Matrix analysis
On an instance of the inverse shortest paths problem
Mathematical Programming: Series A and B
Solving Inverse Spanning Tree Problems Through Network Flow Techniques
Operations Research
Operations Research
Approximating Multiobjective Knapsack Problems
Management Science
Multicriteria Optimization
Inverse problems of some NP-complete problems
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Cutting plane algorithms for the inverse mixed integer linear programming problem
Operations Research Letters
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Inverse multi-objective combinatorial optimization consists of finding a minimal adjustment of the objective functions coefficients such that a given set of feasible solutions becomes efficient. An algorithm is proposed for rendering a given feasible solution into an efficient one. This is a simplified version of the inverse problem when the cardinality of the set is equal to one. The adjustment is measured by the Chebyshev distance. It is shown how to build an optimal adjustment in linear time based on this distance, and why it is right to perform a binary search for determining the optimal distance. These results led us to develop an approach based on the resolution of mixed-integer linear programs. A second approach based on a branch-and-bound is proposed to handle any distance function that can be linearized. Finally, the initial inverse problem is solved by a cutting plane algorithm.