In this paper, an approach based upon Genetic Recombination is proposed, and applied to the Traveling Salesman Problem (TSP). The algorithm is composed of two Sample Genetic Algorithms (SGAs) which only consist of the basic genetic operators such as selection, crossover and mutation. One of the SGAs is named as the Global Genetic Algorithm (GGA), and encompasses the main tours where it is desig...

The most general version of the Prize Collecting Traveling Salesman Problem (PCTSP) was first introduced by Balas [8]. In this problem, a salesman has to collect a certain amount of prizes (the quota) by visiting cities. A known prize can be collected in every city. Furthermore, by not visiting a city, the salesman incurs a pecuniary penalty. The goal is to minimize the total travel distance pl...

We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially b...

We introduce a new extension of Punnen’s exponential neighborhood for the traveling salesman problem (TSP). In contrast to an interesting generalization of Punnen’s neighborhood by De Franceschi, Fischetti and Toth (2005), our neighborhood is searchable in polynomial time, a feature that invites exploitation by heuristic and metaheuristic procedures for the TSP and related problems, including t...

The Traveling Salesman Problem (TSP) has been studied extensively in the literature with the assumption that all cities to be visited are stationary. In this paper, we investigate a non-stationary version of TSP (NTSP) where all cities (objects/targets) are moving at known velocities. This problem is motivated by many real life problems in security and defence. We propose a genetic algorithm ba...

I proposed to implement a genetic algorithm [5] to solve the Traveling Salesman Problem. TSP is a classic problem in combinatorial search and optimization that has been well studied. It is often used as a benchmark for combinatorial or black-box optimization algorithms, and is one of the best known problems in graph theory. Applications of TSP include routing (shipping and logistics), job sched...

This paper provides the survey of the heuristics solution approaches for the traveling salesman problem (TSP). TSP is easy to understand, however, it is very difficult to solve. Due to complexity involved with exact solution approaches it is hard to solve TSP within feasible time. That’s why different heuristics are generally applied to solve TSP. Heuristics to solve TSP are presented here with...

The Traveling Salesman Problem (TSP) and its allied problems like Vehicle Routing Problem (VRP) are one of the most widely studied problems in combinatorial optimization. It has long been known to be NP-hard and hence research on developing algorithms for the TSP has focused on approximate methods in addition to exact methods. Tabu search is one of the most widely applied metaheuristic for solv...

Traveling Salesman Problem (TSP) is classical and most widely studied problem in Combinatorial Optimization (Applegate D. L. et al., 2006). It has been studied intensively in both Operations Research and Computer Science since 1950s as a result of which a large number of techniques were developed to solve this problem. Much of the work on TSP is not motivated by direct applications, but rather ...

We intend to show in this paper that metaheuristics based on GRASP and VNS can give good results for a generalization of the Traveling Salesman Problem (TSP) called Traveling Purchaser Problem (TPP) when compared with the Tabu Search algorithm proposed by Voss [13] for this algorithm, concerning the quality of solutions in similar execution times. In these algorithms, several simple and well kn...