A network flow method for solving some inverse combinatorial optimization problems

1 January 1996

journal article
research article
Published by Taylor & Francis in Optimization

Vol. 37 (1) , 59-72
https://doi.org/10.1080/02331939608844197

Abstract

We consider a set of inverse combinatorial optimization problems including inverse problems of minimum spanning tree problem, assignment problem and shortest path tree problem, etc. We suggest a method to solve these problems which first uses optimality conditions to formulate the inverse problems as some linear programming problems, find their dual problems, and then construct suitable network models to convert the dual problems into maximum-weight circulation problems. By using this method, the class of inverse problems can be handled uniformly with a strongly polynomial complexity.

Keywords

This publication has 3 references indexed in Scilit:

A column generation method for inverse shortest path problems
Mathematical Methods of Operations Research, 1995
An inverse problem of the weighted shortest path problem
Japan Journal of Industrial and Applied Mathematics, 1995
On an instance of the inverse shortest paths problem
Mathematical Programming, 1992