Ones Assignment Method For Solving Traveling Salesman Problem

Abstract

This paper presents an approach namely, ones assignment method, for solving the traveling salesman problem. We have previously used this method for the assignment problem. We have slightly modified the procedure to get a tour of the traveling salesman problem. First we define the distance matrix, then by using determinant representation we obtain a reduced matrix which has at least one 1 in each row and each column. Then by using the new method, we obtain an optimal solution for traveling salesman problem by assigning ones to each row and each column. The new method is based on creating some ones in the distance matrix and then try to find a complete solution to their ones. At the end, this method is illustrated with some numerical examples.

Gezgi̇n Satici Problemi̇ni̇n Çözümü İçi̇n Macar Algori̇tmasi Esasli Yeni̇ Bi̇r Çözüm Yaklaşimi

“…Lucena (1990) (Nayak vd., 2017). Basirzadeh (2014) atama yaklaşımı ile asimetrik GSP için bir çözüm yaklaşımı önermiş ve iki küçük örnek üzerinde önerilen yöntemin çözümlerini göstermiştir. Mondal vd.…”

Neutrosophic Assignment Problem via BnB Algorithm

“…3 Assignment Method [6,8,9,11,12] Mathematically a TFNAP is formulated as minimize z= n i=1 n j =1 (C ij ) I where i = 1, 2, 3, ., ., ., .n, j = 1, 2, 3, ., ., ., .n Subject to…”

“…Researchers like Chen [6], Chen Liang-Hsuan et al [5], and Long-Sheng Huang et al [10] have explored various concepts for solving assignment problems. Ones assignment method for unraveling assignment problems was put forth by Hadi Basirzadeh [8]. Yager [16] has introduced a new method to rank the fuzzy subsets of unit interval.…”

Solving Fuzzy Transportation Problem: Exploring a Novel Particle Swarm Optimization Approach

“…A Fuzzy Transportation Problem (FTP) is a variation of the traditional Transportation Problem in which the transportation cost, supply and demand are fuzzy quantities [4]. There are several researches relied on fuzzy environment, proving that fuzzy decision-making method is becoming paramount.…”