We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequa...

We present an approximation algorithm for the Traveling Salesman Problem when the vehicle is constrained to move forward along paths with bounded curvature (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turning radius and Dmin is the minimum E...

In this paper, an improved self-organizing map approach to solving the traveling salesman problem is proposed by fixing the number of nodes in the output layer of neural network, modifying the neighhorhood function, and modifying the weight update rules. An overview of previous work on solving the traveling salesman problem is given. An extension of the prcposed algorithm can also be used to so...

We present an approximation algorithm for the traveling salesman problem when the vehicle is constrained to move forward along paths with bounded curvatures (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turn radius and Dmin is the minimum Euc...

Abstract In this short note, the dual problem for the traveling salesman problem is constructed through the classic Lagrangian. The existence of optimality conditions is expressed as a corresponding inverse problem. A general 4-cities instance is given, and the numerical experiment shows that the classic Lagrangian may not be applicable to the traveling salesman problem.

in press. 17 H and L chain preparations in 1 M propionic acid were mixed in the ratio of 3: 1 based on O.D. and then dialyzed against cold water followed by borate buffer. 18 This arc was not apparent in the plate of the original y-globulin nor in any of the other plates. It did not appear when the horse anti-rabbit globulin was absorbed with normal rabbit 72-globulin prior to diffusion. Since ...