Abstract
In this paper we discuss a variant of the 0-1 knapsack problem, where there are multiple knapsacks to fill with items that have profits and sizes associated with them. The objective is to maximise the profit by selecting items to fill the knapsacks within their space constraints. In the version of the problem considered in this paper, some of the items are incompatible with each other, and cannot be placed together in the same knapsack. We apply some newly developed heuristics to the problem and compare the results with those found by a commercial optimisation package. Computational results are presented. The contributions of this paper are an upper bound, and the heuristics developed and tested in this paper.
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