Two- and three-index formulations of the minimum cost multicommodity k-splittable flow problem

Gamst, Mette; Jensen, Peter Neergaard; Pisinger, David; Plum, Christian Edinger Munk

doi:10.1016/j.ejor.2009.05.014

Cited by 18 publications

(10 citation statements)

References 16 publications

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“…Gamst et al. () compared two formulations (two‐index and three‐index) of the minimum‐cost MC k FP and used the branch‐and‐price as a solution approach.…”

Section: Literature Review Of Mcfpmentioning

confidence: 99%

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Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

Masri¹,

Krichen

Guitouni

2017

Int Trans Operational Res

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Single‐path multicommodity flow problem (SMCFP) is a well‐known combinatorial optimization problem, in which the flow of each commodity can be transmitted using only one path linking its destination to an appropriate origin within the addressed network. In this paper, we study the SMCFP in a multiobjective context by considering the simultaneous optimization of paths' delay and average reliability. The network is modeled as a finite set of nodes that can communicate using preestablished connections where each connection is characterized by a capacity, a lead time, and a reliability. A node can be an information producer or/and information consumer. The contention problem is solved by assigning a path and a dedicated bandwidth to each flow. The problem is formulated as a biobjective nonlinear optimization problem. This biobjective problem has not been considered in the literature. We design three alternative procedures for approximating the Pareto front. We proposed an MGA based on NSGA‐II, a multiobjective variable neighborhood search and a new distance‐based hybrid metaheuristic. The hybridization integrates a local search into the framework of genetic algorithm to effectively drive the search toward a better approximating of the Pareto front. The propounded algorithms' efficiencies are experimentally investigated on a test bed of instances applied to a planar and a grid network. A comparative study is conducted based on different multiobjective performance indicators.

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“…Gamst et al. () compared two formulations (two‐index and three‐index) of the minimum‐cost MC k FP and used the branch‐and‐price as a solution approach.…”

Section: Literature Review Of Mcfpmentioning

confidence: 99%

“…In the first stage, the best k paths are generated, while in the second stage the amount of flow on each path is optimized. Gamst et al (2010) compared two formulations (two-index and three-index) of the minimum-cost MCkFP and used the branch-and-price as a solution approach.…”

Section: Maximum Flowmentioning

confidence: 99%

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

Masri¹,

Krichen

Guitouni

2017

Int Trans Operational Res

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“…Hence, for an algorithm of running time O(n) of the problem (P), one can find another algorithm with reduced execution time O(logn) which solves the same problem [6]. For example, in the framework of the implementation of a heuristic for the minimization of the cost for a flow problem, the performance of a three-index algorithm has been improved by a two-index algorithm, in terms of running time and the number of solved instances [11]. Moreover, in case of multi-index problem, the running time of an algorithm can be reduced to polynomial time by adopting a parallelism approach as in [12,7].…”

Section: Introductionmentioning

confidence: 99%

From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series

Essessinou

Degla

Ndiaye

2019

JAMCS

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The quarterly disaggregation of an annual economic aggregate, by a mathematical method with a cyclical indicator, gives rise to a problem of minimization to make the quarterly economic aggregate smooth. This involves two indexes for the quarter and the year, which sometimes can make the resolution algorithm less efficient if the problem is large. In this paper we propose a method of indexing quarterly variables based on an isomorphic transformation of a two-index program into a one-index program, in order to minimize the cost of the algorithm of resolution. This method of continuous indexing of variables, applied to national accounts, shows that the algorithm with a single index is more efficient than the algorithm with two indexes when solving the optimization program of the quarterly disaggregation.

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“…Container routing problems are very similar to multi-commodity flow problems (MCF) studied in the field of operations research (e.g., Tomlin, 1966;Ahuja et al, 1993;Gamst et al, 2010). MCF can be solved in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

A novel hybrid-link-based container routing model

Wang

2014

Transportation Research Part E: Logistics and Transportation Re

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Two- and three-index formulations of the minimum cost multicommodity k-splittable flow problem

Cited by 18 publications

References 16 publications

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

Metaheuristics for solving the biobjective single‐path multicommodity communication flow problem

From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series

A novel hybrid-link-based container routing model

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