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.

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 Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Naila Rafiq ◽  
Naveed Yaqoob ◽  
Nasreen Kausar ◽  
Mudassir Shams ◽  
Nazir Ahmad Mir ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Real Life ◽  
Triangular Fuzzy Number ◽  
Test Problems

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.

scholarly journals Economic fish production inventory model for perishable fish items with the detoriation rate and the added value under pentagonal fuzzy number

2020 ◽  
Author(s):  
V. Kuppulakshmi ◽  
C. Sugapriya ◽  
D. Nagarajan
Keyword(s):  
Fuzzy Number ◽  
Economic Value ◽  
Constraint Equation ◽  
Added Value ◽  
Sensitivity Analyses ◽  
Fish Production ◽  
Annual Fish ◽  
Total Cost ◽  
Fuzzy Environment ◽  
Production Quantity

Abstract In marine fishing, a considerable planning is required for developing socio-economic value of fishermen. This research explores the discussion in optimal fish manufacturing quantity for perishable fish items in the vessel during yachting. The rate of deterioration is treated as a Pentagonal Fuzzy Number (PFN) to obtain the optimal total cost. The convexity of the model is proved by satisfying the constraint equation in a fuzzy environment. An efficient procedure is applied to find the annual fish production quantity and the production in a single period to avoid the faulty measurement in the demand for fish items and the supply to the retailers. In addition, a few sensitivity analyses are carried out for the repair cost and the added value cost to indicate the existence of the total cost in the least possible range. Some managerial discrimination is also included.

A MEMBERSHIP FUNCTION APPROACH FOR COST-RELIABILITY TRADE-OFF OF COTS SELECTION IN FUZZY ENVIRONMENT

2011 ◽  
Vol 18 (06) ◽  
pp. 573-595 ◽  
Author(s):  
PANKAJ GUPTA ◽  
SHILPI VERMA ◽  
MUKESH KUMAR MEHLAWAT
Keyword(s):  
Real World ◽  
Fuzzy Optimization ◽  
Delivery Time ◽  
Minimum Threshold ◽  
Trade Off ◽  
Total Cost ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
The Cost ◽  
Cots Selection

The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadeh's extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.

A Survey to Nature Inspired Soft Computing

2017 ◽  
Vol 8 (2) ◽  
pp. 112-133 ◽  
Author(s):  
Deepak Kumar ◽  
Sushil Kumar ◽  
Rohit Bansal ◽  
Parveen Singla
Keyword(s):  
Genetic Algorithms ◽  
Particle Swarm Optimization ◽  
Real World ◽  
Firefly Algorithm ◽  
Travelling Salesman Problem ◽  
Cuckoo Search ◽  
Travelling Salesman ◽  
Swarm Optimization ◽  
Physical Chemical ◽  
Time Problem

This article describes how swarm intelligence (SI) and bio-inspired techniques shape in-vogue topics in the advancements of the latest algorithms. These algorithms can work on the basis of SI, using physical, chemical and biological frameworks. The authors can name these algorithms as SI-based, inspired by biology, physics and chemistry as per the basic concept behind the particular algorithm. A couple of calculations have ended up being exceptionally effective and consequently have turned out to be the mainstream devices for taking care of real-world issues. In this article, the reason for this survey is to show a moderately complete list of the considerable number of algorithms in order to boost research in these algorithms. This article discusses Ant Colony Optimization (ACO), the Cuckoo Search, the Firefly Algorithm, Particle Swarm Optimization and Genetic Algorithms in detail. For ACO a real-time problem, known as Travelling Salesman Problem, is considered while for other algorithms a min-sphere problem is considered, which is well known for comparison of swarm techniques.

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 

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