A New Moth-Flame Optimization Algorithm for Discounted {0-1} Knapsack Problem

The discounted {0-1} knapsack problem may be a kind of backpack issue with gathering structure and rebate connections among things. A moth-flame optimization algorithm has shown good searchability combined with an effective solution presentation designed for the discounted {0-1} knapsack problem. A new encoding scheme used a shorter length binary vector to help reduce the search domain and speed up the computing time. A greedy repair procedure is used to help the algorithm have fast convergence and reduce the gap between the best-found solution and the optimal solution. The experience results of 30 discounted {0-1} knapsack problem instances are used to evaluate the proposed algorithm. The results demonstrate that the proposed algorithm outperforms the two binary PSO algorithms and the genetic algorithm in solving 30 DKP01 instances. The Wilcoxon rank-sum test is used to support the proposed declarations.