Binary artificial algae algorithm for multidimensional knapsack problems

Abstract

The multidimensional knapsack problem (MKP) is a well-known NP-hard optimization problem. Various meta-heuristic methods are dedicated to solve this problem in literature. Recently a new meta-heuristic algorithm, called artificial algae algorithm (AAA), was presented, which has been successfully applied to solve various continuous optimization problems. However, due to its continuous nature, AAA cannot settle the discrete problem straightforwardly such as MKP. In view of this, this paper proposes a binary artificial algae algorithm (BAAA) to efficiently solve MKP. This algorithm is composed of discrete process, repair operators and elite local search. In discrete process, two logistic functions with different coefficients of curve are studied to achieve good discrete process results. Repair operators are performed to make the solution feasible and increase the efficiency. Finally, elite local search is introduced to improve the quality of solutions. To demonstrate the efficiency of our proposed algorithm, simulations and evaluations are carried out with total of 94 benchmark problems and compared with other bio-inspired state-of-the-art algorithms in the recent years including MBPSO, BPSOTVAC, CBPSOTVAC, GADS, bAFSA, and IbAFSA. The results show the superiority of BAAA to many compared existing algorithms.