Probabilistic local search algorithms for concave cost transportation network problems

In practice concave cost transportation problems are characterized as NP-hard, therefore cost functions are usually simplified as linear in order to facilitate problem solving. However, linear cost functions may not reflect actual operations, which generally results in decreased operational performance. This research employs the techniques of simulated annealing and threshold accepting to develop several heuristics that would efficiently solve these concave cost transportation network problems. A network generator has also been designed to generate many instances on an HP workstation to test the heuristics. The preliminary results show that these heuristics are potentially useful.

[1]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

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

[3]  Erik Demeulemeester,et al.  A Random Activity Network Generator , 1993, Oper. Res..

[4]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[5]  A. Alfa,et al.  Experimental analysis of simulated annealing based algorithms for the layout problem , 1992 .

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  Panos M. Pardalos,et al.  A polynomial time solvable concave network flow problem , 1993, Networks.

[8]  H. Kuhn,et al.  An approximative algorithm for the fixed‐charges transportation problem , 1962 .

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

[10]  D. Blumenfeld,et al.  Analyzing trade-offs between transportation, inventory and production costs on freight networks , 1985 .

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

[12]  Attahiru Sule Alfa,et al.  A 3-OPT based simulated annealing algorithm for vehicle routing problems , 1991 .

[13]  Randolph W. Hall,et al.  Direct versus terminal freight routing on a network with concave costs , 1987 .

[14]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

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

[16]  M. Florian,et al.  DETERMINISTIC PRODUCTION PLANNING WITH CONCAVE COSTS AND CAPACITY CONSTRAINTS. , 1971 .

[17]  Mikael Rönnqvist,et al.  A Lagrangean heuristic for the capacitated concave minimum cost network flow problem , 1994 .

[18]  Phan Thien Thach.  A decomposition method using a pricing mechanism for min concave cost flow problems with a hierarchical structure , 1992, Math. Program..

[19]  Larry J. LeBlanc.  Global Solutions for a Nonconvex Nonconcave Rail Network Model , 1976 .

[20]  B. Golden,et al.  Using simulated annealing to solve routing and location problems , 1986 .

[21]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[22]  Reginald R. Souleyrette,et al.  Implementing Vehicle Routing Models , 1990 .

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