A New Strategy for Solving Multiple-Choice Multiple-Dimension Knapsack Problem in PRAM Model

This paper presents a new heuristic algorithm for the MultipleChoice Multi-Dimension Knapsack Problem (MMKP) in PRAM model. MMKP is a variant of the classical 0-1 knapsack problem, has a knapsack with multidimensional capacity constraints, groups of items, each item having a utility value and multidimensional resource constraints. The problem is to maximize the total value of the items in the knapsack with the constraint of not exceeding the knapsack capacity. Since MMKP is an NP-Hard problem, its exact solution is not suitable for real time problems, so heuristic based approximation algorithms are developed. We present a parallel heuristic algorithm here that runs in )) log log log (log (log l m n nl O + + time in CRCW PRAM machine; taking )) (log log ( ml n n n O + operations. Experimental results show that it achieves 95% optimal solution on average. This also means that we have a sequential heuristic running in )) (log log ( ml n n n O + time which seems to be remarkable since M-HEU, a celebrated sequential heuristic although achieves 96% of optimal value, takes ) 2 2 ( l mn O running time.