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 ...

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) ...

The Fuzzy Adaptive Neighborhood Search (FANS) method was previously presented and succesfully compared against a genetic algorithm and simulated annealing doing minimization of functions in Rn. Here we propose to evaluate FANS on instances of knapsack with multiple restrictions problems, making comparison against the cited algorithms in order to gain knowledge about the behaviour of our method.

a theorem was recently introduced to establish a relationship betweengoal programming and fuzzy programming for vectormaximum problems.in this short note it is shown that the relationship does not exist underall circumstances. the necessary correction is proposed.

Fuzzy rule based termination criteria are introduced in two conventional and exact algorithms solving Knapsack Problems. As a consequence two new solution algorithms are obtained. These algorithms are heuristic ones with a high performance. The efficiency of the algorithms obtained is illustrated by solving some numerical examples.

We present here a co-operative multithread metaheuristic. Each thread employs a (possibly) different optimization strategy and they are controlled by a Coordinator process. A relevant point is the use of a fuzzy rule base embedded in the Coordinator to control and modify the behavior of the optimization threads. Preliminary results over the knapsack problem show the benefits of the proposal.

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...

Three Tabu Search algorithms are presented for the 0-1 multi-dimensional multi-objective knapsack problem. Experiments are carried out to study the role of different diversification techniques for TS and to compare TS with well-known evolutionary algorithms.