An algorithm for generating minimum cost network flow problems with specific structure and known optimal solutions

A new algorithm for generating structured, minimum cost network flow problems (transshipment, transportation, assignment, and shortest path) with known optimal solutions is described. The procedure is based on developing problems around an optimal basis so that the characteristics of solutions can be controlled. Computational tests show that the problems generated are as difficult to solve as are those produced by the commonly used generator NETGEN, while allowing the user a much greater degree of control over the resulting problems. © 1994 by John Wiley & Sons, Inc.

[1]  Dexter Kozen,et al.  The Design and Analysis of Algorithms , 1991, Texts and Monographs in Computer Science.

[2]  Brian W. Kernighan,et al.  The C Programming Language , 1978 .

[3]  Harvey J. Greenberg.  Computational Testing: Why, How and How Much , 1990, INFORMS J. Comput..

[4]  Jeffrey L. Arthur,et al.  GENGUB: A generator for linear programs with generalized upper bound constraints , 1993, Comput. Oper. Res..

[5]  Leon S. Lasdon,et al.  OR Practice - The Status of Nonlinear Programming Software: An Update , 1987, Oper. Res..

[6]  Stephen G. Nash,et al.  Guidelines for reporting results of computational experiments. Report of the ad hoc committee , 1991, Math. Program..

[7]  Ronald L. Rardin,et al.  Test Problems for Computational Experiments -- Issues and Techniques , 1982 .

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

[9]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

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

[11]  John M. Mulvey,et al.  On Reporting Computational Experiments with Mathematical Software , 1979, TOMS.

[12]  Joyce J. Elam,et al.  Netgen-II: A System for Generating Structured Network-Based Mathematical Programming Test Problems , 1982 .

[13]  Darwin Klingman,et al.  Enhancements of Spanning Tree Labeling Procedures for Network Optimization. , 1979 .

[14]  Robert E. Bixby,et al.  A Test Set of Real-World Mixed Integer Programming Problems , 1992 .