scholarly journals A branch-and-cut and MIP-based heuristics for the Prize-Collecting Travelling Salesman Problem

2020 ◽  
Author(s):  
Glaubos Climaco ◽  
Luidi Simonetti ◽  
Isabel Rosseti
Keyword(s):  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Minimum Amount ◽  
Travelling Salesman ◽  
Travel Costs ◽  
Prize Collecting

The Prize Collecting Traveling Salesman Problem (PCTSP) represents a generalization of the well-known Traveling Salesman Problem. The PCTSP can be associated with a salesman that collects a prize in each visited city and pays a penalty for each unvisited city, with travel costs among the cities. The objective is to minimize the sum of the costs of the tour and penalties, while collecting a minimum amount of prize. This paper suggests MIP-based heuristics and a branch-and-cut algorithm to solve the PCTSP. Experiments were conducted with instances of the literature, and the results of our methods turned out to be quite satisfactory.

The Algorithm Animation of Genetic Algorithm of Travelling Salesman Problem

2013 ◽  
Vol 411-414 ◽  
pp. 2013-2016 ◽  
Author(s):  
Guo Zhi Wen
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Algorithm Animation ◽  
The Traveling Salesman Problem

The traveling salesman problem is analyzed with genetic algorithms. The best route map and tendency of optimal grade of 500 cities before the first mutation, best route map after 15 times of mutation and tendency of optimal grade of the final mutation are displayed with algorithm animation. The optimal grade is about 0.0455266 for the best route map before the first mutation, but is raised to about 0.058241 for the 15 times of mutation. It shows that through the improvements of algorithms and coding methods, the efficiency to solve the traveling problem can be raised with genetic algorithms.

scholarly journals Implementasi Algoritma Genetika dan Google Maps API Dalam Penyelesaian Traveling Salesman Problem with Time Window (TSP-TW) Pada Penjadwalan Rute Perjalanan Divisi Pemasaran STMIK El Rahma

Teknika ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 110-118
Author(s):  
Herdiesel Santoso ◽  
Rachmad Sanuri
Keyword(s):  
Traveling Salesman Problem ◽  
Time Window ◽  
Travelling Salesman Problem ◽  
Time Windows ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Google Maps

Divisi pemasaran STMIK El Rahma memiliki permasalahan dengan penjadwalan rute kunjungan ketika harus melakukan perjalanan multi destinasi ke sekolah-sekolah untuk melakukan promosi. Perjalanan multi destinasi dengan mempertimbangkan waktu kunjungan merupakan permasalahan Travelling Salesman Problem with Time Windows (TSP-TW). Algoritma Genetika merupakan salah satu metode pencarian yang dapat digunakan untuk memberikan rute perjalanan yang optimal. Rekomendasi yang diberikan tidak hanya mempertimbangkan jarak tetapi juga waktu tempuh didapatkan menggunakan Google Maps API. Skenario pengujian yang dilakukan adalah pengujian banyak generasi optimal, pengujian banyak populasi optimal, pengujian kombinasi probabilitas crossover (Pc) dan proabilitas mutasi (Pm), serta pengujian konsistensi solusi yang dihasilkan Algoritma Genetika. Hasil pengujian menunjukan bahwa jumlah individu terbaik adalah 150 individu dalam satu populasi. Kriteria berhenti jika setelah 127 generasi berturut-turut didapatkan nilai fitness tertinggi yang tidak berubah dan kombinasi probabilitas crossover dan probabilitas mutasi yang paling optimal adalah {0.3 : 0.7}.

scholarly journals Multi Integer Linear Programming and the Traveling Salesman Problem

2021 ◽  
Vol 9 (VI) ◽  
pp. 2417-2421
Author(s):  
S. Sathyapriya
Keyword(s):  
Linear Programming ◽  
Traveling Salesman Problem ◽  
Integer Linear Programming ◽  
Travelling Salesman Problem ◽  
Initial Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Integer Problem ◽  
The Traveling Salesman Problem

The Travelling Salesman problem is considered as a binary integer problem. For this problem, several stop variables and subtours are discussed. The stops are generated and the distance between those stops are found, consequently the graphs are drawn. Further the variables are declared and the constraints are framed. Then the initial problem is visualised along with the subtour constraints in order to achieve the required output.

