In this paper we investigate the design of a coarse-grained parallel implementation of Cga-LK, a hybrid heuristic for the Traveling Salesman Problem (TSP). Cga-LK exploits a compact genetic algorithm in order to generate high-quality tours which are then refined by means of an efficient implementation of the Lin-Kernighan local search heuristic. The results of several experiments conducted on a...

Traveling Salesman Problem (TSP) is an NP-hard Problem, which has so many different real life applications. Precedence Constraint TSP (PCTSP) is one specific type of TSP in which precedence is given to some cities. PCTSP also has numerous applications. Genetic Algorithms [1] are robust and probabilistic search algorithms based on the mechanics of natural selection and survival of fittest. This ...

1.1 Origin The traveling salesman problem (TSP) were studied in the 18th century by a mathematician from Ireland named Sir William Rowam Hamilton and by the British mathematician named Thomas Penyngton Kirkman. Detailed discussion about the work of Hamilton & Kirkman can be seen from the book titled Graph Theory (Biggs et al. 1976). It is believed that the general form of the TSP have been firs...

Bosch and Herman recently described how to use the traveling salesman problem (TSP) to construct a continuous line drawing based on a user-supplied image. They create a distribution of “cities” that approximates the darkness of the source image, and pass the cities to a heuristic TSP solver. We discuss their method and present alternative algorithms for city distribution that yield more attract...

We show that an instance of traveling salesman problem (TSP) of size n with an asymmetric distance matrix can be transformed into an instance of TSP of size 2n with a symmetric distance matrix. This is an improvement over earlier transformations of this kind which triple the size of the problem. Next we use this transformation to obtain a Hamiltonian tour of a general TSP (which may be asymmetr...

We present a new viewpoint on how some combinatorial optimization problems are solved. When applying this viewpoint to the NP -equivalent traveling salesman problem (TSP), we naturally arrive to a conjecture that is closely related to the polynomialtime insolvability of TSP, and hence to the P −NP conjecture. Our attempt to prove the conjecture has not been successful so far. However, the bypro...

The Traveling Salesman Problem (TSP) is one of the most famous optimization problems. Greedy crossover designed by Greffenstette et al, can be used while Symmetric TSP (STSP) is resolved by Genetic Algorithm (GA). Researchers have proposed several versions of greedy crossover. Here we propose improved version of it. We compare our greedy crossover with some of recent crossovers, we use our gree...

The Multiple Traveling Salesman problem (mTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where more than one salesman is allowed to be used in order to visit some cities just once. Furthermore, the formulation of the mTSP applies to a wide range of reallife applications, and can be extended to a wide variety of Vehicle Routing Problems (VRPs) by incorporating some addi...

This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for ...

There has been many strategies used in trying to obtain good solutions for the TSP (Traveling Salesman Problem). The best strategy that runs in polynomial time for general TSP instances is Chained Lin-Kernighan, but it does not always find the optimal solution. We look at hybrid method based on combining multiple runs of (Chained) Lin-Kernighan and Branch-and-Bound in hopes of obtaining an opti...