Abstract
The Multidimensional Knapsack Problem (MKP) has been used to model a variety of practical applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. There have been a variety of heuristics proposed for MKP and a plethora of empirical studies comparing the performance of these heuristics. However, little has been done to garner a deeper understanding of why certain heuristics perform well on certain types of problems and others do not. Using a broad range of practical MKP test problems, we use three representative heuristics and conduct an empirical study aimed at gaining a deeper understanding of heuristic procedure performance as a function of test problem constraint characteristics. Our focus is on the Two-dimensional Knapsack Problem (2KP). New insights developed regarding greedy heuristic performance are exploited to yield two new heuristics whose performance is more robust than that of three legacy heuristics on our test problem set and on benchmark sets of MKP problems. A competitive test of these new heuristics against a set of legacy heuristics, using both existing test problem sets and a new systematically developed test problem set demonstrate the superior, robust performance of our new heuristics.
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