Paper here defines the Travelling Sales Man Problem(TSP) as a problem where Salesman desires to tour around a specified set of cities, and return to the starting city, covering the least total distance. TSP is a NP-hard problem for reducing their complexity we use the different type of techniques. TSP can be solved by multiple techniques such as Parallel search-and-learn technique, Hybrid Metho...

Ant Colony optimization has proved suitable to solve a wide range of combinatorial optimization (or NP-hard) problems as the Travelling Salesman Problem (TSP). The first step of ACO algorithm is to set the parameters that drive the algorithm. The parameter has an important impact on the performance of the ant colony algorithm. The basic parameters that are used in ACO algorithms are; the relati...

We extend our previous work on complexity indices for the travelling salesman problem (TSP) using graph spectral techniques of data mining. A complexity index is an invariant of an instance I by which we can predict the execution time of an exact algorithm for TSP for I. We consider the symmetric travelling salesman problem with instances I represented by complete weighted graphs G. Intuitively...

In the Generalized Traveling Salesman Problem (GTSP), given a weighted complete digraph D and a partition V1, . . . , Vk of the vertices of D, we are to find a minimum weight cycle containing exactly one (at least one) vertex from each set Vi, i = 1, . . . , k. Assignment Problem based approaches are extensively used for the Asymmetric TSP. To use analogs of these approaches for the GTSP, we ne...

The Traveling Salesman Problem (TSP) is a classical problem in discrete optimization. Its paradigmatic character makes it one of the most studied in computer science and operations research and one for which an impressive amount of algorithms (in particular heuristics and approximation algorithms) have been proposed. While in the general case the problem is known not to allow any constant ratio...

Travelling salesman problem (TSP) is a combinatorial optimization problem. It is NP hard problem and TSP is the most intensively studied problem in the area of optimization. There are a number of approximation algorithms and heuristics proposed in the literature which can yield to good solutions. But with the increase in the number of cities, the complexity of the problem goes on increasing. Th...

Genetic algorithms (GAs) are powerful heuristic search techniques that used successfully to solve problems for many different applications. Seeding the initial population is considered as first step of GAs. In this work, a new method proposed, seeding called Multi Linear Regression Based Technique (MLRBT). That divides given large scale TSP problem into smaller sub-problems and technique works ...

Travelling Salesman Problem (TSP) is the problem for finding shortest route starting from start node then visiting number of nodes exactly once and finally go back to node. If a TSP has lot nodes, it will be NP-Hard Problem. Algorithms working based on heuristic metaheuristic can solution solving Savings Algorithm algorithm, so it’s may not best solution, therefore there chance improve it. Gene...

This study presents a novel problem called green travelling salesman problem (GTSP), an extension of the classical travelling salesman problem (TSP). Proposed GTSP considers not just for the route distance, also accounts emitted CO2, consumed fuel, travelling times/speed and their costs with a more comprehensive objective function. The aim of this study is to shed light on the trade-offs betwee...