An Approximate Algorithm for Triangle TSP with a Four-Vertex-Three-Line Inequality

2015 ◽  
Vol 6 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Time Complexity ◽  
Optimization Problem ◽  
Nearest Neighbor ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Exact Algorithms ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
Approximate Algorithm ◽  
Nearest Neighbor Algorithm

Traveling salesman problem (TSP) is a classic combinatorial optimization problem. The time complexity of the exact algorithms is generally an exponential function of the scale of TSP. This work gives an approximate algorithm with a four-vertex-three-line inequality for the triangle TSP. The time complexity is O(n2) and it can generate an approximation less than 2 times of the optimal solution. The paper designs a simple algorithm with the inequality. The algorithm is compared with the double-nearest neighbor algorithm. The experimental results illustrate the algorithm find the better approximations than the double-nearest neighbor algorithm for most TSP instances.

scholarly journals Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Raymond Phillips ◽  
Matthew Woolway ◽  
Dario Fanucchi ◽  
M. Montaz Ali
Keyword(s):  
Branch And Bound ◽  
Optimization Problem ◽  
Float Glass ◽  
Exact Algorithms ◽  
Combinatorial Optimization Problem ◽  
Approximate Algorithm ◽  
Fixed Integer ◽  
Stock Size ◽  
Blank Generation ◽  
Selection Of

This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integerN, generally between 2 and 6 (but potentially larger), we find theNbest sizes for intermediate stock from which to cut a roster of orders. An objective function is formulated with the purpose of minimizing wastage, and the problem is phrased as a combinatorial optimization problem involving the selection of columns of a cost matrix. Some bounds and heuristics are developed, and two exact algorithms (depth-first search and branch-and-bound) are applied to the problem, as well as one approximate algorithm (NOMAD). It is found that wastage reduces dramatically asNincreases, but this trend becomes less pronounced for larger values ofN(beyond 6 or 7). For typical values ofN, branch-and-bound is able to find the exact solution within a reasonable amount of time.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

Performance Evaluation of Population Seeding Techniques of Permutation-Coded GA Traveling Salesman Problems Based Assessment

2021 ◽  
pp. 1074-1115
Author(s):  
Victer Paul ◽  
Ganeshkumar C ◽  
Jayakumar L
Keyword(s):  
Genetic Algorithms ◽  
Nearest Neighbor ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Computation Time ◽  
Search Space ◽  
Population Based ◽  
Vital Role ◽  
Traveling Salesman ◽  
Performance Criteria

Genetic algorithms (GAs) are a population-based meta-heuristic global optimization technique for dealing with complex problems with a very large search space. The population initialization is a crucial task in GAs because it plays a vital role in the convergence speed, problem search space exploration, and also the quality of the final optimal solution. Though the importance of deciding problem-specific population initialization in GA is widely recognized, it is hardly addressed in the literature. In this article, different population seeding techniques for permutation-coded genetic algorithms such as random, nearest neighbor (NN), gene bank (GB), sorted population (SP), and selective initialization (SI), along with three newly proposed ordered-distance-vector-based initialization techniques have been extensively studied. The ability of each population seeding technique has been examined in terms of a set of performance criteria, such as computation time, convergence rate, error rate, average convergence, convergence diversity, nearest-neighbor ratio, average distinct solutions and distribution of individuals. One of the famous combinatorial hard problems of the traveling salesman problem (TSP) is being chosen as the testbed and the experiments are performed on large-sized benchmark TSP instances obtained from standard TSPLIB. The scope of the experiments in this article is limited to the initialization phase of the GA and this restricted scope helps to assess the performance of the population seeding techniques in their intended phase alone. The experimentation analyses are carried out using statistical tools to claim the unique performance characteristic of each population seeding techniques and best performing techniques are identified based on the assessment criteria defined and the nature of the application.

scholarly journals An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yong Deng ◽  
Yang Liu ◽  
Deyun Zhou
Keyword(s):  
Genetic Algorithm ◽  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
Average Error ◽  
Initial Population ◽  
Improved Genetic Algorithm ◽  
Population Strategy ◽  
Series Of Experiments

A new initial population strategy has been developed to improve the genetic algorithm for solving the well-known combinatorial optimization problem, traveling salesman problem. Based on thek-means algorithm, we propose a strategy to restructure the traveling route by reconnecting each cluster. The clusters, which randomly disconnect a link to connect its neighbors, have been ranked in advance according to the distance among cluster centers, so that the initial population can be composed of the random traveling routes. This process isk-means initial population strategy. To test the performance of our strategy, a series of experiments on 14 different TSP examples selected from TSPLIB have been carried out. The results show that KIP can decrease best error value of random initial population strategy and greedy initial population strategy with the ratio of approximately between 29.15% and 37.87%, average error value between 25.16% and 34.39% in the same running time.

