A New Algorithm for Solving a Special Matching Problem with a General Form Value Function under Constraints
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We consider the assignment problem with a special structure with a general form value function and constraints prohibiting certain matchings. In this case, the matching cost may be undefined until some permutation is found. We formulate the problem in terms of graph theory and reduce it to finding a minimal cost path in a graph with nonlocal edge weights. The proposed method for solving the problem is a modification of the Dijkstra’s shortest path algorithm in a weighted directed graph. This research is motivated by well drilling applications. We also show the analysis of our numerical experiments.
Keywordsquadratic assignment problem invalid matchings shortest path in a graph Dijkstra’s algorithm
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- 1.Lovász, L. and Plummer, M., Matching Theory, Amsterdam: Elsevier, 1986. Translated under the title Prikladnye zadachi teorii grafov. Teoriya parosochetanii v matematike, fizike, khimii, Moscow: Mir, 1998.Google Scholar
- 4.Kuhn, H.W., The Hungarian Method for the Assignment Problem, Naval Res. Logist. (NRL), 1955, vol. 2, no. 1–2, pp. 83–97.Google Scholar
- 7.Burkard, R.E. and Cela, E., Linear Assignment Problems and Extensions, in Handbook Combinat. Optim., New York: Springer, 1999, pp. 75–149.Google Scholar
- 15.Maniezzo, V. and Colorni, A., The Ant System Applied to the Quadratic Assignment Problem, IEEE Transact. Knowledge Data Eng., 1999, vol. 11, no. 5, pp. 769–778.Google Scholar
- 17.Jünger, M. and Kaibel, V., A Basic Study of the QAP Polytope, Techincal Report 96.215, Institut für Informatik, Universität zu Köln, Germany, 1996.Google Scholar