School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan
Evol Comput. 2020 Spring;28(1):1-25. doi: 10.1162/evco_a_00243. Epub 2018 Nov 26.
Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.
基于 Pareto 的多目标进化算法在解决多目标优化问题时面临着巨大的挑战，因为它们无法在高维目标空间中同时保持收敛性和多样性。现有的方法通常通过修改选择标准来克服这个问题。与它们不同的是，我们提出了一种新的元目标 (MeO) 方法，它将多目标优化问题转化为新的问题，新的问题通过 Pareto 算法变得更容易解决。MeO 将给定的多目标优化问题转换为一个新的问题，该问题具有与原始问题相同的 Pareto 最优解和目标数量。新问题中的每个元目标由两个组件组成，分别衡量解的收敛性和多样性性能。由于 MeO 仅转换问题的表述，因此它可以很容易地合并到任何多目标进化算法中，包括非 Pareto 算法。特别是，它可以提高 Pareto 算法解决多目标优化问题的能力。由于分别评估解的收敛性和多样性性能，传统的基于密度的选择标准（例如拥挤距离）将不再错误地将具有较差收敛性能的解误认为具有低密度值的解。通过在元目标空间中根据解的收敛性能对其进行惩罚，Pareto 支配性对于多目标优化问题变得更加有效。比较研究验证了所提出的元目标方法在解决多目标优化问题方面的竞争性能。
