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The quality of solution sets generated by decomposition-based evolutionarymultiobjective optimisation (EMO) algorithms depends heavily on the consistencybetween a given problem's Pareto front shape and the specified weights'distribution. A set of weights distributed uniformly in a simplex often lead toa set of well-distributed solutions on a Pareto front with a simplex-likeshape, but may fail on other Pareto front shapes. It is an open problem on howto specify a set of appropriate weights without the information of theproblem's Pareto front beforehand. In this paper, we propose an approach toadapt the weights during the evolutionary process (called AdaW). AdaWprogressively seeks a suitable distribution of weights for the given problem byelaborating five parts in the weight adaptation --- weight generation, weightaddition, weight deletion, archive maintenance, and weight update frequency.Experimental results have shown the effectiveness of the proposed approach.AdaW works well for Pareto fronts with very different shapes: 1) thesimplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) thedisconnect, 5) the degenerated, 6) the badly-scaled, and 7) thehigh-dimensional.

What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-based Evolutionary Multi-Objective Optimisation