Procedures for finding nondominated solutions for multiple objective network programming problems

Procedures for finding nondominated solutions for multiple objective network programming problems are developed and tested. Nondominated solutions are obtained by solving augmented weighted Tchebycheff network programs. The procedures exploit the network structure of the problem in order to speed up the solution process. To use the network structure as much as possible, a weighted-sum network problem and/or a min–max network problem are solved in order to find a basic solution that is close to the optimal solution of the augmented weighted Tchebycheff network program. Starting from this basic solution, the special simplex method for network problems with side constraints is finally applied to solve the augmented weighted Tchebycheff network program. Computational results show that, for the test problems used in this study, up to 70% of computation time can be saved with the proposed procedures as compared with the sole application of the special simplex method for the network problems with side constraints. These procedures can be incorporated into any interactive multiple-objective programming procedure which uses sample nondominated solutions to solve multiple-objective network programming problems.