Pareto Adaptive Scalarising Functions for Decomposition Based Algorithms


Decomposition based algorithms have become increasingly popular for solving multi-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 L-p weighted approaches, and identifies that the p value corresponds to a trade-off between the L-p approach's search ability and its robustness on Pareto front geometries. That is, as the p value increases, the search ability of the L-p 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 the Pareto front shape. MOEA/Dusing Pareto 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 shown to out perform MOEA/Dusing Chebyshev function on all the test problems.