Evaluating the Difficulty of Instances of the Travelling Salesman Problem in the Nearby of the Optimal Solution Based on Random Walk Exploration

2016 ◽  
pp. 299-310 ◽  
Author(s):  
Miguel Cárdenas-Montes
Keyword(s):  
Random Walk ◽  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Travelling Salesman

Slope-to-optimal-solution-based evaluation of the hardness of travelling salesman problem instances

2020 ◽  
Vol 28 (1) ◽  
pp. 45-57 ◽  
Author(s):  
Miguel Cárdenas-Montes
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Random Walk ◽  
Random Forests ◽  
Fitness Landscape ◽  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Travelling Salesman ◽  
Two Cities ◽  
Problem Instances

Abstract The travelling salesman problem is one of the most popular problems in combinatorial optimization. It has been frequently used as a benchmark of the performance of evolutionary algorithms. For this reason, nowadays practitioners request new and more difficult instances of this problem. This leads to investigate how to evaluate the intrinsic difficulty of the instances and how to separate ease and difficult instances. By developing methodologies for separating easy- from difficult-to-solve instances, researchers can fairly test the performance of their combinatorial optimizers. In this work, a methodology for evaluating the difficulty of instances of the travelling salesman problem near the optimal solution is proposed. The question is if the fitness landscape near the optimal solution encodes enough information to separate instances in function of their intrinsic difficulty. This methodology is based on the use of a random walk to explore the closeness of the optimal solution. The optimal solution is modified by altering one connection between two cities at each step, at the same time that the fitness of the altered solution is evaluated. This permits evaluating the slope of the fitness landscape. Later, and using the previous information, the difficulty of the instance is evaluated with random forests and artificial neural networks. In this work, this methodology is confronted with a wide set of instances. As a consequence, a methodology to separate the instances of the travelling salesman problem by their degree of difficulty is proposed and evaluated.

scholarly journals Optimasi Jumlah Produksi dan Biaya Distribusi UMKM Semprong Amoundy Menggunakan Metode Simpleks dan Algoritma Greedy

2021 ◽  
Vol 5 (1) ◽  
pp. 9
Author(s):  
Resa Nofatiyassari ◽  
Rianita Puspa Sari
Keyword(s):  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Production Optimization ◽  
Production Costs ◽  
Travelling Salesman ◽  
Optimal Amount ◽  
Distribution Costs ◽  
House Production ◽  
Distribution Cost ◽  
The Greedy Algorithm

Production optimization must be considered in order to get the optimal amount of production, which is related to company profit. In addition, the distribution route that is not optimal will also cause production costs to expand. These two things are the main problems faced by Semprong Amoundy MSMEs that have not paid attention to optimization of production and optimization of distribution routes. The purpose of this research is to find the optimal solution of the number and type of semprong production to maximize the income of Amoundy MSMEs, and to find a solution for the shortest distribution route to minimize distribution costs of semprong products. The method used to solve this problem is Simplex Method and Travelling Salesman Problem with the Greedy Algorithm approach. The research resulted the decision that Amoundy MSMEs had to produce 18 boxes of large packaged semprong every day to generate maximum income. The distribution route that must be taken to minimize distribution costs is Amoundy House Production – Bontot Delajaya Shop – Erik Shop – Denpasar Shop – Aneka Shop – Oleh-oleh Karawang Outlet – Amoundy House Production, estimated distribution cost of Rp. 20.120,-.Optimasi produksi perlu diperhatikan agar didapatkan jumlah produksi yang optimal, yang mana hal ini akan berhubungan dengan profit perusahaan. Selain itu rute distribusi yang belum optimal juga akan menyebabkan pembengkakan biaya produksi. Kedua hal ini merupakan masalah utama yang dihadapi oleh UMKM Semprong Amoundy yang belum memperhatikan optimasi produksi dan optimasi rute distribusi. Tujuan dilakukannya penelitian ini yaitu untuk mencari solusi optimal dari jumlah dan jenis produksi semprong untuk memaksimalkan pendapatan UMKM Amoundy, serta mencari solusi rute distribusi terpendek untuk meminimalkan biaya pendistribusian produk semprong. Metode yang digunakan untuk adalah Metode simpleks dan  Travelling Salesman Problem dengan pendekatan algoritma greedy. Penelitian menghasilkan keputusan bahwa UMKM Amoundy harus memproduksi 18 box kue semprong kemasan besar setiap hari untuk menghasilkan pendapatan maksimal. Rute distribusi yang harus ditempuh untuk meminimalkan biaya distribusi yaitu Rumah Produksi Amoundy – Toko Bontot Delajaya – Toko Erik – Toko Denpasar – Toko Aneka – Outlet Oleh-oleh Karawang – Rumah Produksi Amoundy dengan taksiran biaya distribusi sebesar Rp. 20.120,-.

scholarly journals Implementasi Simulated Annealing untuk Penentuan Rute pada Jaringan

MATICS ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 42-46
Author(s):  
Gusti Eka Yuliastuti ◽  
Citra Nurina Prabiantissa ◽  
Agung Mustika Rizki
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Computer Network ◽  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Network Routing ◽  
Path Selection ◽  
Travelling Salesman ◽  
Routing Problem ◽  
Stored Information

