Journal Article10.1016/j.cor.2021.105349
Computing representations using hypervolume scalarizations
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TL;DR: In this paper , the hypervolume indicator is used as a scalarizing function for biobjective combinatorial optimization problems and a generic solution approach that determines the nondominated set of a bi-objective optimization problem by solving a sequence of hypervolume scalarizations with appropriate choices of the reference point is described.
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About: This article is published in Computers & Operations Research. The article was published on 01 Jan 2022. The article focuses on the topics: Knapsack problem & A priori and a posteriori.
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Citations
Subset Selection for Evolutionary Multi-Objective Optimization
TL;DR: In this paper , a multi-objective evolutionary algorithm (MOEA) is proposed to solve the problem of subset selection, which selects a subset of solutions according to a certain criterion/indicator.
7
Ordinal Optimization Through Multi-objective Reformulation
TL;DR: In this paper , a bijective linear transformation that transforms ordinal optimization problems to associated standard multi-objective optimization problems with binary cost coefficients is proposed. But the transformation does not consider the complexity of ordinal problems.
The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems
TL;DR: In this paper , the Hypervolume Newton Method (HVN) has been extended to solve unconstrained bi-objective optimization problems with objective functions, where the first and second-order derivatives of the involved functions have to be given either analytically or numerically.
The Hypervolume Indicator Hessian Matrix: Analytical Expression, Computational Time Complexity, and Sparsity
TL;DR: In this paper , the analytical expression of the Hessian matrix of the mapping from a (fixed size) collection of n points in the d-dimensional decision space (or m dimensional objective space) to the scalar hypervolume indicator value is established.
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