A column generation method for inverse shortest path problems
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In this paper we formulate an inverse shortest path problem as a special linear programming problem. A column generation scheme is developed that is able to keep most columns of the LP model implicit and to generate necessary columns by shortest path algorithms. This method can get an optimal solution in finitely many steps. Some numerical results are reported to show that the algorithm has a good performance.
Key wordsInverse shortest path problems Simplex method dual problem column generation methods
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- Burton D, Toint PhL (1992) On an instance of the inverse shortest paths problem. Mathematical Programming 53:45–61Google Scholar
- Burton D, Toint PhL (1994) On the use of an inverse shortest paths algorithm for recovering linearly correlated costs. Mathematical Programming 63:1–22Google Scholar
- Burton D, Pulleyblank B, Toint PhL (1993) The inverse shortest problem with upper bounds on shortest path costs. Internal Report FUNDPGoogle Scholar
- Burton D (1992) On the inverse shortest path problem. Doctoral Dissertation, Facultes Universitaires Notre-Dame de la Paix de Namur, Department de Mathematique, Namur, BelgiumGoogle Scholar
- Xu S, Zhang J: An inverse problem of the weighted shortest path problem. To appear in The Japan Journal of Industrial and Applied MathematicsGoogle Scholar
- Goldfarb D, Idnani A (1983) A numerical stable dual method for solving strictly convex quadratic programs. Mathematical Programming 27:1–33Google Scholar
- Lasdon L (1970) Optimization theory with large systems. Mcmillan, New YorkGoogle Scholar
- Bazaraa M, Jarvis M, Sherali H (1990) Linear programming and network flows. 2nd ed. Wiley, New YorkGoogle Scholar
- Papadimitriou C, Steiglitz K (1982) Combinatorial optimization: Algorithms and complexity. Prentice-Hall, Englewood CliffsGoogle Scholar