A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

Fontes, Dalila B.M.M.; Hadjiconstantinou, Eleni; Christofides, Nicos

doi:10.1016/j.ejor.2005.03.024

Cited by 31 publications

(21 citation statements)

References 28 publications

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“…This set of instances can be downloaded from http://people.brunel.ac.uk/~mastjjb/jeb/orlib/netflowccinfo.html (Last visited on April 8, 2010). The results obtained by the BRKGA were compared with optimal solutions found by a dynamic programming approach (Fontes et al 2006) for problem instances with up to 19 nodes and, for larger instances, to heuristic solutions found by a local search algorithm (Fontes et al 2003).…”

Section: Resultsmentioning

confidence: 99%

Biased random-key genetic algorithms for combinatorial optimization

2010

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Random-key genetic algorithms were introduced by Bean (ORSA J. Comput. 6:154-160, 1994) for solving sequencing problems in combinatorial optimization. Since then, they have been extended to handle a wide class of combinatorial optimization problems. This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems. Biased random-key genetic algorithms are a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. After introducing the basics of biased random-key genetic algorithms, the paper discusses in some detail implementation issues, illustrating the ease in which sequential and parallel heuristics based on biased random-key genetic algorithms can be developed. A survey of applications that have recently appeared in the literature is also given.

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Section: Resultsmentioning

confidence: 99%

Biased random-key genetic algorithms for combinatorial optimization

2010

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“…Dynamic programming is an optimization based approach that is appropriate for studying the path-dependent problems [22]. For example, Zhang et al [23] and Bai et al [24] developed dynamic programming models to explore the optimal stockpiling paths for China's strategic petroleum reserve respectively.…”

Section: Literature Reviewmentioning

confidence: 99%

Study on China’s wind power development path—Based on the target for 2030

Xie

et al. 2015

Renewable and Sustainable Energy Reviews

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“…An excellent survey of the convex multicommodity network flow problem is provided in [22]. For the single-source uncapacitated minimum cost network flow problem with general concave costs, a dynamic programming algorithm is offered in [13] and a genetic algorithm in [12]. For a single commodity convex network flow problem, a convergent Lagrangean heuristic is described in [19].…”

Section: Literature Reviewmentioning

confidence: 99%

Lagrangean‐based decomposition algorithms for multicommodity network design problems with penalized constraints

2009

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This article discusses problems in the context of multicommodity network design where additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to the penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network design problem. This article presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first relies upon dualizing the capacity constraints that results in a flow decomposition, and the second is through relaxing flow constraints that results in an arc decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state-of-the-art nonlinear optimization codes fail to identify feasible solutions.

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A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems

Cited by 31 publications

References 28 publications

Biased random-key genetic algorithms for combinatorial optimization

Biased random-key genetic algorithms for combinatorial optimization

Study on China’s wind power development path—Based on the target for 2030

Lagrangean‐based decomposition algorithms for multicommodity network design problems with penalized constraints

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