An Hybrid Approach for the 0–1 Multi Knapsack Problem

Like for many NP-hard combinatorial optimization problems, both exact and heuristic algorithms have been developed for the MKP01. Existing exact algorithms are essentially based on the branch and bound method [11]. These algorithms are different one from another according to the way the upper bounds are obtained. For instance, in [11], Shih solves, exactly, each of the m single constrained, relaxed knapsack problems and select the minimum of the m objective function values as the upper bound. Better algorithms have been proposed by using tighter upper bounds, obtained with other MKP01 relaxation techniques such as lagrangean, surrogate and composite relaxations [5]. Due to their exponential time complexity, exact algorithms are limited to small size instances (n = 200 and m = 5).