On the use of two reference points in decomposition based multiobjective evolutionary algorithms

Abstract

Decomposition based multiobjective evolutionary algorithms approximate the Pareto front of a multiobjective optimization problem by optimizing a set of subproblems in a collaborative manner. Often, each subproblem is associated with a direction vector and a reference point. The settings of these parameters have a very critical impact on convergence and diversity of the algorithm. Some work has been done to study how to set and adjust direction vectors to enhance algorithm performance for particular problems. In contrast, little effort has been made to study how to use reference points for controlling diversity in decomposition based algorithms. In this paper, we first study the impact of the reference point setting on selection in decomposition based algorithms. To balance the diversity and convergence, a new variant of the multiobjective evolutionary algorithm based on decomposition with both the ideal point and the nadir point is then proposed. This new variant also employs an improved global replacement strategy for performance enhancement. Comparison of our proposed algorithm with some other state-of-theart algorithms is conducted on a set of multiobjective test problems. Experimental results show that our proposed algorithm is promising.

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-Based Evolutionary Multiobjective Optimisation

“…Very recently, Zhang et al [45] designed a weight vector adaptation via a linear interpolation for bi-objective optimisation problems with a discontinuous Pareto front. Wang et al [46] considered both the ideal and nadir points to update the weight vectors in MOEA/D for a better distribution. Cai et al [47] proposed two types of weight (direction) vector adjustments for many-objective problems, with one aiming at the number of the direction vectors and the other aiming at the positions of the direction vectors.…”

A Scalar Projection and Angle-Based Evolutionary Algorithm for Many-Objective Optimization Problems

“…In the first phase, the ideal point is used in the scalarizing (Tchebycheff) function, while the nadir point may be used in the second phase if solutions found in the first phase are more crowded at the intermediate part of the approximated PF than at the boundaries. Recently, Wang et al [36] studied the effect of the reference point setting on the performance of decomposition-based algorithms for problems with either concave or convex PFs. They proposed a new MOEA/D variant, i.e., MOEA/D-MR, where both ideal and nadir points are used.…”

“…For problems with an irregular (i.e., discontinued, degenerated, etc.) PF, such as DTLZ5-7 and WFG3, decomposition-based algorithms with fixed weight vectors may suffer from performance degeneration as some weight vectors may have no intersection with the PF [24], or many subproblems can only find the solutions on the boundary of the PF [36]. Therefore, to deal with problems with irregular PFs, decomposition-based algorithms need to dynamically adjust weight vectors so as to adapt the distribution of search directions to the shape of the PF [24], [37]- [39].…”

“…The ideal point was widely used in most of the decomposition-based approaches, such as MOEA/D [21], MOEA/DD [9], NSGA-III [8], and reference vector guided evolutionary algorithm (RVEA) [40]. As explained in [36] and [41], this may be problematic sometimes. For example, for problems with convex PFs, scalarizing functions using the ideal point may pull most solutions toward the central region of the PF [36], [41]- [43].…”

“…For example, for problems with convex PFs, scalarizing functions using the ideal point may pull most solutions toward the central region of the PF [36], [41]- [43]. It was demonstrated recently in [36] that the simultaneous use of both ideal and nadir points is a feasible way to improve the performance of decomposition-based algorithms for problems with both convex and concave PFs.…”