Solving the Nonlinear Transportation Problem by Global Optimization

Klanšek, Uroš; Pšunder, Mirko

doi:10.3846/transport.2010.39

Cited by 20 publications

(15 citation statements)

References 30 publications

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“…We then describe the parameter settings, experimental comparisons and result analysis on the performances of PrGA, PtGA, and mathematical solvers in solving these MCFP instances. Since our focus is to solve nonlinear non-convex MCFP, we adopt a set of nonlinear non-convex cost functions which are commonly-used in the literature [9,10,15]. Michalewicz et al [15] categorised the nonlinear cost functions as 1) piece-wise linear cost functions; 2) multimodal (nonlinear non-convex) cost functions; 3) smooth cost functions which are mostly used for Operations Research (OR) problems.…”

Section: Experimental Studiesmentioning

confidence: 99%

A Probabilistic Tree-Based Representation for Non-convex Minimum Cost Flow Problems

Ghasemishabankareh

Özlen

Neumann

et al. 2018

Parallel Problem Solving From Nature – PPSN XV

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Network flow optimisation has many real-world applications. The minimum cost flow problem (MCFP) is one of the most common network flow problems. Mathematical programming methods often assume the linearity and convexity of the underlying cost function, which is not realistic in many real-world situations. Solving large-sized MCFPs with nonlinear non-convex cost functions poses a much harder problem. In this paper, we propose a new representation scheme for solving non-convex MCFPs using genetic algorithms (GAs). The most common representation scheme for solving the MCFP in the literature using a GA is priority-based encoding, but it has some serious limitations including restricting the search space to a small part of the feasible set. We introduce a probabilistic tree-based representation scheme (PTbR) that is far superior compared to the priority-based encoding. Our extensive experimental investigations show the advantage of our encoding compared to previous methods for a variety of cost functions.

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Section: Experimental Studiesmentioning

confidence: 99%

A Probabilistic Tree-Based Representation for Non-convex Minimum Cost Flow Problems

Ghasemishabankareh

Özlen

Neumann

et al. 2018

Parallel Problem Solving From Nature – PPSN XV

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“…Type of TP Method(s) and models applied Conclusions Klanšek and Pšunder, 2010 Non-linear TPwhen expenses are nonlinear in relation to the unit of the transported good.…”

Section: Author(s)mentioning

confidence: 99%

Scenario Simulation Model of the Production, Transportation and Asphalt Paving

Galić¹,

Završki²,

Dolaček-Alduk³

2015

OTMCJ

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Organizational processes modelling and scenario simulation is proved to be an efficient tool for the quantitative strengthening of the decision making process. In business of production, transportation and paving of great quantities of asphalt mixture, solving problem of project's fragmented sub-processes has been emphasized by previous researchers as a high priority. Detached process modeling and optimization without taking into account constraints of interrelations among sub-processes cannot offer the optimal or quality solution. Thus, it is necessary to structure a developing and easily adjustable model which will be able to integrate all sub-processes with their interrelations. In this paper authors gave a review of the findings and recommendations of the previous researches. Based on the recommendations, authors structured a developing simulation model for planning and optimization "just in time" chain of processes of production, transportation and paving of great quantities of asphalt mixture. Suggested model is based on the algorithm for scenario simulations which is dynamic and adjustable for changes and updates of the input parameters.

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“…A nonlinear version of the Transportation Problem with a fixed number of sources was studied by Cosares and Hochbaum in [14]. Other approaches to the nonlinear variants of the Transportation Problem (including heuristics) were discussed by Cao and Uebe in [12], Dangalchev in [15], Jo et al in [27] (see also the comments to this paper published by Kannan et al in [28]), Ilich and Simonovic in [26], Klanšek and Pšunder in [29], Tuy et al in [48] and [49].…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Generalized Transportation Problem with convex costs

Anholcer

2015

Croat. Oper. Res. Rev.

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Abstract. We investigate the Nonlinear Generalized Transportation Problem (NGTP), where the transportation costs and the costs that depend on the amount of good delivered to the destination points are strictly convex functions. The amounts of goods change during the transportation process. This model may correspond, for example, with a congested network where the time costs are involved. First, we present the NGTIP model, then provide a method of solving the problems of this type and then we prove convergence of the method. The numerical experiments prove the effectiveness of the presented algorithm.

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Solving the Nonlinear Transportation Problem by Global Optimization

Cited by 20 publications

References 30 publications

A Probabilistic Tree-Based Representation for Non-convex Minimum Cost Flow Problems

A Probabilistic Tree-Based Representation for Non-convex Minimum Cost Flow Problems

Scenario Simulation Model of the Production, Transportation and Asphalt Paving

The Nonlinear Generalized Transportation Problem with convex costs

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