Abstract
Evolutionary multi- and many-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performance metrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.
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Deb, K., Abouhawwash, M., Dutta, J. (2015). An Optimality Theory Based Proximity Measure for Evolutionary Multi-Objective and Many-Objective Optimization. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C. (eds) Evolutionary Multi-Criterion Optimization. EMO 2015. Lecture Notes in Computer Science(), vol 9019. Springer, Cham. https://doi.org/10.1007/978-3-319-15892-1_2
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DOI: https://doi.org/10.1007/978-3-319-15892-1_2
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