A Cooperative Population-Based Method for Solving the Max-Min Knapsack Problem with Multi-scenarios

In this paper, we study the max-min knapsack problem with multi-scenarios, where a cooperative population based method is designed for approximately solving it. Its instance is represented by a knapsack of fixed capacity, a set of items (with weights and profits) and possible scenarios related to overall items. Its goal is to select a subset of items whose total weight fills the knapsack, and whose total profit is maximized in the worst scenario according the whole scenarios. The designed method is based upon the grey wolf optimizer, where a series of local searches are employed for highlighting the performance of the method. It starts with a reference set of positions related to the wolves, which is provided with a random greedy procedure. In order to enhance the behavior of the standard version, a series of exploring strategies is employed. Next, in order to avoid premature convergence, a drop and rebuild strategy is added hopping to exploit new unexplored subspaces. Finally, the behavior of the method is computationally analyzed on benchmark instances of the literature, where its provided results are compared to the best results available in the literature. Encouraging results have been obtained.