scholarly journals GENETIC ALGORITHM FOR OPTIMIZING DISTRIBUTION WITH ROUTE RESTRICTION CONSTRAINT DUE TO TRAFFIC JAMS

2020 ◽  
Vol XLIV-4/W3-2020 ◽  
pp. 295-301
Author(s):  
N. Mouttaki ◽  
J. Benhra ◽  
G. Rguiga
Keyword(s):  
Genetic Algorithm ◽  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Classical Problem ◽  
Traveling Salesman ◽  
Travelling Salesman ◽  
Simple Method ◽  
Traffic Jams ◽  
Better Than

Abstract. The Travelling Salesman Problem (TSP) is a classical problem in combinatorial optimization that consists of finding the shortest tour through all cities such that the salesman visits each city only one time and returns to the starting city. Genetic algorithm is one of the powerful ways to solve problems of traveling salesman problem TSP. The current genetic algorithm aims to take in consideration the constraints happening during the execution of genetic algorithm, such as traffic jams when solving TSP. This program has two important contributions. First one is proposing simple method into taking in consideration an inconvenient route linked to traffic jams. The second one is the use of closeness strategy during the initialization step, which can accelerate the execution time of the algorithm.The results of the experiments show that the improved algorithm works better than some other algorithms. The conclusion ends the analysis with recommendations and future works.

scholarly journals Travelling Salesman Problem Analysis with Complete Enumeration Method, Branch & Bound and Greedy Heuristic

2021 ◽  
Vol 1 (8) ◽  
pp. 752-756
Author(s):  
Ifham Azizi Surya Syafiin ◽  
Sarah Nur Fatimah ◽  
Muchammad Fauzi
Keyword(s):  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Greedy Heuristic ◽  
Problem Analysis ◽  
Heuristic Methods ◽  
Travelling Salesman ◽  
Complete Enumeration ◽  
The Traveling Salesman Problem ◽  
The City

PT XYZ as the best and largest Bed Sheet Set company in Indonesia with products such as Bed Covers, Bed Sheets, Pillowcases, Bolsters and Blankets. The Traveling Salesman Problem (TSP) is a problem faced in finding the best route to visit shops that sell products from PT BIG. A visit to the shop is carried out on the condition that each city can only be visited once except the city of origin. The algorithms applied in this TSP problem include the Complete Enumeration, Branch & Bound and Greedy Heuristic methods.

Metaheuristics Approaches for the Travelling Salesman Problem on a Spherical Surface

2021 ◽  
pp. 94-113
Author(s):  
Yusuf Sahin ◽  
Erdal Aydemir ◽  
Kenan Karagul ◽  
Sezai Tokat ◽  
Burhan Oran
Keyword(s):  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Spherical Surface ◽  
Travelling Salesman Problem ◽  
Traveling Salesman ◽  
Heuristic Methods ◽  
Approximate Algorithms ◽  
Travelling Salesman ◽  
The Traveling Salesman Problem ◽  
Special Case

Traveling salesman problem in which all the vertices are assumed to be on a spherical surface is a special case of the conventional travelling salesman problem. There are exact and approximate algorithms for the travelling salesman problem. As the solution time is a performance parameter in most real-time applications, approximate algorithms always have an important area of research for both researchers and engineers. In this chapter, approximate algorithms based on heuristic methods are considered for the travelling salesman problem on the sphere. Firstly, 28 test instances were newly generated on the unit sphere. Then, using various heuristic methods such as genetic algorithms, ant colony optimization, and fluid genetic algorithms, the initial solutions for solving test instances of the traveling salesman problem are obtained in Matlab®. Then, the initial heuristic solutions are used as input for the 2-opt algorithm. The performances and time complexities of the applied methods are analyzed as a conclusion.

