Abstract
Decomposition-based evolutionary multiobjective algorithms (MOEAs) divide a multiobjective problem into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector-guided evolutionary algorithm (RVEA) by designing an adaptive reference vector adjustment strategy. By adding the strategy, the predefined reference vectors will be adjusted according to the distribution of promising solutions with good overall performance and the subspaces in which the PF lies may be further divided to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increase of objective size. Motivated by that, an improved angle-penalized distance (APD) method is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, and 10-objective MaF1–MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.
Highlights
In the real world, decision makers often encounter some problems with more than one objective to be solved simultaneously. ese problems are called multiobjective optimization problems (MOPs), and if the number of objectives is larger than 3, they are termed as many-objective optimization problems (MaOPs)
A set of solutions representing the trade-off among all the objectives, called Pareto-optimal solutions, can be achieved and pursued by researches. e Pareto-optimal solutions are known as Pareto front (PF) in the objective space and Pareto set (PS) in the decision space, respectively
A large number of algorithms have been developed such as Nondominated Sorting Genetic Algorithm II (NSGA-II) [4], multiobjective evolutionary algorithm based on decomposition (MOEA/D) [5], and so on [6]
Summary
Decision makers often encounter some problems with more than one objective to be solved simultaneously. ese problems are called multiobjective optimization problems (MOPs), and if the number of objectives is larger than 3, they are termed as many-objective optimization problems (MaOPs). Pareto-dominance-based algorithms [4, 7, 8] often divide solutions into different nondominated levels and use a second criterion to select solutions in the last level; decomposition-based MOEAs [9,10,11,12,13] decompose the original MOP into multiple subproblems and solve them in a cooperative way; for indicator-based MOEAs and MaOEAs, such as hypervolume-based many-objective (HypE) [14] and indicator-based multiobjective evolutionary algorithm with reference point adaptation (AR-MOEA) [15], it tends to develop an indicator to evaluate the overall performance and sort the individuals according to their indicator values
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