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 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.

[1]  Hokey Min,et al.  Multiobjective design of transportation networks: taxonomy and annotation , 1986 .

[2]  Ralph E. Steuer,et al.  An interactive weighted Tchebycheff procedure for multiple objective programming , 1983, Math. Program..

[3]  Włodzimierz Ogryczak,et al.  A solver for the multi-objective transshipment problem with facility location , 1989 .

[4]  Minghe Sun,et al.  Solving Multiple Objective Programming Problems Using Feed-Forward Artificial Neural Networks: The Interactive FFANN Procedure , 1996 .

[5]  Ralph E. Steuer Multiple criteria optimization , 1986 .

[6]  P. Simin Pulat,et al.  Bicriteria network flow problems: Continuous case , 1991 .

[7]  Ralph E. Steuer,et al.  A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure , 1993 .

[8]  Minghe Sun,et al.  A Multiple Objective Embedded Network Model for Human Resource Planning and an Implementation of the Tchebycheff Method , 1996 .

[9]  Katta G. Murty,et al.  Network programming , 1992 .

[10]  S. Chen,et al.  A primal algorithm for solving a capacitated network flow problem with additional linear constraints , 1977, Networks.

[11]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[12]  Mark Goh,et al.  Finding integer efficient solutions for bicriteria and tricriteria network flow problems using DINAS , 1998, Comput. Oper. Res..

[13]  Lorraine R. Gardiner,et al.  A Bibliographic Survey of the Activities and International Nature of Multiple Criteria Decision Making , 1996 .

[14]  P. S. Pulat,et al.  Bicriteria network flow problems: Integer case , 1993 .

[15]  Fred W. Glover,et al.  Network models in optimization and their applications in practice , 1992 .

[16]  Lorraine R. Gardiner,et al.  Unified interactive multiple objective programming , 1994 .

[17]  Herminia I. Calvete,et al.  An approach for the network flow problem with multiple objectives , 1995, Comput. Oper. Res..

[18]  John R Current,et al.  Multiobjective design of transportation networks , 1981 .

[19]  Minghe Sun,et al.  Interactive multiple objective programming using Tchebycheff programs and artificial neural networks , 2000, Comput. Oper. Res..

[20]  F. Glover,et al.  The simplex SON algorithm for LP/embedded network problems , 1981 .

[21]  A. Wierzbicki A Mathematical Basis for Satisficing Decision Making , 1982 .

[22]  R. V. Helgason,et al.  Algorithms for network programming , 1980 .

[23]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[24]  Darwin Klingman,et al.  Solving Singly Constrained Transshipment Problems , 1978 .

[25]  P. Simin Pulat,et al.  Efficient solutions for the bicriteria network flow problem , 1992, Comput. Oper. Res..

[26]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[27]  John R. Current,et al.  Multiobjective transportation network design and routing problems: Taxonomy and annotation , 1993 .

[28]  F. Glover,et al.  Basis exchange characterizations for the simplex son algorithm for LP/embedded networks , 1985 .

[29]  Wlodzimierz Ogryczak,et al.  DINAS: A computer-assisted analysis system for multiobjective transshipment problems with facility location , 1992, Comput. Oper. Res..