Abstract
The generalized traveling salesman problem (GTSP) deals with finding the minimum-cost tour in a clustered set of cities. In this problem, the traveler is interested in finding the best path that goes through all clusters. As this problem is NP-hard, implementing a metaheuristic algorithm to solve the large scale problems is inevitable. The performance of these algorithms can be intensively promoted by other heuristic algorithms. In this study, a search method is developed that improves the quality of the solutions and competition time considerably in comparison with Genetic Algorithm. In the proposed algorithm, the genetic algorithms with the Nearest Neighbor Search (NNS) are combined and a heuristic mutation operator is applied. According to the experimental results on a set of standard test problems with symmetric distances, the proposed algorithm finds the best solutions in most cases with the least computational time. The proposed algorithm is highly competitive with the published until now algorithms in both solution quality and running time.
Highlights
Genetic Algorithm (GA) is a search heuristic that mimics the process of natural evolution [1]
GAs belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover
A local-global approach for the generalized traveling salesman problem and an efficient algorithm for solving the problem based on genetic algorithms is proposed in [18, 19]
Summary
Genetic Algorithm (GA) is a search heuristic that mimics the process of natural evolution [1] This heuristic algorithm ( sometimes called a metaheuristic) is routinely used to generate useful solutions to optimization and search problems. GAs belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. A population of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem is evolved toward better solutions. The evolution usually starts from a population of randomly generated individuals and is an iterative process, with each iteration’s population called a generation. The more fit individuals are stochastically selected from the current population, and each individual’s genome is modified (recombined and possibly randomly mutated) to form a new generation. Each node has been connected by one or more arcs from E, so that each arc connects two nodes from different clusters. (i , j ) E i vi , j v j , i j in which R and E compose
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