Solving multiple knapsack problems by cutting planes
In this talk we consider the multiple Knapsack Problem which is defined as follows: Given a set N of items with weights f{sub i}, i {element_of} N, a set M of knapsacks with capacities F{sub k}, k {element_of} M, and a profit function c{sub ik}, i {element_of} N, k {element_of} N, k {element_of} M; find an assignment of a subset of the set of items to the set of knapsacks that yields maximum profit (or minimum cost). This problem arises as a subproblem in several practical applications like layout of electronic circuits and design of processors for mainframe computers. With every instance of this problem we associated a polyhedron whose vertices are in one to one correspondence to the feasible solutions of the instance. For this polytope we present several new classes of inequalities and work out necessary and sufficient conditions under which the corresponding inequalities define facets. We use this inequality description to develop a branch and cut algorithm. We will sketch some of the implementation details of this algorithm including separation and primal heuristics and report on our computational experiences with several practical problems instances.
- OSTI ID:
- 36266
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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