Pareto adaptive scalarising functions for decomposition based algorithms

Abstract

Decomposition based algorithms have become increasingly popular for solvingmulti-objective problems.However, the effect of scalarising functions in decomposition based algorithms is under-explored. This study analyses the search behaviour of a family of frequently used scalarising functions— the Lp weighted approaches, and identifies that the p value corresponds to a trade-off between the Lp approach’s search ability and its robustness on Pareto front geometries. That is, as the p value increases, the search ability of the Lp approach decreases whereas its robustness on Pareto front geometry increases. Based on this observation, we propose to use Pareto adaptive scalarising functions in decomposition based algorithms, where the p value is adaptively fine-tuned based on an estimation of thePareto front shape.MOEA/DusingPareto adaptive scalarising functions (MOEA/D-par) is tested on a set of problems (with up to seven objectives) encompassing three basic Pareto front geometries, i.e., convex, concave and linear, and is shownto outperformMOEA/Dusing Chebyshev function on all the test problems.