Effect of learning strategies in an evolutionary method: the case of the bi-objective quadratic multiple knapsack problem

In this paper, we solve the bi-objective quadratic multiple knapsack problem, an NP-Hard combinatorial optimization problem, with a cooperative evolutionary method. The proposed method starts by generating a first approximate Pareto front by using the \(\varepsilon \)-constraint operator-based approach, that is, the first stage of the evolutionary method. The second stage is based upon an iterative procedure, where the non-dominated sorting genetic algorithm is employed for generating a series of populations. In order to avoid a premature convergence, at each step of the iterative procedure, learning strategies are added: (i) the fusion operator and (ii) the \(\varepsilon \)-constraint operator. These learning strategies are introduced for maintaining the diversity of the series of populations and so trying to avoid premature convergence and stagnations on local optima. The performance of the proposed evolutionary method with learning strategies is evaluated on a set of benchmark instances of the literature containing both medium- and large-scale instances. Its provided results are compared to those achieved by the best methods available in the literature. New results have been obtained.