Automatically Improving the Anytime Behaviour of Multiobjective Evolutionary Algorithms

Abstract. An algorithm that returns as low-cost solutions as possible at any moment of its execution is said to have a good anytime behaviour. The problem of optimising anytime behaviour can be modelled as a biobjective non-dominated front, where the goal is to minimise both time and cost. Using a unary quality measure such as the hypervolume indicator, the analysis of the anytime behaviour can be converted into a single-objective problem. In this manner, available automatic configuration tools can be applied to improve the anytime behaviour of an algorithm. If we want to optimise the anytime behaviour of multi-objective algorithms, we may apply again unary quality measures to obtain a scalar value for measuring the obtained approximation to the Pareto front. Thus, for multi-objective algorithms, the anytime behaviour may be described in terms of the curve of the hypervolume over time, and the quality of this bi-objective tradeoff curve be evaluated according to its hypervolume. Using this approach, we can automatically improve the anytime behaviour of multi-objective evolutionary algorithms (MOEAs). In this article, we first introduce this approach and then experimentally study the improvements obtained considering three MOEAs, namely, IBEA, NSGA-II and SPEA2.