WIN Algorithm for Discrete Online TSP

2011 ◽  
Vol 15 (9) ◽  
pp. 1199-1202
Author(s):  
Yonghua Wu ◽  
◽  
Guohun Zhu ◽  
Huaying Chen ◽  
Jucun Qin ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Metric Space ◽  
Competitive Analysis ◽  
Competitive Ratio ◽  
Traveling Salesman ◽  
Complete Problem ◽  
Competitive Algorithm ◽  
Np Complete

Traveling Salesman Problem (TSP) which is proved as an NP-Complete problem is solved by many algorithms. In this paper, we propose online TSP which is based on general discrete metric space. A Waiting-If-Necessary (WIN) algorithm is proposed that involves with increasing cost caused by zealous algorithms and unnecessary waiting caused by cautious algorithms. We measure the performance of the WIN algorithm using competitive analysis and found that it is a 2-competitive algorithm. The competitive ratio of theWIN algorithm can be improved by setting parameterT0.

scholarly journals FPT-ALGORITHMS FOR MINIMUM-BENDS TOURS

2011 ◽  
Vol 21 (02) ◽  
pp. 189-213 ◽  
Author(s):  
VLADIMIR ESTIVILL-CASTRO ◽  
APICHAT HEEDNACRAM ◽  
FRANCIS SURAWEERA
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Fixed Parameter Tractable ◽  
Line Segments ◽  
Fpt Algorithms ◽  
Fixed Parameter ◽  
Axis Parallel ◽  
Np Complete ◽  
Number Of Bends ◽  
Straight Lines

This paper discusses the κ-BENDS TRAVELING SALESMAN PROBLEM. In this NP-complete problem, the inputs are n points in the plane and a positive integer κ, and we are asked whether we can travel in straight lines through these n points with at most κ bends. There are a number of applications where minimizing the number of bends in the tour is desirable because bends are considered very costly. We prove that this problem is fixed-parameter tractable (FPT). The proof is based on the kernelization approach. We also consider the RECTILINEAR κ-BENDS TRAVELING SALESMAN PROBLEM, which requires that the line-segments be axis-parallel. 1 Note that a rectilinear tour with κ bends is a cover with κ-line segments, and therefore a cover by lines. We introduce two types of constraints derived from the distinction between line-segments and lines. We derive FPT-algorithms with different techniques and improved time complexity for these cases.

scholarly journals ОГЛЯД ЗАВДАНЬ МАРШРУТИЗАЦІЇ, ЩО ЗВОДЯТЬСЯ ДО ЗАДАЧІ КОМІВОЯЖЕРА

2020 ◽  
pp. 152-159
Author(s):  
Ольга Борисовна Маций
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Information Technologies ◽  
Traveling Salesman ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Modern Information ◽  
The Traveling Salesman Problem

The solution to the problem of improving the management of the transport process depends not only on the level of modernization of vehicles and the degree of use of modern information technologies, but also on the choice of routes that reduce the cost of transporting goods and passengers. Actual working conditions of vehicles in road networks put forward a number of tasks for optimizing closed routes, which are based on the classic routing problem (VRP - Vehicle Routing Problem).VRP is one of the generalizations of the hard-to-solve traveling salesman problem. The traveling salesman task is NP-complete. It refers to the main tasks of combinatorial optimization and, forming a continuously replenished set of applications and generalizations, remains an urgent research topic. An exact solution to the traveling salesman problem can be found only by reducing the enumeration of the type of branches and boundaries, which are not always applicable in operational planning by vehicle traffic. Therefore, the development of new and improvement of currently known methods for solving routing problems, reducible to the traveling salesman problem, and their software implementation is both a theoretical and practically important problem.The article considers the class of routing problems reducible to the traveling salesman problem. It is shown that optimization tasks for closed routes (routing problems), which are an important part of transport logistics, occupy key positions in the management of the processes of moving goods and passengers with the support of modern information technologies. An obvious feature that combines the considered list of routing problems (the symmetric traveling salesman problem, the problem of packing in containers, the school bus problem) is that they are formulated as generalizations or variants of the NP-complete traveling salesman problem with restrictions that narrow the scope of feasible solutions. The strongest restrictions become insufficient solvability conditions, stimulating interest in the study of combinatorial optimization problems associated with the traveling salesman problem.

scholarly journals Competitive analysis for two variants of online metric matching problem

