We consider a particular Bin Packing Problem in which some pairs of items may be in conflict and cannot be assigned to the same bin. The problem, denoted as the Bin Packing Problem with Conflicts, is of practical and theoretical interest, because of its many real-world applications and because it generalizes both the Bin Packing Problem and the Vertex Coloring Problem. We present new lower bounds, upper bounds and an exact approach, based on a Set Covering formulation solved through a Branch-and-Price algorithm. We investigate the behavior of the proposed procedures by means of extensive computational results on benchmark instances from the literature

This work presents a new parallel procedure designed to process combinatorial branch-and-bound (B&B) algorithms by using GPU. Our strategy is to perform B&B sequentially until a specific depth, saving the current path in the B&B tree as a node into the Active Set, and then force the backtracking. Each node into the Active Set is a DFS-B&B root that will be concurrently processed by the GPU. We compare our results with multicore and serial versions of the same search schema, using explicit enumeration (all possible solutions) and implicit enumeration (branch-and-bound search), for some asymmetrical traveling salesman problem instances. Our computational results indicate the superiority of our GPU computing-based method mainly for the B&B's worst case.

We present a new iterative algorithm for the molecular distance geometry problem with inaccurate and sparse data, which is based on the solution of linear systems, maximum cliques, and a minimization of nonlinear least-squares function. Computational results with real protein structures are presented in order to validate our approach.

Private enterprises and governments around the world use speed cameras to control traffic flow and limit speed excess. Cameras may be exposed to difficult weather conditions and typically require frequent maintenance. When deciding the order in which maintenance should be performed, one has to consider both the traveling times between the cameras and the traffic flow that each camera is supposed to monitor. In this paper, we study the problem of routing a set of technicians to repair cameras by minimizing the total weighted latency, that is, the sum of the weighted waiting times of each camera, where the weight is a parameter proportional to the monitored traffic. The resulting problem, called the weighted k-traveling repairman problem (wkTRP), is a generalization of the well-known traveling repairman problem and can be used to model a variety of real-world applications. To solve the wkTRP, we propose an iterated local search heuristic and an exact branch-and-cut algorithm enriched with valid inequalities. The effectiveness of the two methods is proved by extensive computational experiments performed both on instances derived from a real-world case study and on benchmark instances from the literature on the wkTRP and on related problems.

We study the equality generalized traveling salesman problem (E-GTSP), which is a variant of the well-known traveling salesman problem. We are given an undirected graph G = (V , E ), with set of vertices V and set of edges E , each with an associated cost. The set of vertices is partitioned into clusters. E-GTSP is to find an elementary cycle visiting exactly one vertex for each cluster and minimizing the sum of the costs of the traveled edges. We propose a multistart heuristic, which iteratively starts with a randomly chosen set of vertices and applies a decomposition approach combined with improvement procedures. The decomposition approach considers a first phase to determine the visiting order of the clusters and a second phase to find the corresponding minimum cost cycle. We show the effectiveness of the proposed approach on benchmark instances from the literature. On small instances, the heuristic always identifies the optimal solution rapidly and outperforms all known heuristics; on larger instances, the heuristic always improves, in comparable computing times, the best known solution values obtained by the genetic algorithm recently proposed by Silberholz and Golden.