Abstract
It is an important task to obtain optimal solutions for multidimensional linear integer problems with multiple constraints. The surrogate constraint method translates a multidimensional problem into an one dimensional problem using a suitable set of surrogate multipliers. In general, there exists a gap between the optimal solution of the surrogate problem and the original multidimensional problem. Moreover, computing suitable surrogate constraints is a computationally difficult task. In this paper we propose a method for computing surrogate constraints of linear problems that evolves sets of surrogate multipliers coded in floating point and uses as fitness function the value of the ε-approximate solution of the corresponding surrogate problem. This method allows the user to adjust the quality of the obtained multipliers by means of parameter ε. Solving 0 − 1 multidimensional knapsack problems we test the effectiveness of our methodology. Experimental results show that our method for computing surrogate constraints for linear 0 − 1 integer problems is at least as effective as other strategies based on Linear Programming as that proposed by Chu and Beasley in [6].
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Montaña, J.L., Alonso, C.L., Cagnoni, S., Callau, M. (2008). Computing Surrogate Constraints for Multidimensional Knapsack Problems Using Evolution Strategies. In: Giacobini, M., et al. Applications of Evolutionary Computing. EvoWorkshops 2008. Lecture Notes in Computer Science, vol 4974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78761-7_61
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DOI: https://doi.org/10.1007/978-3-540-78761-7_61
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