A discrete artificial bee colony for multiple Knapsack problem

Multiple Knapsack Problem (MKP) is a most popular multiple subset selection problem that belongs to the class of NP-Complete problems. The aim is to assign optimal subsets among all original items to some knapsacks, such that the overall profit of all selected items be maximised, while the total weight of all assigned items to any knapsack does not exceed the allowable capacity of it. Artificial Bee Colony (ABC) algorithm is a new meta-heuristic with a stochastic search strategy. In ABC, the neighbourhood area of any best-found solution is searched by the employed bees to achieve better solutions. This paper presents a discrete ABC algorithm for the MKP. In this approach, a hybrid probabilistic mutation scheme is performed for searching the neighbourhood of food sources. The proposed algorithm can guide the search space quickly and improve the local search ability. Experimental results demonstrate that the presented approach has improved the quality and convergence speed than other evolutionary algorithms.