Finding non-dominated solutions in bi-objective integer network flow problems

This paper deals with an algorithm for finding all the non-dominated solutions and corresponding efficient solutions for bi-objective integer network flow problems. The algorithm solves a sequence of ?$?$-constraint problems and computes all the non-dominated solutions by decreasing order of one of the objective functions. The optimal integer solutions for the ?$?$-constraint problems are determined by exploring a branch-and-bound tree. The algorithm makes use of the network structure to perform the computations, i.e., the network structure of the problem is not destroyed with the inclusion of an ?$?$-constraint. This paper presents the main features of the algorithm, the theoretical bases of the proposed approach and some computational issues. Experiments were done and the results are also reported in the paper.