Comparison of Heuristics for Resolving the Traveling Salesman Problem with Information Technology

2014 ◽  
Vol 886 ◽  
pp. 593-597 ◽  
Author(s):  
Wei Gong ◽  
Mei Li
Keyword(s):  
Information Technology ◽  
Traveling Salesman Problem ◽  
Spanning Tree ◽  
Nearest Neighbor ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Problem Class ◽  
The Traveling Salesman Problem ◽  
Random Insertion

Traveling Salesman Problem (Min TSP) is contained in the problem class NPO. It is NP-hard, means there is no efficient way to solve it. People have tried many kinds of algorithms with information technology. Thus in this paper we compare four heuristics, they are nearest neighbor, random insertion, minimum spanning tree and heuristics of Christofides. We dont try to find an optimal solution. We try to find approximated short trips via these heuristics and compare them.

scholarly journals Traveling Salesman Should not be Greedy: Domination Analysis of Greedy-Type Heuristics for the TSP

2001 ◽  
Vol 8 (6) ◽  
Author(s):  
Gregory Gutin ◽  
Anders Yeo ◽  
Alexey Zverovich
Keyword(s):  
Greedy Algorithm ◽  
Nearest Neighbor ◽  
Sharp Contrast ◽  
Traveling Salesman ◽  
Acceptable Level ◽  
Computational Experiments ◽  
Nearest Neighbor Algorithm ◽  
Domination Analysis ◽  
The Greedy Algorithm

<p>Computational experiments show that the greedy algorithm (GR)<br />and the nearest neighbor algorithm (NN), popular choices for tour <br />construction heuristics, work at acceptable level for the Euclidean TSP,<br />but produce very poor results for the general Symmetric and Asymmetric<br /> TSP (STSP and ATSP). We prove that for every n >= 2 there<br />is an instance of ATSP (STSP) on n vertices for which GR finds the<br />worst tour. The same result holds for NN. We also analyze the repetitive<br /> NN (RNN) that starts NN from every vertex and chooses the best<br />tour obtained. We prove that, for the ATSP, RNN always produces<br />a tour, which is not worse than at least n/2 − 1 other tours, but for<br />some instance it finds a tour, which is not worse than at most n − 2<br />other tours, n >= 4. We also show that, for some instance of the STSP<br />on n >= 4 vertices, RNN produces a tour not worse than at most 2^(n−3) tours. These results are in sharp contrast to earlier results by G. Gutin and A. Yeo, and A. Punnen and S. Kabadi, who proved that, for the ATSP, there are tour construction heuristics, including some popular ones, that always build a tour not worse than at least (n − 2)! tours.</p><p>Keywords: TSP, domination analysis, greedy algorithm, nearest<br />neighbor algorithm</p>

scholarly journals Genetiniai algoritmai komivojažieriaus uždaviniui: negatyvieji ir pozityvieji aspektai*

2009 ◽  
Vol 50 ◽  
pp. 173-180
Author(s):  
Alfonsas Misevičius ◽  
Andrius Blažinskas ◽  
Jonas Blonskis ◽  
Vytautas Bukšnaitis
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Optimization Problem ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
High Quality ◽  
Genetic Search ◽  
Local Improvement ◽  
Effi Ciency ◽  
The Traveling Salesman Problem

