In this paper we propose a population-based method for tackling the k-clustering minimum bi-clique completion problem. We investigate the use of the discrete particle swarm optimisation combined with a special neighborhood decent procedure. Often configuration generated by the so-called swarm process induces infeasible solutions. In order to overcome to these situations, we introduce a tolerance strategy, where its aim is to highlight the quality of the current solution where an enlarging search space is considered. The behavior of the designed method is evaluated on some benchmark instances and its provided bounds are compared to those achieved by more recent methods available in the literature. New bounds are discovered.

In this paper, the sphere packing problem is approximately solved with a population-based method. The sphere packing problem, known as the three-dimensional knapsack, occurs in several real-world applications and because of its NP-hardness it is however computationally challenging. The designed method combines a population approach and a tolerance strategy: the population tries to maintain the diversity of a series of subsets of configurations reached throughout an iterative procedure while the tolerance strategy tries to highlight the quality of the solutions throughout the search process. The performance of the designed approach is evaluated on reference instances of the literature, where its achieved bounds are compared to those obtained by more recent algorithms.

The knapsack problem arises in real world applications, like transportation, manufacturing systems, finance, and supply chain management. In this paper, we investigate the use of a cooperative particle swarm optimization for solving the quadratic multiple knapsack problem. The standard swarm optimization is reenforced by using a local search procedure, where the swapping operator is introduced that combines items belonging to different bins (knapsacks) according to their critical items. The performance of the method is evaluated on benchmark instances of the literature, where its results are compared to the best available bounds available in the literature.

In this paper, the identical sphere packing is tackled by applying a particle swarm optimization-based method. An instance of the problem is characterized by a set of equal spheres and a large sphere with unlimited radius. The aim of the problem is to determine a minimum radius of the spherical container that contains all spheres without overlapping. The particle swarm optimization cooperates with an efficient continuous local optimization that serves either to repair the non-feasibility of solutions or improve their quality. The behavior of the proposed method is evaluated on a set of standard benchmark instances taken from the literature and its achieved results are compared to those obtained by the best methods available in the literature. As shown in the experimental part, the proposed approach is very competitive.

In this paper we propose to enhance a width-beam search in order to solve the three-dimensional sphere packing problem. The goal of the problem is to determine the minimum length of the container having fixed width and height, that packs n predefined unequal spheres. The width-beam search uses a greedy selection phase which determines a subset of eligible positions for packing the predefined items in the target object and selects a subset of nodes for exploring some promising paths. We propose to handle lower bounds in the tree and apply a hill-climbing strategy in order to diversify the search process. The performance of the proposed method is evaluated on benchmark instances taken from the literature. The obtained results are compared to those reached by some recent methods available in the literature. Encouraging results have been obtained.