Solving the large-scale knapsack feasibility problem using a distributed computation approach to integer programming

The knapsack feasibility problems have been intensively studied both because of their immediate applications in industry and financial management, but more pronounced for theoretical reasons, as knapsack problems frequently occur by relaxation of various integer programming problems. In this work, the large-scale knapsack feasibility problem is divided into two subproblems. The first subproblem is transforming of the knapsack feasibility problem into a polytope judgement problem which is based on lattice basis reduction. In the next subproblem, a distributed implementation of Dang and Ye’s fixed-point iterative algorithm is introduced to solve the polytope judgement problem generated in the former subproblem. Compared with the branch and bound method, numerical results show that this distributed fixed-point method is effective.

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