A fast particle swarm optimization algorithm for the multidimensional knapsack problem

A fast particle swarm optimization method for the multidimensional knapsack problem is presented. In this approach the potential solutions are represented by vectors of real values; the dimension of each vector corresponds to the number of constraints of the problem rather than the number of items. Each of these values measures the significance of the corresponding constraint and, together with the value of each item, is used to define a ratio of “goodness” for each item. The particle swarm optimization algorithm is used to find the best profit by sorting all items according to the ratio of their goodness and by picking these items in the sorted order. Also, a special initialization phase and an improvement phase are incorporated into the algorithm. The proposed approach was tested on several standard test benchmarks and its results are compared with some other heuristic methods in terms of solution quality and the CPU time. These comparisons show that the proposed method is able to find quality solutions faster than most of other methods. Also, our experiments show that the algorithm is more efficient for the problems in which the number of constraints is smaller than the number of items.