The Robust (Minmax Regret) Quadratic Assignment Problem with Interval Flows

Feizollahi, Mohammad Javad; Averbakh, Igor

doi:10.1287/ijoc.2013.0568

Cited by 16 publications

(12 citation statements)

References 32 publications

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“…But, they provide upper bounds for RQAP while the robust (minmax regret) QAP tabu search in [45] provides neither a lower bound nor an upper bound.…”

Section: Tabu Searchmentioning

confidence: 98%

“…In this section, we first present notation and problem statement for classical QAP which is mostly quoted from [45] with some slight adjustments. Then, we present an efficient MIP equivalent for QAP from the literature.…”

Section: Notation and Problem Statementmentioning

confidence: 99%

“…It is worth mentioning that for a given assignment, finding the worst-case scenario requires sorting δ ij d X ij for (i, j) ∈ J which can be done in O (|J| log(|J|)), i.e polynomial time in size of J and consequently in n. In contrast, obtaining the worst-case scenario in minmax regret QAP requires solving a general QAP which is NPhard [45].…”

Section: Propositionmentioning

confidence: 99%

“…We tested our proposed methods on uncertain QAP instances presented in [45]. These instances have been categorized into two main families.…”

Section: Details Of Problem Instancesmentioning

confidence: 99%

“…Approximated dynamic programming [10], genetic algorithm [11], parallel algorithms [12,13], hybrid algorithms [14], teaching learning based optimization [15], semidefinite programming relaxations [16,17], QAP with uncertain locations was studied in [39]. [45] used a robust deviation (minmax regret) approach to deal with uncertainty in material flows.…”

Section: Introductionmentioning

confidence: 99%

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Robust quadratic assignment problem with budgeted uncertain flows

Feizollahi

Feyzollahi

2015

Operations Research Perspectives

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h i g h l i g h t s• A robust approach for quadratic assignment problem (RQAP) with budgeted uncertainty. • An exact and two heuristic methods to solve RQAP.• Extensive experiments to show performance of methods and quality of solutions.• RQAP can be solved significantly faster than minmax regret QAP. • RQAP has adjustable conservativeness while minmax regret QAP has not. a b s t r a c tWe consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.

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“…But, they provide upper bounds for RQAP while the robust (minmax regret) QAP tabu search in [45] provides neither a lower bound nor an upper bound.…”

Section: Tabu Searchmentioning

confidence: 98%

Section: Notation and Problem Statementmentioning

confidence: 99%

Section: Propositionmentioning

confidence: 99%

“…We tested our proposed methods on uncertain QAP instances presented in [45]. These instances have been categorized into two main families.…”

Section: Details Of Problem Instancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust quadratic assignment problem with budgeted uncertain flows

Feizollahi

Feyzollahi

2015

Operations Research Perspectives

Self Cite

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Exact and heuristic algorithms for the interval min-max regret generalized assignment problem

Iori

Martello

et al. 2018

Computers & Industrial Engineering

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We consider a generalization of the 0-1 knapsack problem in which the profit of each item can take any value in a range characterized by a minimum and a maximum possible profit. A set of specific profits is called a scenario. Each feasible solution associated with a scenario has a regret, given by the difference between the optimal solution value for such scenario and the value of the considered solution. The interval min-max regret knapsack problem (MRKP) is then to find a feasible solution such that the maximum regret over all scenarios is minimized. The problem is extremely challenging both from a theoretical and a practical point of view. Its decision version is complete for the complexity class Σ p 2 hence it is most probably not in N P. In addition, even computing the regret of a solution with respect to a scenario requires the solution of an N P-hard problem. We examine the behavior of classical combinatorial optimization approaches when adapted to the solution of the MRKP. We introduce an iterated local search approach and a Lagrangian-based branch-and-cut algorithm, and evaluate their performance through extensive computational experiments.

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Robust (min–max regret) single machine scheduling with interval processing times and total tardiness criterion

Wang

Wen-li

et al. 2020

Computers & Industrial Engineering

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The Robust (Minmax Regret) Quadratic Assignment Problem with Interval Flows

Cited by 16 publications

References 32 publications

Robust quadratic assignment problem with budgeted uncertain flows

Robust quadratic assignment problem with budgeted uncertain flows

Exact and heuristic algorithms for the interval min-max regret generalized assignment problem

Robust (min–max regret) single machine scheduling with interval processing times and total tardiness criterion

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