We consider the minimization version of the multi-dimensional knapsack problem with bounded integer variables. We propose a greedy approximation algorithm that runs in O(mn) time and has a guarantee of m + 1, where n is the number of items and m is the number of knapsack constraints. The guarantee of the algorithm can be improved in case of easy coefficients in the constraints associated with s...

This chapter reviews our recent work on applying hybrid collaborative techniques that integrate Branch and Bound (B&B) and Memetic Algorithms (MAs) in order design effective heuristics for the Multidimensional Knapsack Problem (MKP). To this end, let us recall that Branch and Bound (B&B) [1] is an exact algorithm for finding optimal solutions to combinatorial problems, that, basically works by ...

This paper deals with the bi-objective multi-dimensional knapsack problem. We propose the adaptation of the core concept that is effectively used in single objective multidimensional knapsack problems. The main idea of the core concept is based on the “divide and conquer” principle. Namely, instead of solving one problem with n variables we solve several sub-problems with a fraction of n variab...