| M. Yagiura, T. Ibaraki and F. Glover, "An ejection chain approach for the generalized assignment problem," INFORMS Journal on Computing, 16 (2004) to appear. |
....structures even when using a best improvement pivoting rule. However, a recent trend in the design of local search algorithms is to look for large neighbourhoods that can be explored efficiently. For many problems like the traveling salesperson problem [24, 30] the generalized assignment problem [38], and many others [11, 3] local search algorithms exploiting large neighbourhoods are currently at the core of new state of the art algorithms. In this paper, we investigate a new neighbourhood search method that uses a very large scale neighbourhood, and we propose an algorithm that allows us ....
M. Yagiura, T. Ibaraki, and F. Glover. An ejection chain approach for the generalized assignment problem. Technical Report 99013, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 1999.
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M. Yagiura, T. Ibaraki and F. Glover, "An ejection chain approach for the generalized assignment problem," INFORMS Journal on Computing, 16 (2004) to appear.
.... The proposed algorithm is compared with many existing heuristic algorithms including recent path relinking approaches by Alfandari, Plateau and Tolla [1, 2] tabu search by Daz and Fernandez [5] a Lagrangian heuristic algorithm by Haddadi and Ouzia [12] tabu search by Yagiura, Ibaraki and Glover [23], variable depth search algorithms by Yagiura, Yamaguchi and Ibaraki [24, 25] another variable depth search algorithm by Racer and Amini [20] tabu search by Laguna et al. 15] MAX MIN ant system by Lourenco and Serra [17] genetic algorithm by Chu and Beasley [3] and a general integer ....
....used to reduce the computation time to search the swap neighborhood. As a result, the practical neighborhood size of our local search is much smaller than O(n ) and is quite e#cient especially for large scale instances. The resulting local search is called EC probe. For details of EC probe, see [23]. When the search visits the infeasible region, we evaluate the solutions by an objective function penalized by infeasibility: pcost(#) cost(#) i#I # i p i (#) 1) where p i (#) max 0, j#J, #(j) i a ij b i denotes the amount of infeasibility at agent i. The parameters # i ....
[Article contains additional citation context not shown here]
M. Yagiura, T. Ibaraki and F. Glover, "An ejection chain approach for the generalized assignment problem," INFORMS Journal on Computing, to appear.
....if Nr is less than 1; e.g. if Nr 0.9, the probability is not less than 1 0.28610974: 0.71389026. Next, we investigate the value of Nr that satisfies EX(Yodd) 1. Note first that N N k: 1 o(1) holds if k N 1 2 e for any constant 6 0, where o(1) converges to 0 if N becomes large [14]. In other words, for any constant c [0, 1) and 6 (0, 1 2) there exists No such that N N c holds for k N 1 2 e and N No. Hence, for Nr: 1, we have Nr 1 c c EX(Yodd) E 2k (Nr) E 2k 4 3 k N, k:odd k:odd ln(LN1 2 =J) O(1) The last equality is from El k 1 k : lnl ....
M. Yagiura, T. Ibaraki and F. Glover, An Ejection Chain Approach for the Generalized Assignment Problem, Technical Report 99013, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 1999.
....to individual constraints and tune them separately. The use of the penalty function method is not limited to combinatorial optimization. It has been used in wide rage of optimization problems for long time. Here we mention some recent applications of this method to combinatorial optimization [52, 86, 164, 165, 163]. Note that feasible solutions will not be found if the penalty weights are too small. To avoid this, the penalty weights are adaptively controlled in some applications (e.g. 52, 163] by gradually increasing the penalty weights on those constraints not satis ed for long time. Evaluation ....
....long time. Here we mention some recent applications of this method to combinatorial optimization [52, 86, 164, 165, 163] Note that feasible solutions will not be found if the penalty weights are too small. To avoid this, the penalty weights are adaptively controlled in some applications (e.g. [52, 163]) by gradually increasing the penalty weights on those constraints not satis ed for long time. Evaluation functions f need not be directly related to the objective function f . For example, Johnson et al. part II of [86] used the following function for GCP, where the number of colors k is ....
[Article contains additional citation context not shown here]
M. Yagiura, T. Ibaraki and F. Glover, \An ejection chain approach for the generalized assignment problem," Technical Report #99013, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 1999.
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