Review of Multiple Traveling Salesman Model and Its Application

As a generalization of the classical traveling salesman problem (TSP), the multiple traveling salesman problem (MTSP) is one of the well-known combinatorial optimization problems. However, as a classical NP hard problem, the problem scale and computational complexity of the multiple traveling salesman problem have very high requirements for the solution method. This paper focuses on the multiple traveling salesman problem. Firstly, several characteristics, objective functions, problem constraints and variants of MTSP model are subdivided. Secondly, it classifies and sorts out the specific methods of several common heuristic algorithms in solving MTSP, and compares the similarities and differences of optimization objectives and solutions under different algorithms, so as to understand the general methods of solving multiple traveling salesman problems among different algorithms more intuitively. With the continuous development of multiple traveling salesman problem, scholars are not satisfied with simply solving mathematical problems, and try to regard many practical problems that meet conditions as multiple traveling salesman problems. This paper summarizes the specific construction methods of MTSP model in the context of practical applications such as logistics distribution, wireless sensor network, emergency rescue and UAV collaborative task planning. From the perspective of application results, using MTSP model to solve practical problems can not only reduce enterprise and individual costs, improve revenue, but also promote the development of this field towards a more efficient and intelligent direction. This paper mainly studies the multiple traveling salesman model and its application, which fills the gap in this research field

Phase transition in the assignment problem for random matrices

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=ep

Current applications of ant systems for subset problems

Early applications of Ant Colony Optimization (ACO) have been mainly concerned with solving ordering problems (e.g., the Traveling Salesman Problem). In this report we describe an Ant System algorithm, which would be appropriate for solving additional subset problems as was showed for solving the multiple knapsack problem in previous works. The experiments on progress show the potential power of the ACO approach for solving different subset problems.Eje: Sistemas inteligentes. Metaheurísticas.Red de Universidades con Carreras en Informática (RedUNCI

Current applications of ant systems for subset problems

Early applications of Ant Colony Optimization (ACO) have been mainly concerned with solving ordering problems (e.g., the Traveling Salesman Problem). In this report we describe an Ant System algorithm, which would be appropriate for solving additional subset problems as was showed for solving the multiple knapsack problem in previous works. The experiments on progress show the potential power of the ACO approach for solving different subset problems.Eje: Sistemas inteligentes. Metaheurísticas.Red de Universidades con Carreras en Informática (RedUNCI

Evaluation of Ant Colony Optimization Algorithm Compared to Genetic Algorithm, Dynamic Programming and Branch and Bound Algorithm Regarding Travelling Salesman Problem

We use ant colony optimization (ACO) algorithm for solving combinatorial optimization problems such as the traveling salesman problem. Some applications of ACO are: vehicle routing, sequential ordering, graph coloring, routing in communications networks, etc. In this paper, we compare the performance of ACO to that of a few other state-of-the-art algorithms currently in use and thus measure the effectiveness of ACO as one of the major optimization algorithms in regard with a few more algorithms. The performance of the algorithms is measured by observing their capacity to solve a traveling salesman problem (TSP). This paper will help to find the proper algorithm to be used for routing problems in different real-life situations

A review of the Tabu Search Literature on Traveling Salesman Problems

The Traveling Salesman Problem (TSP) is one of the most widely studied problems inrncombinatorial optimization. It has long been known to be NP-hard and hence research onrndeveloping algorithms for the TSP has focused on approximate methods in addition to exactrnmethods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. Inrnthis paper, we review the tabu search literature on the TSP, point out trends in it, and bringrnout some interesting research gaps in this literature.