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In this paper, we investigate the use of a hybrid guided neighborhood search for solving the disjunctively constrained knapsack problem. The studied problem may be viewed as a combination of two NP-hard combinatorial optimization problems: the weighted-independent set and the classical binary knapsack. The proposed algorithm is a hybrid approach that combines both deterministic and random local searches. The deterministic local search is based on a descent method, where both building and exploring procedures are alternatively used for improving the solution at hand. In order to escape from a local optima, a random local search strategy is introduced which is based on a modified ant colony optimization system. During the search process, the ant colony optimization system tries to diversify and to enhance the solutions using some informations collected from the previous iterations. Finally, the proposed algorithm is computationally analyzed on a set of benchmark instances available in the literature. The provided results are compared to those realized by both the Cplex solver and a recent algorithm of the literature. The computational part shows that the obtained results improve most existing solution values.

In this paper, the three-dimensional sphere packing problem is solved by using a dichotomous search-based heuristic. An instance of the problem is defined by a set of $ n $ unequal spheres and an object of fixed width and height and, unlimited length. Each sphere is characterized by its radius and the aim of the problem is to optimize the length of the object containing all spheres without overlapping. The proposed method is based upon beam search, in which three complementary phases are combined: (i) a greedy selection phase which determines a series of eligible search subspace, (ii) a truncated tree search, using a width-beam search, that explores some promising paths, and (iii) a dichotomous search that diversifies the search. The performance of the proposed method is evaluated on benchmark instances taken from the literature where its obtained results are compared to those reached by some recent methods of the literature. The proposed method is competitive and it yields promising results.

This paper reviews the most relevant literature on efficient models and methods for packing circular objects/items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional. These packing problems are NP hard optimization problems with a wide variety of applications. They have been tackled using various approaches-based algorithms ranging from computer-aided optimality proofs, to branch-and-bound procedures, to constructive approaches, to multi-start nonconvex minimization, to billiard simulation, to multiphase heuristics, and metaheuristics.