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.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.