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In this paper, we present a heuristic which derives a feasible solution for the Multiple Knapsack Problem (MKP). The proposed heuristic called RCH, is a recursive method that performs computation on the core of knapsacks. The RCH heuristic is compared with the MTHM heuristic of Martello and Toth. Computational results on randomly generated instances show that the proposed approach gives better gap and smaller restitution times.

This article presents an exact cooperative method for the solution of the multidimensional knapsack problem (MKP) which combines dynamic programming and branch and bound. Our method makes cooperate a dynamic programming heuristics based on surrogate relaxation and a branch and bound procedure. Our algorithm was tested for several randomly generated test sets and problems in the literature. Solution values of the first step are compared with optimal values and results provided by other well-known existing heuristics. Then, our exact cooperative method is compared with a classical branch and bound algorithm. [Received 8 October 2008; Revised 28 May 28 2009; Revised 10 December 2009; Accepted 11 December 2009]

Quantum Optics: It is now possible to conduct optical experiments on systems that exhibit strongly correlated behavior.