An Improved Iterated Local Search Algorithm for Invest Strongly Correlated 0/1 Knapsack Problem

This paper proposed an improved iterated local search algorithm named iZHKnap for the Invest strongly correlated 0/1 knapsack problem based on its special properties and the combinatorial correlation between the optimum value and the items in the object set upon the classical non-increasing profit-to-weight ratio greedy policy. In order to evaluate the performance of our deterministic algorithm, we compare its average performance with Combo´s in the same test set for Combo algorithm is still the deterministic state-of-the-art algorithm in solving 0/1 knapsack problem though it is about 10 year ago. The experimental results show that iZHKnap outperforms Combo algorithm in polynomial time in terms of the average solution quality and the coverage of the problem instances and prove that the solutions from iZHKnap have no relation with both the coefficients of the items and the gap between the integer optimum and the linear optimum. Instead, such solutions relate only to the combination of the items´ weight and the fraction derived with the greedy policy applied. This results in iZHKnap´s strong competitive performance as well as in solving the Sub-set sum problem.