Abstract—Recently computer networks are increasingly complex. It needs to be a supporting device for network management such as a router. Router is a device that plays an important role in the routing process. In a router stored information in the form of routing paths, where the information includes data and which routers will be passed. In certain cases, a router can have more than one gateway. This is because the router needs to send data packets to several networks that have different segments. Such cases can be handled by using the appropriate routing path selection rules. The routing problem can be regarded as a traveling salesman problem (TSP), where a mechanism is needed to determine the shortest route to be traversed. The author implements the Simulated Annealing Algorithm because it can produce an optimal solution with light computing, so that the routing process can be more effective and efficient. Index Terms—Computer Network, Routing, Simulated Annealing, Travelling Salesman Problem Abstrak–-Jaringan komputer saat ini semakin kompleks. Perlu adanya suatu perangkat pendukung untuk manajemen jaringan seperti router. Router merupakan perangkat yang berperan penting dalam proses routing. Pada sebuah router tersimpan informasi berupa jalur routing, dimana informasi tersebut mencakup data dan router mana saja yang akan dilewati. Pada kasus tertentu, router dapat memiliki lebih dari satu gateway. Hal ini disebabkan karena router perlu mengirimkan paket data ke beberapa jaringan yang memiliki segmen berbeda. Kasus tersebut dapat ditangani dengan menggunakan aturan pemilihan jalur routing yang tepat. Permasalahan routing dapat dikatakan sebagai suatu permasalahan travelling salesman problem (TSP), dimana diperlukan suatu mekanisme dalam menentukan rute terpendek untuk dilalui. Penulis mengimplementasikan Algoritma Simulated Annealing karena dapat menghasilkan solusi yang optimal dengan komputasi ringan, sehingga proses routing dapat lebih efektif dan efisien. Kata Kunci—Jaringan Komputer, Penentuan Rute, Travelling Salesman Problem, Algoritma Simulated Annealing 

scholarly journals GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems

2019 ◽  
Vol 24 (10) ◽  
pp. 7197-7210
Author(s):  
Xiaolong Xu ◽  
Hao Yuan ◽  
Peter Matthew ◽  
Jeffrey Ray ◽  
Ovidiu Bagdasar ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithms ◽  
Travelling Salesman Problem ◽  
Natural Extension ◽  
Optimal Solution ◽  
Traffic Information ◽  
Travelling Salesman ◽  
Practical Applications ◽  
Real Time Traffic ◽  
Two Sides

Abstract The dynamic travelling salesman problem (DTSP) is a natural extension of the standard travelling salesman problem, and it has attracted significant interest in recent years due to is practical applications. In this article, we propose an efficient solution for DTSP, based on a genetic algorithm (GA), and on the one-by-one revision of two sides (GORTS). More specifically, GORTS combines the global search ability of GA with the fast convergence feature of the method of one-by-one revision of two sides, in order to find the optimal solution in a short time. An experimental platform was designed to evaluate the performance of GORTS with TSPLIB. The experimental results show that the efficiency of GORTS compares favourably against other popular heuristic algorithms for DTSP. In particular, a prototype logistics system based on GORTS for a supermarket with an online map was designed and implemented. It was shown that this can provide optimised goods distribution routes for delivery staff, while considering real-time traffic information.

scholarly journals Neutrosophic Triangular Fuzzy Travelling Salesman Problem Based on Dhouib-Matrix-TSP1 Heuristic

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Souhail Dhouib
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Travelling Salesman Problem ◽  
Numerical Test ◽  
Optimal Solution ◽  
Triangular Fuzzy Number ◽  
Travelling Salesman ◽  
Total Cost ◽  
Fuzzy Environment ◽  
Neutrosophic Number

In this paper, the Travelling Salesman Problem is considered in neutrosophic environment which is more realistic in real-world industries. In fact, the distances between cities in the Travelling Salesman Problem are presented as neutrosophic triangular fuzzy number. This problem is solved in two steps: At first, the Yager’s ranking function is applied to convert the neutrosophic triangular fuzzy number to neutrosophic number then to generate the crisp number. At second, the heuristic Dhouib-Matrix-TSP1 is used to solve this problem. A numerical test example on neutrosophic triangular fuzzy environment shows that, by the use of Dhouib-Matrix-TSP1 heuristic, the optimal or a near optimal solution as well as the crisp and fuzzy total cost can be reached.

scholarly journals Exact and Local Search Methods for Solving Travelling Salesman Problem with Practical Application

2019 ◽  
Vol 60 (5) ◽  
pp. 1138-1153
Author(s):  
Sajjad Majeed Jasim ◽  
Faez Hassan Ali
Keyword(s):  
Local Search ◽  
Travelling Salesman Problem ◽  
Optimal Solution ◽  
Search Method ◽  
Practical Application ◽  
Travelling Salesman ◽  
Search Methods ◽  
Total Cost ◽  
Local Search Methods ◽  
The Traveling Salesman Problem

This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA). The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with the existence of successive rules. The problem of the total cost of Iraqi cities was also discussed and solved by some methods in addition to local search methods to obtain the optimal solution.

Sign in / Sign up

Export Citation Format

Share Document