A hybrid reactive search for solving the max-min knapsack problem with multi-scenarios

Abstract

Several practical applications depend on different criteria or scenarios and belong to the combinatorial optimization family. For example, in engineering design of a car, two criteria may be needed to optimize its production: the profit that can bring a car as well as its reliability for the customer. In water distribution networks, designing contaminant warning system of water is necessary. In this case, the problem consists in determining the level of protection under the worst possible scenario on the sensors that should be placed. In this paper, a max-min problem under several scenarios is tackled, called max-min knapsack problem with multi-scenarios. We propose to solve it by using a hybrid reactive search algorithm that uses two main features: (i) the restoring/exploring phase and the perturbation phase. The first phase yields a feasible solution and tries to improving it by using an intensification search. The second phase can be viewed as a diversification search in which a series of subspaces are investigated in order to make a quick convergence to a global optimum. Finally, the proposed method is evaluated on a set of benchmark instances taken from the literature, whereby its obtained results are compared to those reached by recent methods available in the literature. The results show that the method is competitive and it is able to provide better solutions than those already published.