Abstract
Tabu Search is a very effective method for approximately solving hard combinatorial problems. In the current work we implement Tabu Search for solving the Planar Three-Index Assignment Problem. The problem deals with finding the minimum cost assignment between elements of three distinct sets demanding that every pair of elements, each representing a different set, appears in the same solution exactly once. The solutions of the problems correspond to Latin squares. These structures form the basis of the move generation mechanism employed by the Tabu Search procedures. Standard Tabu Search ideas such as candidate move list, variable tabu list size, and frequency-based memory are tested. Computational results for a range of problems of varying dimensions are presented.
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References
Areibi S. and Vannelli A. (1994), Advanced Search Techniques for Circuit Partitioning, in Pardalos P. and Wolkowicz H. (eds.), Quadratic Assignment and Related Problems, DIMACS Series 16, American Mathematical Society, 77–98.
BalasE. and SaltzmanM.J. (1991), An algorithm for the three-index assignment problem, Operations Research 39(1), 150–161.
BurkardR.E. and FrolichK. (1980), Some remarks on 3-dimensional assignment problems, Methods Operations Research 36, 31–36.
ChakrapaniJ. and Skorin-KapovJ. (1993), Connection Machine Implementation of a Tabu Search Algorithm for the Travelling Salesman Problem, Journal of Computing and Information Technology 1(1), 29–36.
EulerR., BurkardR.E., and GrommesR. (1986), On Latin Squares and the facial structure of related polytopes, Discrete Mathematics 62, 155–181.
FriezeA.M. (1983), Complexity of a 3-dimensional assignment problem, European Journal of Oper. Res. 13, 161–164.
Gilbert K.C. and Hofstra R.B. (March 1987), An algorithm for a class of three-dimensional assignment problems arising in scheduling applications, IIE Transactions, 29–33.
GloverF. (1989), Tabu Search — Part I, ORSA Journal on Computing 1, 190–206.
GloverF. (1990), Tabu Search — Part II, ORSA Journal on Computing 2, 4–32.
Glover F. and Laguna M. (1993) Tabu Search, in Colin Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems, Blackwell Scientific Publishing, 70–141.
HaleyB. (1962), The solid transportation problem, Operations Research 10, 448–463.
HertzA. and DeWerraD. (1990), The Tabu Search Metaheuristic: How We Used It, Ann. Math. and Artificial Intelligence 1, 111–121.
LagunaM. and GloverF. (1993a), Bandwidth Packing: A Tabu Search Approach, Management Science 39(4), 492–500.
LagunaM. and GloverF. (1993b), Integrating Target Analysis and Tabu Search for Improved Scheduling Systems, Expert Systems with Applications 6, 287–297.
MagosD. and MiliotisP. (1994), An Algorithm for the Planar Three-index Assignment Problem, European Journal of Oper. Res 77, 141–153.
OsmanI.H. (1993), Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problem, Annals of Operations Research 41, 421–451.
RyserJ.H. (1963), Combinatorial Mathematics — The Carus Mathematical Monographs 14, Wiley, New York.
TailardE. (1990), Robust Tabu Search for the Quadratic Assignment Problem, Parallel Computing 17, 443–445.
VlachM. (1967), Branch and bound method for the three-index assignment problem, Ekonomicko-Matematicky Obzor 3, 181–191.
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Magos, D. Tabu Search for the planar three-index assignment problem. J Glob Optim 8, 35–48 (1996). https://doi.org/10.1007/BF00229300
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DOI: https://doi.org/10.1007/BF00229300