Wang, H.; Emmerich, M.; Deutz, A.; Hernández, V.A.S.; Schütze, O. The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems. Math. Comput. Appl.2023, 28, 10.
Wang, H.; Emmerich, M.; Deutz, A.; Hernández, V.A.S.; Schütze, O. The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems. Math. Comput. Appl. 2023, 28, 10.
Wang, H.; Emmerich, M.; Deutz, A.; Hernández, V.A.S.; Schütze, O. The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems. Math. Comput. Appl.2023, 28, 10.
Wang, H.; Emmerich, M.; Deutz, A.; Hernández, V.A.S.; Schütze, O. The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems. Math. Comput. Appl. 2023, 28, 10.
Abstract
Recently, the Hypervolume Newton method (HVN) has been proposed as fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions that are at least twice continuously differentiable. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton-Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily be applied to solve equality constraints with a high precision problems, and to some extend also inequalities. We finally use HVN as local search engine within a MOEA and show the benefit of this hybrid method on several benchmark problems.
Computer Science and Mathematics, Data Structures, Algorithms and Complexity
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