Genetic Algorithms and the Travelling Salesman Problem

Genetic algorithms are an evolutionary technique that use crossover and mutation operators to solve optimization problems using a survival of the fittest idea. They have been used successfully in a variety of different problems, including the traveling salesman problem. In the traveling salesman problem we wish to find a tour of all nodes in a weighted graph so that the total weight is minimized. The traveling salesman problem is NP-hard but has many real world applications so a good solution would be useful. Many different crossover and mutation operators have been devised for the traveling salesman problem and each give different results. We compare these results and find that operators that use heuristic information or a matrix representation of the graph give the best results

GeneTS : a relational-functional genetic algorithm for the traveling salesman problem

This work demonstrates a use of the relational-functional language RelFun for specifying and implementing genetic algorithms. Informal descriptions of the traveling salesman problem and a solution strategy are given. From these a running RelFun application is developed, whose most important parts are presented. This application achieves good approximations to traveling salesman problems by using a genetic algorithm variant with particularly tailored data representations. The feasibility of implementing sizable applications in RelFun is discussed

Review of Traveling Salesman Problem for the genetic algorithms

Genetic Algorithms (GAs) are an evolutionary technique that uses the operators like mutation, crossover and the selection of the most fitted element as solution for problems optimization. The Traveling Salesman Problem (TSP) finds a path with minimal length, closed within a weighted graph in all its nodes and it visits each of them once. This problem is found in many real world applications and where a good solution might help. There are applied many methods for finding a solution for the TSP, but during this study GAs are used as an approximate method of TSP

GR-252 Solving Multiple Traveling Salesman Problem using K Means Clustering and Mixed Integer Programming - An Integrated Approach

In this research paper, we explore an efficient algorithm for multiple Traveling Salesman Problem (m-TSP) using an approach which combines K Means clustering algorithm and Mixed Integer Programming (MIP). The Traveling Salesman problem is an NP hard problem which relates to generation of minimum cost round trip tours for multiple salesmen visiting several cities in their territory. Our novel approach has the promise of reaching closer to the optimal solution as compared to heuristics-based approaches such as genetic algorithms

Shared Crossover Method for Solving Traveling Salesman Problem

Abstract. Genetic algorithms (GA) are evolutionary techniques that used crossover and mutation operators to solve optimization problems using a survival of the fittest idea. They have been used successfully in a variety of different problems, including the traveling salesman problem. The main idea of Traveling Salesman Problem (TSP) is to find the minimum traveling cost for visiting cities; the salesman must visit each city exactly once and return to the starting point of origin. Genetic algorithms are search methods that employ processes found in natural biological evolution. These algorithms search on a given population of potential solutions to find those that pass some specifications or criteria. In this paper, we apply modified genetic algorithm methodology for finding near-optimal solutions for TSP problem using shared neighbours to insure that the closest cities to have the highest priorities to be carried out to the next generation

Algorithms for Variants of Routing Problems

In this thesis, we propose mathematical optimization models and algorithms for variants of routing problems. The first contribution consists of models and algorithms for the Traveling Salesman Problem with Time-dependent Service times (TSP-TS). We propose a new Mixed Integer Programming model and develop a multi-operator genetic algorithm and two Branch-and-Cut methods, based on the proposed model. The algorithms are tested on benchmark symmetric and asymmetric instances from the literature, and compared with an existing approach, showing the effectiveness of the proposed algorithms. The second work concerns the Pollution Traveling Salesman Problem (PTSP). We present a Mixed Integer Programming model for the PTSP and two mataheuristic algorithms: an Iterated Local Search algorithm and a Multi-operator Genetic algorithm. We performed extensive computational experiments on benchmark instances. The last contribution considers a rich version of the Waste Collection Problem (WCP) with multiple depots and stochastic demands using Horizontal Cooperation strategies. We developed a hybrid algorithm combining metaheuristics with simulation. We tested the proposed algorithm on a set of large-sized WCP instances in non-cooperative scenarios and cooperative scenarios

Genetic algorithms for the traveling salesman problem using edge assembly crossovers

The central issue in creating new genetic algorithms is the algorithm\u27s crossover method. My focus is on a particular crossover known as the Edge Assembly Crossover, or EAX, by Nagata and Kobayashi. The basics of a what make up a genetic algorithm is reviewed. The traveling salesman problem is defined. The EAX as an algorithm within an algorithm is explained. The crossover\u27s implementation is original and is listed. The use of the graphic user interface, TSP View, used to run algorithms is explained as well as the extensions to the interface that were implemented for this study. The results of running a genetic algorithm using the EAX against traveling salesman problems, with a focus on ATT532, is discussed and compared to runs using other optimization algorithms. The question of why EAX works is addressed with conjectures for a possible future research path

A COMPARATIVE STUDY OF CROSSOVER OPERATORS FOR GENETIC ALGORITHMS TO SOLVE TRAVELLING SALESMAN PROBLEM

Genetic algorithms (GAs) represent a method that mimics the process of natural evolution in effort to find good solutions. In that process, crossover operator plays an important role. To comprehend the genetic algorithms as a whole, it is necessary to understand the role of a crossover operator. Today, there are a number of different crossover operators that can be used , one of the problems in using genetic algorithms is the choice of crossover operator Many crossover operators have been proposed in literature on evolutionary algorithms, however, it is still unclear which crossover operator works best for a given optimization problem. This paper aims at studying the behavior of different types of crossover operators in the performance of genetic algorithm. These types of crossover are implemented on Traveling Salesman Problem (TSP); Whitley used the order crossover (OX) depending on specific parameters to solve the traveling salesman problem, the aim of this paper is to make a comparative study between order crossover (OX) and other types of crossover using the same parameters which was Whitley used