A new grouping genetic algorithm for the Multiple Knapsack Problem

The multiple knapsack problem (MKP) is the problem of assigning (packing) objects of various weights and values (profits) to a set of containers (bins) of various capacities, in order to maximize the total profit of the items assigned to the containers. We propose a new genetic algorithm for the MKP which searches a space of undominated candidate solutions. We compare the new algorithm to previous heuristics for the MKP, as well as alternative evolutionary algorithms, and show experimentally that our new algorithm yields the best performance on difficult instances where item weights and profits are highly correlated.