The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance

Nguyen, Kien Trung; Chassein, André

doi:10.1016/j.ejor.2015.06.064

Cited by 28 publications

(4 citation statements)

References 18 publications

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“…Concerning this purpose, the ordered median function was coined by Nickel and Puerto [19] to generalize a class of functions, where the median and the center functions are among them. Then, the inverse ordered median location problem was also taken into account, for instance, in [20,21,22,23]. The following facts motivates further research on the topic of inverse combinatorial optimization with universal objective function.…”

Section: Introductionmentioning

confidence: 98%

The inverse k-max combinatorial optimization problem

Nhan

Nguyen

Hung

et al. 2023

YUGOSLAV J OPERATION

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Classical combinatorial optimization concerns finding a feasible subset of a ground set in order to optimize an objective function. We address in this article the inverse optimization problem with the k-max function. In other words, we attempt to perturb the weights of elements in the ground set at minimum total cost to make a predetermined subset optimal in the fashion of the k-max objective with respect to the perturbed weights. We first show that the problem is in general NP-hard. Regarding the case of independent feasible subsets, a combinatorial O(n2 log n) time algorithm is developed, where n is the number of elements in E. Special cases with improved complexity are also discussed.

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Section: Introductionmentioning

confidence: 98%

The inverse k-max combinatorial optimization problem

Nhan

Nguyen

Hung

et al. 2023

YUGOSLAV J OPERATION

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“…They showed the NP-completeness of the problem on cactus graphs and then developed linear time algorithms to solve the problem on cycles and on trees. Additionally, the inverse location problem was investigated with complexity result and efficient solution approach; for example, [1,9,10,[19][20][21], to mention a few. On a counter part, the reverse optimization problem on a network aims to modify parameters within a given budget so that the behavior network is improved as much as possible.…”

Section: Introductionmentioning

confidence: 99%

The reverse total weighted distance problem on networks with variable edge lengths

Trung

Thanh

2021

Filomat

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We address the problem of reducing the edge lengths of a network within a given budget so that the sum of weighted distances from each vertex to others is minimized. We call this problem the reverse total weighted distance problem on networks. We first show that the problem is NP-hard by reducing the set cover problem to it in polynomial time. Particularly, we develop a linear time algorithm to solve the problem on a tree. For the problem on cycles, we devise an iterative approach without mentioning the exact complexity. Additionally, if the cycle has uniform edge lengths, we can prove that the specified approach runs in O(n3) time as each edge of the cycle can be reduced at most once, where n is the number of vertices in the underlying cycle.

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“…As a special case of variable-sized robust optimization, we consider the following question: Given only a nominal problem (P) with objective ĉ, how large can an uncertainty set become, such that the nominal solution still remains optimal for the resulting robust problem? Due to the similarity in our question to inverse optimization problems, see, e.g., [AO01,Heu04,ABP09,NC15] we denote this as the inverse perspective to robust optimization. The approach from [CN03] is remotely related to our perspective.…”

Section: Introductionmentioning

confidence: 99%

Variable-sized uncertainty and inverse problems in robust optimization

Chassein

Goerigk

2018

European Journal of Operational Research

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In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min-max robust solutions and give bounds on their size.A special case of this perspective is to analyze for which uncertainty sets a nominal solution ceases to be a robust solution, which amounts to an inverse robust optimization problem. We consider this problem with a min-max regret objective and present mixed-integer linear programming formulations that can be applied to construct suitable uncertainty sets.Results on both variable-sized uncertainty and inverse problems are further supported with experimental data.

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The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance

Cited by 28 publications

References 18 publications

The inverse k-max combinatorial optimization problem

The inverse k-max combinatorial optimization problem

The reverse total weighted distance problem on networks with variable edge lengths

Variable-sized uncertainty and inverse problems in robust optimization

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