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.
@cite_64: Decomposition-based methods are an increasingly popular choice for a posteriori multi-objective optimization. However the ability of such methods to describe a trade-off surface depends on the choice of weighting vectors defining the set of subproblems to be solved. Recent adaptive approaches have sought to progressively modify the weighting vectors to obtain a desirable distribution of solutions. This paper argues that adaptation imposes a non-negligible cost -- in terms of convergence -- on decomposition-based algorithms. To test this hypothesis, the process of adaptation is abstracted and then subjected to experimentation on established problems involving between three and 11 conflicting objectives. The results show that adaptive approaches require longer traversals through objectivespace than fixed-weight approaches. Since fixed weights cannot, in general, be specified in advance, it is concluded that the new wave of decomposition-based methods offer no immediate panacea to the well-known conflict between convergence and distribution afflicting Pareto-based a posteriori methods.
Adapting the weight vectors affects the convergence of the algorithm. Varying the weight vectors essentially changes the subproblems. After a change of the subproblems, their associated solutions need to readjust the search directions. This could lead to the solutions to in the objective space during the optimisation process @cite_64 .