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...

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper...

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper...

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...

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.

The topic of this paper is a Genetic Algorithm solution to the Vehicle Routing Problem with Time Windows, a variant of one of the most common problems in contemporary operations research. The paper will introduce the problem starting with more general Traveling Salesman and Vehicle Routing problems and present some of the prevailing strategies for solving them, focusing on Genetic Algorithms. A...

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