Solving randomized time-varying knapsack problems by a novel global firefly algorithm

In this paper, a novel global firefly algorithm (GFA) is proposed for solving randomized time-varying knapsack problems (RTVKP). The RTVKP is an extension from the generalized time-varying knapsack problems (TVKP), by dynamically changing the profit and weight of items as well as the capacity of knapsack. In GFA, two-tuples which consists of real vector and binary vector is used to represent the individual in a population, and two principal search processes are developed: the current global best-based search process and the trust region-based search process. Moreover, a novel and effective two-stage repair operator is adopted to modify infeasible solutions and optimize feasible solutions as well. The performance of GFA is verified by comparison with five state-of-the-art classical algorithms over three RTVKP instances. The results indicate that the proposed GFA outperform the other five methods in most cases and that GFA is an efficient algorithm for solving randomized time-varying knapsack problems.