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 Modelling and Prediction of Monthly Global Irradiation Using Different Prediction Models

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2332
Author(s):  
Cecilia Martinez-Castillo ◽  
Gonzalo Astray ◽  
Juan Carlos Mejuto
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Random Forests ◽  
Prediction Models ◽  
Meteorological Station ◽  
Ann Model ◽  
Global Irradiation ◽  
Artificial Neural ◽  
Input Variables ◽  
Using Data

Different prediction models (multiple linear regression, vector support machines, artificial neural networks and random forests) are applied to model the monthly global irradiation (MGI) from different input variables (latitude, longitude and altitude of meteorological station, month, average temperatures, among others) of different areas of Galicia (Spain). The models were trained, validated and queried using data from three stations, and each best model was checked in two independent stations. The results obtained confirmed that the best methodology is the ANN model which presents the lowest RMSE value in the validation and querying phases 1226 kJ/(m2∙day) and 1136 kJ/(m2∙day), respectively, and predict conveniently for independent stations, 2013 kJ/(m2∙day) and 2094 kJ/(m2∙day), respectively. Given the good results obtained, it is convenient to continue with the design of artificial neural networks applied to the analysis of monthly global irradiation.

scholarly journals Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maha Ata Al-Furhud ◽  
Zakir Hussain Ahmed
Keyword(s):  
Genetic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Genetic Algorithm ◽  
Travelling Salesman ◽  
Complex Optimization ◽  
Problem Instances ◽  
Search Approach ◽  
Multiple Travelling Salesman Problem

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.

EXTENDED DAILY EXCHANGE RATES FORECASTS USING WAVELET TEMPORAL RESOLUTIONS

2005 ◽  
Vol 01 (01) ◽  
pp. 79-107 ◽  
Author(s):  
MAK KABOUDAN
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Exchange Rate ◽  
Random Walk ◽  
Genetic Programming ◽  
Exchange Rates ◽  
Us Dollar ◽  
Artificial Neural ◽  
Japanese Yen ◽  
The One

Applying genetic programming and artificial neural networks to raw as well as wavelet-transformed exchange rate data showed that genetic programming may have good extended forecasting abilities. Although it is well known that most predictions of exchange rates using many alternative techniques could not deliver better forecasts than the random walk model, in this paper employing natural computational strategies to forecast three different exchange rates produced two extended forecasts (that go beyond one-step-ahead) that are better than naïve random walk predictions. Sixteen-step-ahead forecasts obtained using genetic programming outperformed the one- and sixteen-step-ahead random walk US dollar/Taiwan dollar exchange rate predictions. Further, sixteen-step-ahead forecasts of the wavelet-transformed US dollar/Japanese Yen exchange rate also using genetic programming outperformed the sixteen-step-ahead random walk predictions of the exchange rate. However, random walk predictions of the US dollar/British pound exchange rate outperformed all forecasts obtained using genetic programming. Random walk predictions of the same three exchange rates employing raw and wavelet-transformed data also outperformed all forecasts obtained using artificial neural networks.

scholarly journals An Analysis of the Fitness Landscape of Travelling Salesman Problem

2016 ◽  
Vol 24 (2) ◽  
pp. 347-384 ◽  
Author(s):  
Mohammad-H. Tayarani-N. ◽  
Adam Prügel-Bennett
Keyword(s):  
Principal Component Analysis ◽  
Fitness Landscape ◽  
Travelling Salesman Problem ◽  
Principal Component ◽  
Component Analysis ◽  
Global Optimum ◽  
Local Optimum ◽  
Travelling Salesman ◽  
Local Optima ◽  
Expected Fitness

The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.

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,-.

Sign in / Sign up

Export Citation Format

Share Document