the traveling salesman problem (tsp) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. the tsp is probably the most famous and extensively studied problem in the field of combinatorial optimization. because this problem is an np-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

In this paper, we consider the Generalized Bin Covering problem: We are given m bin types, where each bin of type i has profit pi and demand di. Furthermore, there are n items, where item j has size sj . A bin of type i is covered if the set of items assigned to it has total size at least the demand di. In that case, the profit of pi is earned and the objective is to maximize the total profit. ...

Let P = {C1, C2, . . . , Cn} be a set of color classes, where each color class Ci consists of a set of points. In this paper, we address a family of covering problems, in which one is allowed to cover at most one point from each color class. We prove that the problems in this family are NP-complete (or NP-hard) and offer several constant-factor approximation algorithms.

Given a clustered graph (G,V), that is, a graph G = (V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0-1 matrix M(G,V). Nevertheless, we observe that, given (G,V), it i...