Enhanced Adjacent Extreme-point Search and Tabu Search for the Minimum Concave-cost Uncapacitated Transshipment Problem

Practicable methods for optimising concave-cost, uncapacitated transshipment networks are non exact. In this paper, one such effective method, that of adjacent extreme point search, is further developed to enhance its overall computational efficiency. The enhanced search algorithm is then imbedded in a tabu search scheme which proved capable of finding better solutions, by a wide margin in some instances. Another tabu search scheme, somewhat inferior in terms of solution quality but computationally more efficient, is also developed to provide an alternative solution vehicle for larger networks. Results of extensive computational testing are included.

[1]  D. de Werra,et al.  A property of minimum concave cost flows in capacitated networks , 1971 .

[2]  Giorgio Gallo,et al.  Concave cost minimization on networks , 1979 .

[3]  Giorgio Gallo,et al.  An algorithm for the min concave cost flow problem , 1980 .

[4]  Hiroshi Konno.  Minimum concave cost production system: A further generalization of multi-echelon model , 1988, Math. Program..

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

[6]  Minghe Sun,et al.  Tabu search applied to the general fixed charge problem , 1993, Ann. Oper. Res..

[7]  Yves Smeers,et al.  Using shortest paths in some transshipment problems with concave costs , 1977, Math. Program..

[8]  Ilker Baybars,et al.  A heuristic method for facility planning in telecommunications networks with multiple alternate routes , 1988 .

[9]  Clyde L. Monma,et al.  Send-and-Split Method for Minimum-Concave-Cost Network Flows , 1987, Math. Oper. Res..

[10]  Fred W. Glover,et al.  Least-cost network topology design for a new service , 1991, Ann. Oper. Res..

[11]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[12]  M. Minoux,et al.  Multiflots de coût minimal avec fonctions de coût concaves , 1976 .

[13]  W. Zangwill.  A Deterministic Multi-Period Production Scheduling Model with Backlogging , 1966 .

[14]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[15]  Michel Minoux,et al.  Networks synthesis and optimum network design problems: Models, solution methods and applications , 1989, Networks.

[16]  W. Zangwill.  Minimum Concave Cost Flows in Certain Networks , 1968 .

[17]  Éric D. Taillard,et al.  Robust taboo search for the quadratic assignment problem , 1991, Parallel Comput..

[18]  Bernard Yaged,et al.  Minimum cost routing for static network models , 1971, Networks.

[19]  J. B. Rosen,et al.  Methods for global concave minimization: A bibliographic survey , 1986 .

[20]  Michael Florian,et al.  Nonlinear cost network models in transportation analysis , 1986 .

[21]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[22]  Panos M. Pardalos,et al.  Minimum concave-cost network flow problems: Applications, complexity, and algorithms , 1991 .

[23]  Richard M. Soland,et al.  Optimal Facility Location with Concave Costs , 1974, Oper. Res..

[24]  G. Gallo,et al.  Adjacent extreme flows and application to min concave cost flow problems , 1979, Networks.

[25]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[26]  P. Pardalos.  Enumerative techniques for solving some nonconvex global optimization problems , 1988 .

[27]  Norman Zadeh,et al.  On building minimum cost communication networks , 1973, Networks.

[28]  Ronald L. Rardin,et al.  Optimal Design of Regional Wastewater Systems: A Fixed-Charge Network Flow Model , 1978, Oper. Res..