A reference vector adaptive strategy for balancing diversity and convergence in many-objective evolutionary algorithms

Decomposition-based multiobjective evolutionary algorithms (MOEA/D) have achieved great success in the field of evolutionary multiobjective optimization, and their outstanding performance in solving for the Pareto-optimal solution set has attracted attention. This type of algorithm uses reference vectors to decompose the multiobjective problem into multiple single-objective problems and searches them collaboratively, hence the choice of reference vectors is particularly important. However, predefined reference vectors may not be suitable for dealing with many-objective optimization problems with complex Pareto fronts (PFs), which can affect the performance of MOEA/D. To solve this problem, we introduce a reference vector initialization strategy, namely, scaling of the reference vectors (SRV), and also propose a new reference vector adaptation strategy, that is, transformation of the solution positions (TSP) based on the ideal point solution, to deal with irregular PFs. The TSP strategy can adaptively redistribute the reference vectors through periodic adjustment to endow that the solution set with better convergence and a better distribution. Both strategies are introduced into a representative MOEA/D, called.-DEA-TSP, which is compared with five state-of-the-art algorithms to verify the effectiveness of the proposed TSP strategy.