We have used the metaphor of ant colonies to define "the Ant system", a class of distributed algorithms for combinatorial optimization. To test the Ant system we used the travelling salesman problem. In this paper we analyze some properties of Ant-cycle, the up to now best performing of the ant algorithms we have tested. We report many results regarding its performance when varying the values o...

We investigate per-instance algorithm selection techniques for solving the Travelling Salesman Problem (TSP), based on the two state-of-the-art inexact TSP solvers, LKH and EAX. Our comprehensive experiments demonstrate that the solvers exhibit complementary performance across a diverse set of instances, and the potential for improving the state of the art by selecting between them is significa...

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 multiple Travelling Salesman Problem (mTSP) is the general form of TSP, in which one or more than one salesmen can be used in the solution set. The Constraint in the optimization task is that each salesman returns to starting point at end of trip, travelling to a specific set of cities in between and except for the first one, each and every city is visited by exactly one salesman. The idea ...

In this paper we consider graph traversal problems (Euler and Travelling Salesman traversals) that arise from a particular technology for DNA sequencing sequencing by hybridization (SBH). We first explain the connection of the graph problems to SBH and then focus on the traversal problems. We describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of dir...

In 1975, Kalmanson proved that if the distance matrix in the travelling salesman problem (TSP) fulfills certain combinatorial conditions (that are nowadays called the Kalmanson conditions) then the TSP is solvable in polynomial time [Canad. J. Math., 27 (1995), pp. 1000– 1010]. We deal with the problem of deciding, for a given instance of the TSP, whether there is a renumbering of the cities su...

In Genetic Algorithm (GA), the fitness or quality of individual solutions in the initial population plays a significant part in determining the final optimal solution. The traditional GA with random population seeding technique is simple and proficient however the generated population may contain poor fitness individuals, which take long time to converge to the optimal solution. On the other ha...

2014 We study the travelling salesman problem on dilute lattices where the cities are represented by random lattice sites, occupied with concentration p, and the salesman intends to visit a finite fraction f of the total number of cities. The variation of the average optimal travel distance per city L (p, f) against f are investigated here for various values of p. The values of the normalised t...

The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well known Traveling Salesman Problem (TSP), where along with a weighted graph G = (V, E,w) we are given by a partition of its node set V = V1 ∪ . . .∪Vk into disjunctive subsets or clusters. The goal is to find a minimum cost cycle such that each cluster is hit by exactly one node of this cycle. We consider a geometri...

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...