doi:10.1016/j.ejor.2004.09.042 
Copyright © 2004 Elsevier B.V. All rights reserved.
Discrete Optimization
A hybrid genetic algorithm for the Three-Index Assignment Problem
Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Received 18 December 2003;
accepted 29 September 2004.
Available online 15 December 2004.
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Abstract
The Three-Index Assignment Problem (AP3) is well-known problem which has been shown to be 
-hard. This problem has been studied extensively, and many exact and heuristic methods have been proposed to solve it. Inspired by the classical assignment problem, we propose a new local search heuristic which solves the problem by simplifying it to the classical assignment problem. We further hybridize our heuristic with the genetic algorithm (GA). Extensive experimental results indicate that our hybrid method is superior to all previous heuristic methods including those proposed by Balas and Saltzman [Operations Research 39 (1991) 150–161], Crama and Spieksma [European Journal of Operational Research 60 (1992) 273–279], Burkard et al. [Discrete Applied Mathematics 65 (1996) 123–169], and Aiex et al. [GRASP with path relinking for the three-index assignment problem, Technical report, INFORMS Journal on Computing, in press. Available from: <http://www.research.att.com/~mgcr/doc/g3index.pdf>].
Keywords: Combinatorial optimization; Heuristic; Genetic algorithms; Assignment
Fig. 1. A random initial assignment for bs_4_5.dat.
Fig. 2. Optimize permutation q.
Fig. 3. Optimize permutation p.
Fig. 4. Optimize the index permutation.
Fig. 5. Iterative local search.
Fig. 6. Structure of genetic algorithm.
Fig. 7. Examples for PMX.
Fig. 8. Structure of LSGA.
Fig. 9. Comparison between GA, multiLS and LSGA.
Table 1.
Balas and Saltzman Dataset (12 * 5 instances)
Table 2.
Crama and Spieksma Dataset, Type I (six instances)
Table 3.
Crama and Spieksma Dataset, Type II (six instances)
Table 4.
Crama and Spieksma Dataset, Type III (six instances)
Table 5.
Burkard, Rudolf and Woeginger Dataset (700 instances)
Table 6.
CPU Benchmark from SPEC (http://www.specbench.org/osg/cpu2000/)
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