2021 ◽  
pp. 2150156
Author(s):  
Toshiya Itoh ◽  
Shuichi Miyazaki ◽  
Makoto Satake
Keyword(s):  
Greedy Algorithm ◽  
Lower Bounds ◽  
Metric Space ◽  
Competitive Analysis ◽  
Assignment Problem ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Upper And Lower Bounds ◽  
Matching Problem ◽  
Metric Matching

In the online metric matching problem, there are servers on a given metric space and requests are given one-by-one. The task of an online algorithm is to match each request immediately and irrevocably with one of the unused servers. In this paper, we pursue competitive analysis for two variants of the online metric matching problem. The first variant is a restriction where each server is placed at one of two positions, which is denoted by OMM([Formula: see text]). We show that a simple greedy algorithm achieves the competitive ratio of 3 for OMM([Formula: see text]). We also show that this greedy algorithm is optimal by showing that the competitive ratio of any deterministic online algorithm for OMM([Formula: see text]) is at least 3. The second variant is the online facility assignment problem on a line. In this problem, the metric space is a line, the servers have capacities, and the distances between any two consecutive servers are the same. We denote this problem by OFAL([Formula: see text]), where [Formula: see text] is the number of servers. We first observe that the upper and lower bounds for OMM([Formula: see text]) also hold for OFAL([Formula: see text]), so the competitive ratio for OFAL([Formula: see text]) is exactly 3. We then show lower bounds on the competitive ratio [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] for OFAL([Formula: see text]), OFAL([Formula: see text]) and OFAL([Formula: see text]), respectively.

scholarly journals Exact and Heuristic Algorithms for Routing AGV on Path with Precedence Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Liang Xu ◽  
Yao Wang ◽  
Lin Liu ◽  
Jiaxing Wang
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
Polynomial Time ◽  
Heuristic Algorithms ◽  
Exact Algorithm ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Automated Guided Vehicle ◽  
Np Complete

A new problem arises when an automated guided vehicle (AGV) is dispatched to visit a set of customers, which are usually located along a fixed wire transmitting signal to navigate the AGV. An optimal visiting sequence is desired with the objective of minimizing the total travelling distance (or time). When precedence constraints are restricted on customers, the problem is referred to as traveling salesman problem on path with precedence constraints (TSPP-PC). Whether or not it is NP-complete has no answer in the literature. In this paper, we design dynamic programming for the TSPP-PC, which is the first polynomial-time exact algorithm when the number of precedence constraints is a constant. For the problem with number of precedence constraints, part of the input can be arbitrarily large, so we provide an efficient heuristic based on the exact algorithm.

SCHEDULING TWO SALESMEN IN A NETWORK

1996 ◽  
Vol 07 (04) ◽  
pp. 353-358
Author(s):  
WILLIAM F. KLOSTERMEYER
Keyword(s):  
Metric Space ◽  
Complete Problem ◽  
Server Problem ◽  
Np Complete

The two-server problem is concerned with the movement of two servers to request points in a metric space. We consider an offline version of the problem in a graph in which the requests may be served in any order. A family of approximations algorithms is developed for this NP-complete problem.

scholarly journals An application and Parallel Tabu Search Algorithm for Solving the PTSP Under the OpenMP-MPI Environment

2020 ◽  
Author(s):  
Mohamed Abdellahi Amar ◽  
Walid Khaznaji
Keyword(s):  
Tabu Search ◽  
Traveling Salesman Problem ◽  
Search Algorithm ◽  
A Priori ◽  
Traveling Salesman ◽  
Deterministic Models ◽  
Expected Length ◽  
Np Complete ◽  
Parallel Tabu Search ◽  
Real World Problems

<div>This paper reviews some real-world problems modeling</div><div>as Probabilistic Traveling Salesman Problem (PTSP), by</div><div>presenting the important results found in the literature. It</div><div>illustrates the usefulness of the inclusion of probabilistic elements in deterministic models. We propose a new modeling of the PTSP by the deviations of the routing of a robot in order to avoid obstacles which are not foreseen in its path. The Probabilistic Traveling Salesman Problem(PTSP) is a variation of the classic Traveling Salesman Problem (TSP) where each node i is present</div><div>with probability pi. The solution for the PTSP consists in finding an a priori tour that visits all the cities that minimizes the expected length of the tour. From the litterateur the PTSP is NP-Complete, therefore the execution time is a prime factor in its resolution. In the last of his paper we present a new parallel Tabu search heuristic for solving PTSP by using the Open MPI environment.</div>

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