Bicriteria Optimisation of Average and Worst-Case Performance Using Coevolutionary Algorithms

A common aim in real-world optimisation problems is to seek a solution offering highest performance on expected scenarios, but at the same time guaranteeing an at least acceptable performance on worst-case scenarios. Competitive coevolution evolves a population of solutions alongside a population of difficult scenarios in order to find so-called robust solutions. However, solutions with maximal worst-case performance often exhibit poor performance on more typical scenarios. Existing coevolutionary approaches generally favour such solutions over ones which sacrifice only a small amount of average performance for an almost as large gain in worst-case performance, despite the latter being favourable in most practical applications. We present a new coevolutionary algorithm which treats average performance and worst-case performance as two objectives of a bicriteria optimisation problem and seeks the corresponding Pareto front. Such an algorithm enables the discovery of solutions with strong performance in both of these metrics, which would otherwise be rejected if optimising for only one. Our algorithm constitutes the first coevolutionary approach to this solution concept. We also provide experimental results on the performance of this algorithm on the design of smart controllers for the management of energy flow between buildings, renewable energy sources, and electric vehicles.