Traveling Salesman Problem

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Abstract. We study the Maximal Covering Salesman Problem with the Average Traveling Cost Constraints (MCSPATCC) where the objective is to find a subset of customers with their tour so that the number of covered demand points is maximized. This paper presents a mathematical model to select a profitable subset of demand points to be covered. We also propose an effective heuristic algorithm with three elimination methods to remove unprofitable demand points. The proposed algorithm is based on the genetic algorithm (GA) hybridized with different local search strategies to solve this problem. Parameters of the algorithm are analyzed for calibration by means of the Taguchi method. Extensive computational experiments on a set of standard problems…show more content…
Its associated problems were introduced by William Hamiltone and Thomas Kirkman in 18th century first time. Then, some mathematicians such as Karl Mengerfrom Harvard and Hustler Whitney from Princeton studied the general form of the traveling salesman problem [1], which is a reputable combinatorial optimization problem. Traveling salesman problem is consisting of a set of demand points and the distances each demand point. The objective of traveling salesman problem is to find the shortest possible route that visits each demand point (city) exactly once and returns to the origin city [1]. There are many practical applications for this type of problems such as finding an optimal tour for postmen and tourists [2], process planning for rotating items [3], flow shop scheduling [4], the robotic manipulator control [5], vehicle routing problem [6], computer network design [7],…show more content…
The problem consists of a central depot and a set of cities as demand points. The distance (time) between each two demand point and between the depot and each city is determined. A traveling salesman starts and ends the travel from/to the central depot. The salesman tries to cover some selected demand points among different demand points so that the average traveling cost, which is a function of distance, would not exceed a specified value and also the whole covered demands are maximized. In fact, the goal is to maximize the whole covered
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