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A Dichotomic Algorithm for Transportation Network and Land Use Problem

Author

Listed:
  • Mamadou Koné
  • Mouhamadou A.M.T. Baldé
  • Babacar M. Ndiaye

Abstract

Redeveloping sites to accommodate housing or new economic activities is a major urban policy challenge. This problem belongs to the class of NP-hard problems. In this paper, we present an attractive mixed integer nonlinear programming formulation for the transportation network and land use problem. We first introduce a new useful nonlinear formulation of this challenging combinatorial optimization problem. Then, an alternative to considering a linearity of the constraints is to reformulate the problem as a new exact, compact discrete linear model. The problem is solved by our new algorithm and numerical results are presented for a number of test problems in academics instances.

Suggested Citation

  • Mamadou Koné & Mouhamadou A.M.T. Baldé & Babacar M. Ndiaye, 2019. "A Dichotomic Algorithm for Transportation Network and Land Use Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 42-56, February.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:1:p:42
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    References listed on IDEAS

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    1. Alain Billionnet & Sourour Elloumi & Amélie Lambert, 2013. "An efficient compact quadratic convex reformulation for general integer quadratic programs," Computational Optimization and Applications, Springer, vol. 54(1), pages 141-162, January.
    2. Jen-Jia Lin & Cheng-Min Feng, 2003. "A bi-level programming model for the land use – network design problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 37(1), pages 93-105, February.
    3. Duranton, Gilles & Puga, Diego, 2015. "Urban Land Use," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 467-560, Elsevier.
    4. Lawrence J. Watters, 1967. "Letter to the Editor—Reduction of Integer Polynomial Programming Problems to Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 15(6), pages 1171-1174, December.
    5. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    6. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
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    Keywords

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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