We describe an artificial ant colony capable of solving the traveling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to bo...

— Using an approach that seems to be patterned after that of Yannakakis, Hofman argues that an NP-complete problem cannot be formulated as a polynomial bounded-sized linear programming problem. He then goes on to propose a " construct " that he claims to be a " counterexample " to recently published linear programming formulations of the Traveling Salesman Problem (TSP) and the Quadratic Assign...

This paper describes an implementation of the Lin±Kernighan heuristic, one of the most successful methods for generating optimal or near-optimal solutions for the symmetric traveling salesman problem (TSP). Computational tests show that the implementation is highly e€ective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 13,509-city prob...

13.1 Introduction Many geometric optimization problems which are interesting and important in practice have been shown to be NP-hard. However, for some cases it is possible to compute approximate solutions in polynomial time. This chapter describes approaches to nd polynomial time algorithms that compute approximate solutions to various geometric optimization problems in Eu-clidean metric space...

In this paper, a novel algorithm of genetic ant colony optimization (GACO) is proposed for traveling salesman problem (TSP). TSP is to minimize the cost of travel of a salesman in visiting all the cities in a given set, and return to the starting city. Basically, the proposed algorithm combines ant colony optimization (ACO) with genetic algorithm (GA) and can explore and exploit search spaces. ...

Simple Genetic Algorithms are used to solve optimization problems. Genetic Algorithm also comes with a parallel implementation as Parallel Genetic Algorithm (PGA). PGA can be used to reduce the execution time of SGA and also to solve larger size instances of problems. In this paper, different implementations for PGA have been discussed with their frameworks. In this implementation, all PGA are ...

The Traveling Salesman Problem (TSP) is a classical NPhard combinatorial problem that has been intensively studied through several decades. A large amount of literature is dedicated to this problem. TSP can be directly applied to some real life problems, and to be generalized to some other set of important combinatorial problems. Nowadays, a large collection of TSP instances can be found such a...

Local search with k-exchange neighborhoods, k-opt, is the most widely used heuristic method for the traveling salesman problem (TSP). This paper presents an effective implementation of k-opt in LKH-2, a variant of the Lin–Kernighan TSP heuristic. The effectiveness of the implementation is demonstrated with experiments on Euclidean instances ranging from 10,000 to 10,000,000 cities. The runtime ...

Inspired by nature, genetic algorithms (GA) are among the greatest meta-heuristics optimization methods that have proved their effectiveness to conventional NP-hard problems, especially the traveling salesman problem (TSP) which is one of the most studied supply chain management problems. This paper proposes a new crossover operator called Jump Crossover (JMPX) for solving the travelling salesm...

Imagine you have traveled to an unfamiliar city. Before you start your daily tour around the city, you need to know a good route. In Network Theory (NT), this is the traveling salesman problem (TSP). A dynamic programming algorithm is often used for solving this problem. However, when the road network of the city is very complicated and dense, which is usually the case, it will take too long fo...