art EAs on benchmark problems and demonstrates that reference vectors are effective and cost‑efficient for articulating preferences.

Abstract

In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.