Heuristic algorithm of the multiple-choice multidimensional knapsack problem (MMKP) for cluster computing

This paper presents two heuristic algorithms of the MMKP (a variant of 0–1 knapsack problem) for cluster computing. We present an architecture of a cluster, such that algorithm requires small message passing. The algorithms divide the problem among computational nodes. Each node solves its sub problem using a sequential heuristic. This naïve divide and conquer approach cannot achieve good revenue. The revenue is the value achieved by the solution of MMKP. To improve the revenue, it accumulates the unused resources from every node, and assigns to the node, which gives maximum revenue over all nodes. This is the residue exploitation (RE) strategy. The solution quality can be improved by a novel resource-division policy rather than equal division. The policy divides the resource among all nodes such that total revenue increases. A sequential heuristic calculates the solution incrementally for different amounts of resource capacity, and the best combination is taken as the solution. This is the resource adjustment (RA) strategy. We experiment the algorithm using MPI (Message Passing Interface). The proposed algorithms show encouraging results.