in this paper, a robust model presented is developed for hub covering flow problem in which hubs have capacity. this problem has two objective functions converting to a single-objective problem by using weighting method. firstly, the problem will be formulated in a certain case. then, by considering the demand as a non-random variable, it will be modeled by robust optimization. finally, by usin...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...

This paper defines the Stochastic Eulerian Tour Problem (SETP) and investigates several characteristics of this problem. Given an undirected Eulerian graph , a subset =) of the edges in E that require service, and a probability distribution for the number of edges in R that have to be visited in any given instance of the graph, the SETP seeks an a priori Eulerian tour of minimum expected length...

For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...

The Stochastic Eulerian Tour Problem was introduced in 2008 [1] as a stochastic variant of the well-known Eulerian Tour Problem. In a follow-up paper the same authors investigated some heuristics for solving the Stochastic Eulerian Tour Problem [2]. After a thorough study of these two publications a few issues emerged. In this short research commentary we would like to discuss these issues. For...

In the Euclidean Traveling Salesman Problem, a set of points in the plane is given, and we look for a shortest closed curve through these lines (a \tour"). We treat two special cases of this problem which are solvable in polynomial time. The rst solvable case is the N-line Traveling Salesman Problem, where the points lie on a small number (N) of parallel lines. Such problems arise for example i...