Šiame straipsnyje nagrinėjami klausimai, susiję su genetinių algoritmų taikymu, sprendžiant gerai žinomą kombinatorinio optimizavimo uždavinį – komivojažieriaus uždavinį (KU) (angl. traveling salesman problem). Svarstoma, jog genetinio algoritmo efektyvumui didelę įtaką turi uždavinio specifi nės savybės, todėl labai svarbu kūrybiškai sudaryti genetinį algoritmą konkrečiam sprendžiamam uždaviniui. Pateikiami eksperimentų, atliktų su realizuotu genetiniu algoritmu, rezultatai, iliustruojantys skirtingų veiksnių įtaką rezultatų kokybei. Konstatuojama, kad tinkamas genetinių operatorių ir lokaliojo individų (sprendinių) gerinimo derinimas leidžia gerokai padidinti genetinės paieškos efektyvumą.On the Genetic Algorithms for the Traveling Salesman Problem: Negative and Positive AspectsAlfonsas Misevičius, Andrius Blažinskas, Jonas Blonskis, Vytautas Bukšnaitis SummaryIn this paper, we discuss some issues related to the application of genetic algorithms (GAs) to the well-known combinatorial optimization problem – the traveling salesman problem (TSP). The results obtained from the experiments with the different variants of the genetic algorithm are presented as well. Based on these results, it is concluded that the effi ciency of the genetic search is much infl uenced by both the specifi c nature of the problem and the features of the algorithm itself. In particular, it should be emphasized that the incorporation of the (postcrossover) procedures for the local improvement of offspring has one of the crucial roles in obtaining high-quality solutions.

Performance Evaluation of Population Seeding Techniques of Permutation-Coded GA Traveling Salesman Problems Based Assessment

2019 ◽  
Vol 10 (2) ◽  
pp. 55-92 ◽  
Author(s):  
Victer Paul ◽  
Ganeshkumar C ◽  
Jayakumar L
Keyword(s):  
Genetic Algorithms ◽  
Nearest Neighbor ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Computation Time ◽  
Search Space ◽  
Population Based ◽  
Vital Role ◽  
Traveling Salesman ◽  
Performance Criteria

Genetic algorithms (GAs) are a population-based meta-heuristic global optimization technique for dealing with complex problems with a very large search space. The population initialization is a crucial task in GAs because it plays a vital role in the convergence speed, problem search space exploration, and also the quality of the final optimal solution. Though the importance of deciding problem-specific population initialization in GA is widely recognized, it is hardly addressed in the literature. In this article, different population seeding techniques for permutation-coded genetic algorithms such as random, nearest neighbor (NN), gene bank (GB), sorted population (SP), and selective initialization (SI), along with three newly proposed ordered-distance-vector-based initialization techniques have been extensively studied. The ability of each population seeding technique has been examined in terms of a set of performance criteria, such as computation time, convergence rate, error rate, average convergence, convergence diversity, nearest-neighbor ratio, average distinct solutions and distribution of individuals. One of the famous combinatorial hard problems of the traveling salesman problem (TSP) is being chosen as the testbed and the experiments are performed on large-sized benchmark TSP instances obtained from standard TSPLIB. The scope of the experiments in this article is limited to the initialization phase of the GA and this restricted scope helps to assess the performance of the population seeding techniques in their intended phase alone. The experimentation analyses are carried out using statistical tools to claim the unique performance characteristic of each population seeding techniques and best performing techniques are identified based on the assessment criteria defined and the nature of the application.

An Novel Estimation of Distribution Algorithm for TSP

2013 ◽  
Vol 373-375 ◽  
pp. 1089-1092
Author(s):  
Fa Hong Yu ◽  
Wei Zhi Liao ◽  
Mei Jia Chen
Keyword(s):  
Optimization Problem ◽  
Population Diversity ◽  
Combinatorial Optimization Problem ◽  
Estimation Of Distribution Algorithm ◽  
Traveling Salesman ◽  
Estimation Of Distribution Algorithms ◽  
Np Hard ◽  
Estimation Of Distribution ◽  
Np Hard Problem ◽  
Distribution Algorithms

Estimation of distribution algorithms (EDAs) is a method for solving NP-hard problem. But it is hard to find global optimization quickly for some problems, especially for traveling salesman problem (TSP) that is a classical NP-hard combinatorial optimization problem. To solve TSP effectively, a novel estimation of distribution algorithm (NEDA ) is provided, which can solve the conflict between population diversity and algorithm convergence. The experimental results show that the performance of NEDA is effective.

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