International Journal of Engineering Trends and Applications (IJETA) – Volume 8 Issue 3, May-Jun 2021 ISSN: 2393-9516 www.ijetajournal.org Page 36 A Review: Optimized Solutions for Travelling Sales Person Problem Tejinder Kaur, Dr. Anil Kumar Lamba, Dr. Rajneesh Talwar Assistant Professor, Prof. & Head, HOD CSE Director Department of Computer Science and Engineering, Chandigarh Group of College Jhanjeri, Mohali – India ABSTRACT Travelling sales person or simply TSP problem is one of the most common problems related to many research areas to find out direct route. The main aim of this problem is to search the shortest tour for a salesman to visit all cities exactly once and return back to the starting city. This paper presents review of different algorithms used to solve travelling salesmen problem previously discussed.There are different algorithms reviewed in this paper like Genetic algorithm, Ant Colony algorithm, Bee colony algorithm, Neural networks based Genetic algorithm, Particle Swarm Optimization Technique and M-crossover operator etc. Keywords: -Travelling Salesman Problem, Genetic Algorithm, Ant Colony Algorithm, Bee Colony Algorithm, Lin– Kernighan algorithm. I. INTRODUCTION Traveling Salesman Problem The traveling salesman problem was studied in the 18th century by a mathematician from Ireland named Sir William Rowam Hamilton and by the British mathematician named Thomas PenyngtonKirkman. The traveling salesman problem is one which has commanded much attention of mathematicians and computer scientists specifically because it is very much easy to describe the problem but much more difficult to solve this problem.The problem can be stated as: “If a traveling salesman wishes to visit exactly once each of a list of m cities andthen return to the home city, what should be the least costly and smallest route the traveling salesman can take.” There are many researchers who solved TSP with different algorithms is discussed below: R. Baragliaet al (2001), Weimin Liu et al (2009) and Yu Yang et al (2010). Figure 1: Input nodes, Non optimized tour and Optimized tour. II. ALGORITHMS 1. Ant Colony Algorithm: Real ants are capable of finding the shortestpath from a food source to the nest without using visual cues. Also, theyare capable of adapting tochanges in the environment, e.g. finding a new shortest path once the oldone is no longer feasible due to a new obstacle. ConsiderFig. 2A: ants are moving on a straight line thatconnects a food source to their nest.This elementary behavior of real ants can be used toexplain how theycan find the shortest path thatreconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path (Fig. 2B). In fact, once the obstacle as appeared, those ants which are just infront of the obstacle cannot continue to followthe pheromone trail and therefore they have to choose between turning right or left. In thissituation it can be expected that half the ants to choose to turnright and the other half to turn left.A very similarsituation can be found on the other side of theobstacle (Fig. 2C). It is interesting to note thatthose ants which choose, by chance, the shorterpath around the obstacle will more rapidly reconstitute the interruptedpheromone RESEARCH ARTICLE OPEN ACCESS