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We consider the linearization problem associated with the quadratic traveling salesman problem (QTSP). Necessary and sufficient conditions are given for a cost matrix Q of QTSP to be linearizable. It is shown that these conditions can be verified in O(n) time. Some simpler sufficient conditions for linearization are also given along with related open problems.

Let apply this cutting procedure for ... 3 2 1 − − − → → N N N R R R sub-routes. One can readily see that there will be progressive increasing in the disturbances of sub-routes length, i.e. | ) ( ) ( | | ) ( ) ( | 1 1 − + − ≤ − k k k k R D R D R D R D , ,... 3 , 2 − − = N N k As result of application these transformations sequence, we should obtain N P r r r r R ∈ = 2 1 2 1 2 , }, , { sub-route...

The edges of the complete bipartite graph Kn,n are assigned independent lengths from uniform distribution on the interval [0, 1]. Let Ln be the length of the minimum travelling salesman tour. We prove that as n tends to infinity, Ln converges in probability to a certain number, approximately 4.0831. This number is characterized as the area of the region x, y ≥ 0, (1 + x/2) · e + (1 + y/2) · e ≥...

In layout problem of manufacturing cells, cells have rectangular shapes and must be positioned without overlapping. The objective is to minimize the total transportation cost. RRR 1-2014, May 2014 Page 1

In this paper we use marker method and propose a new mutation operator that selects the nearest neighbor among all near neighbors solving Traveling Salesman Problem.

We study how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. We first consider feasibility issues. This includes finding the smallest vehicle capacity and some initial load such that a given tour is fea...