Multiple objective minimum cost flow problems: A review

Hamacher, Horst W.; Pedersen, Christian Roed; Ruzika, Stefan

doi:10.1016/j.ejor.2005.09.033

Cited by 47 publications

(31 citation statements)

References 38 publications

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“…The most recent survey on multi-objective minimum cost flow problems is by Hamacher, Pedersen, and Ruzika (2007). We will therefore briefly mention only newer published work on multiobjective network flow problems, one of which considers multiple commodities.…”

Section: Literaturementioning

confidence: 98%

A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem

Moradi

Raith

Ehrgott

2015

European Journal of Operational Research

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Available online xxxKeywords: Network flows Bi-objective multi-commodity minimum cost flow problem Dantzig-Wolfe decomposition Column generation Bi-objective simplex method a b s t r a c tWe present a column generation algorithm for solving the bi-objective multi-commodity minimum cost flow problem. This method is based on the bi-objective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using Dantzig-Wolfe decomposition. Then, similar to the bi-objective simplex method, our algorithm iteratively moves from one non-dominated extreme point to the next one by finding entering variables with the maximum ratio of improvement of the second objective over deterioration of the first objective. Our method reformulates the problem into a bi-objective master problem over a set of capacity constraints and several single objective linear fractional sub-problems each over a set of network flow conservation constraints. The master problem iteratively updates cost coefficients for the fractional sub-problems. Based on these cost coefficients an optimal solution of each sub-problem is obtained. The solution with the best ratio objective value out of all sub-problems represents the entering variable for the master basis. The algorithm terminates when there is no entering variable which can improve the second objective by deteriorating the first objective. This implies that all nondominated extreme points of the original problem are obtained. We report on the performance of the algorithm on several directed bi-objective network instances with different characteristics and different numbers of commodities.

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Section: Literaturementioning

confidence: 98%

A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem

Moradi

Raith

Ehrgott

2015

European Journal of Operational Research

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“…However, one can transform the fuzzy problem into a multi-objective variant (Karsak, 2004). Multi-objective MCFP is an important concept in practice and theory (Hamacher, Pedersen, & Ruzika, 2007). Sedeno-Noda and Gonzalez-Martin (2001) and SedenoNoda and Gonzalez-Martin (2003) developed two network simplex methods for bi-objective MCFP and found all Pareto solutions utilizing non-polynomial time algorithm.…”

Section: Introductionmentioning

confidence: 99%

Preemptive priority-based algorithms for fuzzy minimal cost flow problem: An application in hazardous materials transportation

Ghatee

Hashemi

Zarepisheh

et al. 2009

Computers & Industrial Engineering

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“…However, the special features of BONF can be exploited to design more efficient algorithms. An excellent survey on BONF problem has recently been published by Hamacher et al (2007). Among the approaches proposed in the literature are a generalization of the out-of-kilter technique used by Malhotra and Puri (1984) and Lee and Pulat (1991).…”

Section: Introductionmentioning

confidence: 99%