Empirical Analysis of Various Multi-Dimensional Knapsack Heuristics

Since the multidimensional knapsack problems are NP-hard problems, the exact solutions of knapsack problems often need excessive computing time and storage space. Thus, heuristic approaches are more practical for multidimensional knapsack problems as problems get large. This thesis presents the results of an empirical study of the performance of heuristic solution procedures based on the coefficients correlation structures and constraint slackness settings. In this thesis, the three representative greedy heuristics, Toyoda, Senju and Toyoda, and Loulou and Michaelides' methods, are studied. The purpose of this research is to explore which heuristic of the three representative greedy heuristics performs best under certain combinations of conditions between constraint slackness and correlation structures. This thesis examines three heuristics over 1120 problems which are all the two-dimensional knapsack problems (2KPs) with 100 variables created by four constraint slackness settings and 45 feasible correlation structures. Then we analyze why the best heuristic behaves as it does as a function of problem characteristics. Finally we present two new heuristics using knowledge gained in the study. When these new heuristics are competitively tested against the three representative greedy heuristics, the results show the new heuristics perform better.