# THE TRAVELING SALESMAN PROBLEM A COMPUTATIONAL STUDY PDF

This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sound . Request PDF on ResearchGate | The Traveling Salesman Problem: A Computational Study | This book presents the latest findings on one of the most intensely. We review the recent book authored by David L. Applegate, Robert E. Bixby, Vasěk Chvatal and William J. Cook, The traveling salesman problem: a computational study, Princeton Series in Applied Mathematics. Abstract We review the recent book authored by David L. Applegate, Robert.

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techniques to attack computational problems in general. Our primary Before studying Concorde we take a look at the history of the TSP and discuss some of. The traveling salesman problem, or TSP for short intensely studied problems in computational unknown, for over 50 years its study has led. 9 Statistical analysis of the results of the λ-optimal and λ-optimal greedy .. A further computational complexity analysis of the TSP requires the definition of more.

The effectiveness and the parameter sensitivity of the list-based cooling schedule are illustrated through benchmark TSP problems. The LBSA algorithm, whose performance is robust on a wide range of parameter values, shows competitive performance compared with some other state-of-the-art algorithms.

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Introduction Simulated annealing SA algorithm, which was first independently presented as a search algorithm for combinatorial optimization problems in [ 1 , 2 ], is a popular iterative metaheuristic algorithm widely used to address discrete and continuous optimization problems.

The key feature of SA algorithm lies in means to escape from local optima by allowing hill-climbing moves to find a global optimum. One of the major shortages of SA is that it has several parameters to be tuned, and its performance is sensitive to the values of those control parameters.

There are two special strategies for parameter tuning: the online parameter tuning and the off-line parameter tuning. In the online approach, the parameters are controlled and updated dynamically or adaptively throughout the execution of the SA algorithm [ 3 — 7 ], whereas in the off-line approach, the values of different parameters are tuned before the execution of the SA algorithm and are fixed during its execution.

Fine-tuning parameter values is not trivial, and those parameters are quite often very poorly made by trial and error. So, SA algorithm, which has less parameter or is less sensitive to parameter setting, is very attractive for practical users. Recently, a metaheuristic algorithm called the list-based threshold-accepting LBTA algorithm has been developed and has shown significant performance for combinatorial optimization problems that are NP-complete.

The advantage of LBTA over the majority of other neighbourhood search-based metaheuristic methods is that it has fewer controlling parameters that have to be tuned in order to produce satisfactory solutions. Since its appearance, LBTA has been successfully applied to many combinatorial optimization problems [ 8 — 14 ]. Different classes of applications, modeling approaches, and exact or heuristic solution techniques are identified and compared. Conclusions emphasize the interest of this class of problems, with respect to applications as well as theoretical results.

Exnar Filip et al. For a 15 node problem four matrix were All rights reserved by www.

## The Traveling Salesman Problem

It was found that the shortest route was taking the highest amount of time and the fastest route was the longest in terms of distance.

So the nodes were divided into two parts; one part transporting the goods by owns vehicle and other by subcontracting. The main aim was to economically benefit the company. Mohammad Asim et al. Through this paper authors describe how the traveling salesman problem is solved by the heuristic method of genetic algorithms.

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The purpose is to find the most approximate solution that gives the least distance, which is the shortest route for traversing the cities given in the data set such that each city is passed through just once and the traveling salesman comes back to the initial city from where he started.

Authors accomplish this by carrying out the algorithm through generating a fitness formula and with the help of genetic operators like selection, crossover and mutation.

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 met heuristic for solving the TSP. Author review the tabu search literature on the TSP and its variations, point out trends in it, and bring out some interesting research gaps in this literature.

Younis Elhaddad et al.

## List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

This hybrid method helps the GA to take a jump as it gets stuck after 20 consecutive iterations. Using a CPU having Matlab 7. The distances between the nodes of the benchmark instances were considered as the time so as to take the time windows into consideration. This problem has a number of important practical applications, including scheduling and routing.

The problem is regarded as NP-complete, and hence traditional optimization algorithms are inefficient when applied to solve larger scale TSPTW problems. Consequently, the development of approximation algorithms has received considerable attention in recent years.

Ant colony optimization ACO , inspired by the foraging behavior of real ants, is one of the most attractive approximation algorithms. Imdat Kara et al.

## List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

It would be useful to develop a new model solvable by any optimizer directly. In this paper, we propose a new integer linear programming formulation having O n2 binary variables and O n2 constraints, where n equals the number of nodes of the underlying graph. The objective function is stated to minimize the total travel time plus the total waiting time. A computational comparison is made on a suite of test problems with 20 and 40 nodes.

The performances of the proposed and existing formulations are analyzed with respect to linear programming relaxations and the CPU times. The new formulation considerably outperforms the existing one with respect to both the performance criteria.

Adaptation of our formulation to the Multi-traveler case and some additional restrictions for special situations are illustrated. Jeffrey W. Ohlmann et al. Instead of using the traditional simulated annealing, the method used to solve the TSPTW was variable penalty approach of compressed annealing.

Comparison with the benchmark problem was done in every step. For most of the cases the solutions obtained were nearly optimal even for constrained problems. Jing-Quan Li [8] presents a bi-directional resource-bounded label correcting algorithm for the traveling salesman problem with time windows, in which the objective is to minimize travel times. Label extensions and dominance start simultaneously in both forward and backward directions: The resultant label extension process scans much smaller the space than in single directional dynamic programming, substantially reducing the number of non-dominated labels.

The labels for both the forward direction and backward direction are ultimately joined to form a complete route if all relevant feasibility conditions are satisfied. John N. Tsitsiklis [9] considered a complete directed graph in which each arc has a given length.

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The resulting book provides not only a map for understanding TSP computation, but should be the starting point for anyone interested in launching a computational assault on any combinatorial optimization problem.

It is very well written, with a vivid style that captures the reader's attention. Many examples are provided that are very useful to motivate and help the reader to better understand the results presented in the book. Ever since the early days of discrete optimization, the traveling salesman problem has served as the model for computationally hard problems. The authors are main players in this area who forged a team in to push the frontiers on how good we are in solving hard and large traveling salesman problems.

Now they lay out their views, experience, and findings in this book. Subject Areas. Mathematics - Applied. Princeton Series in Applied Mathematics. Shopping Cart Options For eBooks Many of our ebooks are available through library electronic resources including these platforms: Our eBook editions are available from many of these online vendors:Santoro, and E. Boyd, S. At the beginning, the SA algorithm have been used to generate an initial solution for the ITS algorithm.

In robotic machining or drilling applications, the "cities" are parts to machine or holes of different sizes to drill, and the "cost of travel" includes time for retooling the robot single machine job sequencing problem. As a subset of NP problems, the NP -complete problems are those whose solutions are sufficient to deal with any other NP problems in polynomial time.