Solving pessimistic bilevel optimisation problems with evolutionary algorithms
M. Antoniou, G. Papa
14th ECCOMAS Thematic Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control EUROGEN 2021
Athens, Greece, 17-19 May, 2021
It is common in practice, an optimal solution of a decision-maker to depend heavily on the response of another decision-maker, formulating a bilevel optimization problem. The optimization of a bilevel problem aims to achieve the optimum solution of the upper-level, taking into consideration the optimal lower-level values too. When the lower-level problem is multimodal, meaning that it has several global optima, an ambiguity about the optimal upper-level solution appears. The optimistic approach assumes that the follower will respond with an optimal solution, that is favorable by the upper-level as well. In the pessimistic approach, the upper-level is optimising for the worst case. Various evolutionary algorithms have been implemented successfully to solve the optimistic approach of the bilevel problem. To the best of our knowledge, these algorithms have not been extended to the pessimistic approach. In this paper, we use a multi-population nested Differential Evolution to solve the pessimistic bilevel problem when the lower-level has multiple global optima. The performance of the algorithm is examined by solving a test-problem taken from the literature.
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