Computing Surrogate Constraints for Multidimensional Knapsack Problems Using Evolution Strategies

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 Ɛ-approximate solution of the corresponding surrogate problem. This method allows the user to adjust the quality of the obtained multipliers by means of parameter Ɛ. 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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