New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.