Date of Award
Doctor of Philosophy (PhD)
Department of Operational Sciences
James T. Moore, PhD
Raymond R. Hill, PhD
The multidimensional knapsack problem (MKP) has been used to model a variety of practical optimization and decision-making applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. While there have been a variety of heuristics proposed for the MKP, and a plethora of empirical studies comparing the performance of these heuristics, little has been done to garner a deeper understanding of heuristic performance as a function of problem structure. This dissertation presents a research methodology, empirical and theoretical results explicitly aimed at gaining a deeper understanding of heuristic procedural performance as a function of test problem characteristics. This work first employs an available, robust set of two-dimensional knapsack problems in an empirical study to garner performance insights. These performance insights are tested against a larger set of problems, five-dimensional knapsack problems specifically generated for empirical testing purposes. The performance insights are found to hold in the higher dimensions. These insights are used to formulate and test a suite of three new greedy heuristics for the MKP, each improving upon its successor. These heuristics are found to outperform available legacy heuristics across a complete spectrum of test problems. Problem reduction heuristics are examined and the subsequent performance insights garnered are used to derive a new problem reduction heuristic, which is then further extended to employ a local improvement phase. These problem reduction heuristics are also found to outperform currently available approaches. Available problem test sets are shown lacking along multiple dimensions of importance for viable empirical testing. A new problem generation methodology is developed and shown to overcome the current limitations in available problem test sets. This problem generation methodology is used to generate a new set of empirical test problems specifically designed for competitive computational tests. This new test set is shown to stress existing heuristics; not only does the computational time required by these legacy heuristics increase with problem size, but solution quality is found to decrease with problem size. However, the solution quality obtained by the suite of heuristics developed in this dissertation are shown to be unaffected by problem size thereby providing a level of robust solution quality not previously seen in heuristic development for the MKP. This research demonstrates that the test problems can have a profound, and sometimes misleading, impact on the general insights gained via empirical testing, provides six new quality heuristics, and two new robust sets of test problems, one focused on empirical testing, the other focused on competitive testing.
DTIC Accession Number
Cho, Yong Kun, "Developing New Multidimensional Knapsack Heuristics Based on Empirical Analysis of Legacy Heuristics" (2005). Theses and Dissertations. 2379.