Local Branching Strategy-Based Method for the Knapsack Problem with Setup

Samah Boukhari, Isma Dahmani, Mhand Hifi
2020 Computer Science & Information Technology (CS & IT)   unpublished
In this paper, we propose to solve the knapsack problem with setups by combining mixed linear relaxation and local branching. The problem with setups can be seen as a generalization of 0–1 knapsack problem, where items belong to disjoint classes (or families) and can be selected only if the corresponding class is activated. The selection of a class involves setup costs and resource consumptions thus affecting both the objective function and the capacity constraint. The mixed linear relaxation
more » ... linear relaxation can be viewed as driving problem, where it is solved by using a special blackbox solver while the local branching tries to enhance the solutions provided by adding a series of invalid / valid constraints. The performance of the proposed method is evaluated on benchmark instances of the literature and new large-scale instances. Its provided results are compared to those reached by the Cplex solver and the best methods available in the literature. New results have been reached.
doi:10.5121/csit.2020.101606 fatcat:ou3wsglxxngtrlzzeofyx4qydq