Vehicle routing problem (VRP) is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, to provide the efficient vehicle serving to the customer through different services by visiting the number of cities or stops, the VRP follows the Travelling Salesman Problem (TSP), in which each of vehicle visiting a set of cities such that every city is vis...

We describe a hybrid meta-heuristic algorithm for combinatorial optimization problems with a specific reference to the travelling salesman problem (TSP). The method is a combination of a genetic algorithm (GA) and greedy randomized adaptive search procedure (GRASP). A new adaptive fuzzy a greedy search operator is developed for this hybrid method. Computational experiments using a wide range of...

The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Corresp...

Travelling salesman problem is a NP complete problem and can be solved using approximation algorithm. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once. Often, the model is a complete graph. An algorithm that returns near-optimal solutions is called approximation algorithms. Through analyzing the Metric TSP the performa...

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with [Formula: see text], the objective function sums the costs for travelling from one city to each of the next q cities in the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic a...

We consider the travelling salesman problem (TSP) problem on (the metric completion of) 3-edge-connected cubic graphs. These graphs are interesting because of the connection between their optimal solutions and the subtour elimination LP relaxation. Our main result is an approximation algorithm better than the 3/2-approximation algorithm for TSP in general. © 2004 Elsevier B.V. All rights reserved.

Some scheduling problems, including the Travelling Salesman Problem (TSP), have a “big valley” search landscape: the best solutions have common building blocks, so crossover works well. Unfortunately, in a realistic single-machine problem (TSP with batching, sequence-dependent setups, and multi-level precedence constraints) the best solutions have little in common. A mutation-only approach

The Travelling Salesman problem is one of the most popular problems from the NP set, it is also one of the hardest too. The solution to this problem enjoys wide applicability in a variety of practical fields. Thus it highly raises the need for an efficient solution for this NP Hard problem. However even the most common deterministic solutions to the problem are known to possess an exponential t...

It is known that in case the distance matrix in the Travelling Salesman Problem (TSP) fulllls certain combinatorial conditions (e.g. the Demidenko conditions , the Kalmanson conditions or the Supnick conditions) then the TSP is solvable in polynomial time. This paper deals with the problem of recognizing Euclidean instances of the TSP for which there is a renumbering of the cities such that the...