Improving the Optimality Verification and the Parallel Processing of the General Knapsack Linear Integer Problem

Abstract

The chapter presents a new approach to improve the verification process of optimality for the general knapsack linear integer problem. The general knapsack linear integer problem is very difficult to solve. A solution for the general knapsack linear integer problem can be accurately estimated, but it can still be very difficult to verify optimality using the brach and bound related methods. In this chapter, a new objective function is generated that is also used as a more binding equality constraint. This generated equality constraint can be shown to significantly reduce the search region for the branch and bound-related algorithms. The verification process for optimality proposed in this chapter is easier than most of the available branch and bound-related approaches. In addition, the proposed approach is massively parallelizable allowing the use of the much needed independent parallel processing.