  The quality of solution sets generated by decomposition-based evolutionary
multiobjective optimisation (EMO) algorithms depends heavily on the consistency
between a given problem's Pareto front shape and the specified weights'
distribution. A set of weights distributed uniformly in a simplex often lead to
a set of well-distributed solutions on a Pareto front with a simplex-like
shape, but may fail on other Pareto front shapes. It is an open problem on how
to specify a set of appropriate weights without the information of the
problem's Pareto front beforehand. In this paper, we propose an approach to
adapt the weights during the evolutionary process (called AdaW). AdaW
progressively seeks a suitable distribution of weights for the given problem by
elaborating five parts in the weight adaptation --- weight generation, weight
addition, 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) the
simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the
disconnect, 5) the degenerated, 6) the badly-scaled, and 7) the
high-dimensional.