A branch-and-cut algorithm for the undirected prize collecting traveling salesman problem

Networks ◽  
2009 ◽  
Vol 54 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Jean-François Bérubé ◽  
Michel Gendreau ◽  
Jean-Yves Potvin
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Prize Collecting

scholarly journals Some Analytical Considerations Regarding the Traveling Salesman Problem Solved with Wolfram Mathematica Applications

2020 ◽  
pp. 68-77
Author(s):  
Bogdan-Vasile Cioruța ◽  
Alexandru Lauran ◽  
Mirela Coman
Keyword(s):  
Traveling Salesman Problem ◽  
Execution Time ◽  
Travelling Salesman Problem ◽  
Emergent Behavior ◽  
Traveling Salesman ◽  
Ant Colony Optimisation ◽  
Travelling Salesman ◽  
Wolfram Mathematica ◽  
Computational Program ◽  
The Traveling Salesman Problem

The paper presents an introduction to the Ant Colony Optimisation (ACO) algorithm and methods for solving the Travelling Salesman Problem (TSP). Documenting, understanding and knowledge of concepts regarding the emergent behavior and intelligence swarms optimization, easily led on solving the Travelling Salesman Problem using a computational program, such as Mathematics Wolfram via Creative Demostration Projects (*.cdf) module. The proposed application runs for a different number of ants, a different number of ants, a different number of leaders (elite ants), and a different pheromone evaporation index. As a result it can be stated that the execution time of the algorithm to solve the TSP is direct and strictly proportional to the number of ants, cities and elite ants considered, the increase of the execution time increasing significantly with the increase of the variables.

scholarly journals Prize Collecting Traveling Salesman Problem with Ridesharing

2020 ◽  
Vol 27 (2) ◽  
pp. 13-29
Author(s):  
Ygor Alcântara de Medeiros ◽  
Marco Cesar Goldbarg ◽  
Elizabeth Ferreira Gouvêa Goldbarg
Keyword(s):  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Mathematical Formulation ◽  
Maximum Amount ◽  
Traveling Salesman ◽  
Heuristic Methods ◽  
Travel Costs ◽  
Prize Collecting ◽  
The Cost ◽  
Capacitated Vehicle

The Prize Collecting Traveling Salesman Problem with Ridesharing is a model that joins elements from the Prize Collecting Traveling Salesman and the collaborative transport. The salesman is the driver of a capacitated vehicle and uses a ridesharing system to minimize travel costs. There are a penalty and a bonus associated with each vertex of a graph, G, that represents the problem. There is also a cost associated with each edge of G. The salesman must choose a subset of vertices to be visited so that the total bonus collection is at least a given a parameter. The length of the tour plus the sum of penalties of all vertices not visited is as small as possible. There is a set of persons demanding rides. The ride request consists of a pickup and a drop off location, a maximum travel duration, and the maximum amount the person agrees to pay. The driver shares the cost associated with each arc in the tour with the passengers in the vehicle. Constraints from ride requests, as well as the capacity of the car, must be satisfied. We present a mathematical formulation for the problem investigated in this study and solve it in an optimization tool. We also present three heuristics that hybridize exact and heuristic methods. These algorithms use a decomposition strategy that other enriched vehicle routing problems can utilize.

scholarly journals Using genetic algorithm to solve multiple traveling salesman problem and considering Carbon emissions

2020 ◽  
Vol 13 (36) ◽  
pp. 3707-3715
Author(s):  
Chris Jojo Obi ◽  
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Carbon Emission ◽  
Travelling Salesman Problem ◽  
Time Windows ◽  
Traveling Salesman ◽  
Transport Cost ◽  
Travelling Salesman ◽  
Insertion Method ◽  
Multiple Travelling Salesman Problem

Objectives: The Multiple Travelling Salesman problem is a complex combinatorial optimization problem which is a variance of the Traveling Salesman Problem,where a lot of salesmen are utilized in the solution. In this work a cold chain logistics and route optimization model with minimum transport cost, carbon cost and Refrigeration cost are constructed. Methods: A genetic algorithm is then proposed to solve for the Multiple Travelling Salesman Problem with time windows while transport cost, carbon emission cost and refrigeration cost is minimized. Findings: It was observed that the algorithm evolved towards the direction of the optimal value of the fitness function. Novelty: There are a number of studies that considered tournament selection strategy but just a few have applied genetic algorithm considering insertion method to solve a Multiple Travelling salesman Problem. This study uses insertion method to obtain optimal solution. Also, the researcher considered time windows, transport cost, carbon emission cost and refrigeration cost. Keywords: Genetic algorithm method; cold-logistics; multiple travelling salesman problem

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