An adaptive tabu-simulated annealing for concave cost transportation problems

The transportation problem (TP) is one of the most popular network problems because of its theoretical and practical importance. If the transportation cost linearly depends on the transported amount of the product, then TP is solvable in polynomial time with linear programming methods. However, in the real world, the transportation costs are generally nonlinear, frequently concave where the unit cost for transporting products decreases as the amount of products increases. Since concave cost transportation problems (ccTPs) are NP-hard, solving large-scale problems is time consuming. In this study, we propose a hybrid algorithm based on the concepts borrowed from tabu search (TS) and simulated annealing (SA) to solve the ccTP. This algorithm, called ATSA (adaptive tabu-simulated annealing), is an SA approach supplemented with a tabu list and adaptive cooling strategy. The effectiveness of ATSA has been investigated in two stages using a set of TPs with different sizes. The first stage includes performance analysis of ATSA using SA, ASA (adaptive simulated anealing) and TS, which are basic forms of ATSA. In the second stage, ATSA has been compared with the heuristic approaches given in the literature for ccTP. Statistical analysis shows that ATSA exhibits better performance than its basic forms and heuristic approaches.

[1]  Alice E. Smith,et al.  Local search genetic algorithm for optimal design of reliable networks , 1997, IEEE Trans. Evol. Comput..

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

[3]  Ibrahim H. Osman,et al.  Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem , 1993, Ann. Oper. Res..

[4]  Alice E. Smith,et al.  Optimal Design of Reliable Computer Networks: A Comparison of Metaheuristics , 2003, J. Heuristics.

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

[6]  M. Gen,et al.  Solving Multi-objective Transportation Problems by Spanning Tree-based Genetic Algorithm , 1998 .

[7]  Z. Michalewicz,et al.  A genetic algorithm for the linear transportation problem , 1991, IEEE Trans. Syst. Man Cybern..

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

[9]  Huang,et al.  AN EFFICIENT GENERAL COOLING SCHEDULE FOR SIMULATED ANNEALING , 1986 .

[10]  De-fu Zhang,et al.  An effective hybrid algorithm for the problem of packing circles into a larger containing circle , 2005, Comput. Oper. Res..

[11]  I. C. Parmee.  Adaptive Computing in Design and Manufacture , 1998 .

[12]  G. D. Smith,et al.  Solving the Graphical Steiner Tree Problem Using Genetic Algorithms , 1993 .

[13]  Yves Crama,et al.  Local Search in Combinatorial Optimization , 2018, Artificial Neural Networks.

[14]  Bruce W. Lamar,et al.  An improved branch and bound algorithm for minimum concave cost network flow problems , 1989, J. Glob. Optim..

[15]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[16]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[17]  Reiner Horst,et al.  An integer concave minimization approach for the minimum concave cost capacitated flow problem on networks , 1994, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[18]  Jae-Chul Kim,et al.  Application of simulated annealing and tabu search for loss minimization in distribution systems , 2004 .

[19]  Shangyao Yan,et al.  Probabilistic local search algorithms for concave cost transportation network problems , 1999, Eur. J. Oper. Res..

[20]  K. Ida,et al.  Solving Multi-Objective Transportation Problem by Spanning Tree-Based Genetic Algorithm , 1999 .

[21]  Mitsuo Gen,et al.  Genetic Algorithms & Engineering Optimization , 2000 .

[22]  F. L. Hitchcock.  The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

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

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

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

[26]  Gengui Zhou,et al.  A genetic algorithm approach on tree-like telecommunication network design problem , 2003, J. Oper. Res. Soc..

[27]  Kathryn A. Dowsland,et al.  General Cooling Schedules for a Simulated Annealing Based Timetabling System , 1995, PATAT.

[28]  Saeed Zolfaghari,et al.  Adaptive temperature control for simulated annealing: a comparative study , 2004, Comput. Oper. Res..

[29]  Manoj Kumar Tiwari,et al.  Modeling machine loading problem of FMSs and its solution methodology using a hybrid tabu search and , 2004 .

[30]  Rainer E. Burkard,et al.  Linear Approximations in a Dynamic Programming Approach for the Uncapacitated Single-Source Minimum Concave Cost Network Flow Problem in Acyclic Networks , 2001, J. Glob. Optim..

[31]  Mitsuo Gen,et al.  Solving a nonlinear side constrained transportation problem by using spanning tree-based genetic algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[32]  Minghe Sun,et al.  A Tabu Search Heuristic Procedure for Solving the Transportation Problem with Exclusionary Side Constraints , 1998, J. Heuristics.

[33]  Zbigniew Michalewicz,et al.  A Nonstandard Genetic Algorithm for the Nonlinear Transportation Problem , 1991, INFORMS J. Comput..

[34]  Mitsuo Gen,et al.  Spanning tree-based genetic algorithm for the bicriteria fixed charge transportation problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[35]  Buyang Cao,et al.  Solving transportation problems with nonlinear side constraints with tabu search , 1995, Comput. Oper. Res..

[36]  E. Beale,et al.  Applications of Mathematical Programming Techniques. , 1971 .

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

[38]  Minghe Sun,et al.  A tabu search heuristic procedure for the fixed charge transportation problem , 1998, Eur. J. Oper. Res..

[39]  Loo Hay Lee,et al.  Heuristic methods for vehicle routing problem with time windows , 2001, Artif. Intell. Eng..

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

[41]  W. Walker.  A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem , 1976 .

[42]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

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

[44]  Fred Glover,et al.  Tabu Search: A Tutorial , 1990 .

[45]  A. F. Adams,et al.  The Survey , 2021, Dyslexia in Higher Education.

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

[47]  S. Vajda.  Applications of Mathematical Programming Techniques , 1971 .

[48]  S. Zolfaghari,et al.  Jointly solving the group scheduling and machining speed selection problems: A hybrid tabu search and simulated annealing approach , 1999 .

[49]  Christos Koulamas,et al.  A survey of simulated annealing applications to operations research problems , 1994 .

[50]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[51]  Mitsuo Gen,et al.  Spanning tree-based genetic algorithm for the bicriteria fixed charge transportation problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[52]  Godfrey A. Walters,et al.  EVOLUTIONARY DESIGN ALGORITHM FOR OPTIMAL LAYOUT OF TREE NETWORKS , 1995 .

[53]  Mitsuo Gen,et al.  Solving exclusionary side constrained transportation problem by using a hybrid spanning tree-based genetic algorithm , 2003, J. Intell. Manuf..

[54]  Richard W. Eglese,et al.  Simulated annealing: A tool for operational research , 1990 .