S-metric calculation by considering dominated hypervolume as klee's measure problem
Evolutionary Computation
Updating exclusive hypervolume contributions cheaply
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Correction to "a fast incremental hypervolume algorithm"
IEEE Transactions on Evolutionary Computation
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Achieving balance between proximity and diversity in multi-objective evolutionary algorithm
Information Sciences: an International Journal
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
Theoretical Computer Science
Many-hard-objective optimization using differential evolution based on two-stage constraint-handling
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Parameterized average-case complexity of the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Speeding up many-objective optimization by Monte Carlo approximations
Artificial Intelligence
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When hypervolume is used as part of the selection or archiving process in a multiobjective evolutionary algorithm, it is necessary to determine which solutions contribute the least hypervolume to a front. Little focus has been placed on algorithms that quickly determine these solutions and there are no fast algorithms designed specifically for this purpose. We describe an algorithm, IHSO, that quickly determines a solution's contribution. Furthermore, we describe and analyse heuristics that reorder objectives to minimize the work required for IHSO to calculate a solution's contribution. Lastly, we describe and analyze search techniques that reduce the amount of work required for solutions other than the least contributing one. Combined, these techniques allow multiobjective evolutionary algorithms to calculate hypervolume inline in increasingly complex and large fronts in many objectives.