A modified flower pollination algorithm for the multidimensional knapsack problem: human-centric decision making

In this paper, a new modified version of the flower pollination algorithm based on the crossover for solving the multidimensional knapsack problems called (MFPA) is proposed. MFPA uses the sigmoid function as a discretization method to deal with the discrete search space. The penalty function is added to the evaluation function to recognize the infeasible solutions and assess them. A two-stage procedure is called FRIO is used to treat the infeasible solutions. MFPA uses an elimination procedure to decrease any duplication in the population in order to increase the diversity. The proposed algorithm is verified on a set of benchmark instances, and a comparison with other algorithms available in literature is shown. Several statistical and descriptive analysis was done such as recoding the results of the best, mean, worst, standard deviation, success rate, and time to prove the effectiveness and robustness of MFPA. The empirical results show that the proposed algorithm can be an effective algorithm as human-centric decision-making model for solving the multidimensional knapsack problems.