Definition The traveling salesman problem (TSP) is the following optimization problem. Given a complete graph G with edge costs, find a Hamiltonian cycle of minimum cost in G. Definition The metric traveling salesman problem (∆-TSP) is the TSP restricted to instances satisfying the triangle inequality Definition The traveling salesman problem (TSP) is the following optimization problem. Given a...

We present a genetic algorithm for solving the traveling salesman problem by genetic algorithms to optimality for traveling salesman problems with up to 442 cities. Mlihlenbein et al. [MGK 88], [MK 89] have proposed a genetic algorithm for the traveling salesman problem, which generates very good but not optimal solutions for traveling salesman problems with 442 and 531 cities. We have improved...

A metaheuristic is an intelligent, iterative process that guides a search and can be applied towards optimization problems, such as the Traveling Salesman Problem. Two well studied techniques for solving optimization problems are Genetic Algorithms and Ant Colony Systems. However, each metaheuristic has different strengths and weaknesses. Genetic Algorithms are able to quickly find near optimal...

We consider the generalized traveling salesman problem in which a graph with nodes partitioned into clusters is given. The goal is to identify a minimum cost round trip visiting exactly one node from each cluster. For solving difficult instances of this problem heuristically, we present a new Variable Neighborhood Search (VNS) approach that utilizes two complementary, large neighborhood structu...

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res. 25 443–454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the m...

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-...

This paper introduces the family traveling salesperson problem (FTSP), a variant of the generalized traveling salesman problem. In the FTSP, a subset of nodes must be visited for each node cluster in the graph. The objective is to minimize the distance traveled. We describe an integer programming formulation for the FTSP and show that the commercial-grade integer programming solver CPLEX 11 can...

The Generalized Traveling Salesman Problem is a variation of the well known Traveling Salesman Problem in which the set of nodes is divided into clusters; the objective is to find a minimum-cost tour passing through one node from each cluster. We present an effective heuristic for this problem. The method combines a genetic algorithm (GA) with a local tour improvement heuristic. Solutions are e...

Vehicle routing is an area of both practical and theoretical importance. Unfortunately, routing problems are notably difficult to solve since almost all vehicle routing problems are NP-hard. However, we have discovered that when reduced to its simplest form, solving a single vehicle routing problem, without capacity and time window constraints is quite similar to the Traveling Salesman Problem ...