A Review of Traveling Salesman Problem with Time Window Constraint (original) (raw)
Literature Review on Travelling Salesman Problem
International Journal of Research, 2018
The Traveling Salesman Problem (TSP) is a classical combinatorial optimization problem, which is simple to state but very difficult to solve. The problem is to find the shortest tour through a set of N vertices so that each vertex is visited exactly once. This problem is known to be NP-hard, and cannot be solved exactly in polynomial time. Many exact and heuristic algorithms have been developed in the field of operations research (OR) to solve this problem. In this paper we provide overview of different approaches used for solving travelling salesman problem.
Springer eBooks, 2013
This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances. This is a preliminary version of one of the chapters of the volume "Networks" edited by M.O. Ball, T.
A compressed annealing approach to the traveling salesman problem with time windows
This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling salesman problem with time windows (TSPTW). Augmenting temperature from tra-ditional simulated annealing with the concept of pressure (analogous to the value of the penalty multi-plier), compressed annealing integrates a penalty method with heuristic search to address the TSPTW. Computational results validate the value of a variable penalty method versus a static penalty approach. Compressed annealing compares favorably with benchmark results in the literature, obtaining best-known results in numerous instances.
Traveling Salesman Problem with Transportation
Computer Science, 2006
Traveling Salesman Problem (TSP) is a generic name that includes diverse practical models. Motivated by applications, a new model of TSP is examined -a synthesis of classical TSP and classical Transportation Problem. Algorithms based on Integer Programming cutting-plane methods and Branch and Bound Techniques are obvious.
The multiple traveling salesman problem: an overview of formulations and solution procedures
The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. Moreover, the characteristics of the mTSP seem more appropriate for real-life applications, and it is also possible to extend the problem to a wide variety of vehicle routing problems (VRPs) by incorporating some additional side constraints. Although there exists a wide body of the literature for the TSP and the VRP, the mTSP has not received the same amount of attention. The purpose of this survey is to review the problem and its practical applications, to highlight some formulations and to describe exact and heuristic solution procedures proposed for this problem.
Heuristics and Meta-Heuristics optimization methods in solving Traveling Salesman Problem TSP
2020
In modern societies there are increasingly more often problems of various kinds, and tests are needed to solve them in experimental ways. Although, develop a mathematical model that closely matches the reality to solve a real life problem is very complicated, since many of these models might has to contain very large number of variables (as a heuristic model that optimizes problems solving results). Furthermore, these shows as difficult problems in controlling subjec-tive behaviours, so They are making it even more complicated than these models resemble reality (wrong solving model leads to a more complex level). The purpose of this research is the study of combinatorial optimization problems using approximate methods. In particular, this work focuses on the analysis of meta-heuristics algorithms based on history and population related to the solu-tion of Travelling Salesman Problem (TSP) like Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Simulated Annealing (SA)...
Traveling salesman problem heuristics: Leading methods, implementations and latest advances
European Journal of Operational Research, 2011
Heuristics for the traveling salesman problem (TSP) have made remarkable advances in recent years. We survey the leading methods and the special components responsible for their successful implementations, together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric TSP benchmark problems. The foremost algorithms are represented by two families, deriving from the
An integer programming approach for the time-dependent TSP
Electronic Notes in Discrete Mathematics, 2010
The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider the formulations proposed in Picard and Queryanne [8] and Vander Wiel and Sahinidis [10], analyze the relationship between them and derive some valid inequalities and facets. Computational results are also presented for a Branch and Cut algorithm (B&C)that uses these inequalities, which showed to be very effective.
Traveling Salesman Problem with Time Windows Solved with Genetic Algorithms
The Traveling Salesman Problem (TSP) is a very common problem in many applications. It appears in the transportation of goods and not only. As we know this problem is NP hard. Time Windows (TW) brings us some additional constraints to solve. In case there are many Time Windows the problem constraints determine almost the whole solution of the problem and in some cases we can solve the problem. We restrict the cardinality of Time Windows. In our work we define the following conditions without loss of generality: 1. The salesman has to visit one town each day 2. The distance between two towns can be performed in a day 3. We have maximum two Time Windows 4. We have routes between every two towns, but the cost of the routes may differ in case we go from town A to town B, or we go from town B to town A. Genetic algorithms are powerful tools for solving NP hard problems. They utilize search and optimization procedures that operate in a similar way to the evolutionary processes observed in...
The Travelling Salesman Problem and Related Problems
New formulations are presented for the Travelling Salesman problem, and their relationship to previous formulations is investigated. The new formulations are extended to include a variety of transportation scheduling problems, such as the Multi-Travelling Salesman problem, the Delivery problem, the School Bus problem and the Dial-a-Bus problem. A Benders decomposition procedure is applied on the new formulations and the resulting computational rocedure is seen to be identical to previous methods for solving the Travelling Salesman problem. Based on the Lagrangean Relaxation method, a new procedure is suggested for generating lagrange multipliers for a subgradient optimization procedure.
Performance Analysis of Optimization Methods for Solving Traveling Salesman Problem
Innovative Technologies and Scientific Solutions for Industries, 2021
The subject of this research is distance and time of several city tour problems which known as traveling salesman problem (tsp). The goal is to find out the gaps of distance and time between two types of optimization methods in traveling salesman problem: exact and approximate. Exact method yields optimal solution but spends more time when the number of cities is increasing and approximate method yields near optimal solution even optimal but spends less time than exact methods. The task in this study is to identify and formulate each algorithm for each method, then to run each algorithm with the same input and to get the research output: total distance, and the last to compare both methods: advantage and limitation. Methods used are Brute Force (BF) and Branch and Bound (B&B) algorithms which are categorized as exact methods are compared with Artificial Bee Colony (ABC), Tabu Search (TS) and Simulated Annealing (SA) algorithms which are categorized as approximate methods or known a...