In our paper, we have taken an Asymmetric Travelling Salesman problem only. There are various algorithms which can be implemented to find the shortest path for travelling salesmen. Some of them are meta-heuristic problems such as ant colony optimization, genetic algorithm, but in this paper, we have used a Nearest Neighbour algorithm to find the shortest path for the Travelling Salesman. It was the first algorithm to find the shortest path for Travelling salesman problem developed around 1950’s. The idea of this algorithm was given by J. G. Skellam and the later research work was done by P. J. Clark and F. C. Evans to find the shortest
In this one salesman has to travel a set of cities (exactly once) such that the total travel cost/distance/time is minimized. An extension of this problem is Vehicle Routing Problem (VRP). It was introduced by Dantzig and Ramser in 1959. It is the one of the problem in field of transportation that has been given a lot of attention nowadays. Fig.
The Traveling Salesman Problem (TSP) is defined by N cities and distance matrix D=d_(( i,j)N×N ) it gives distances between all cities. In TSP, the main object is to visit every city exactly once with in minimum distance . The tour can be as a cyclic permutation is π=(π(1),π(2)…π(N)) of cities from 1 to N if π(i) is interpreted to the city visited in step i,i=1,…N. The cost of tour is defined as: f(π)=∑_i^(N-1)▒〖d_(π(i)π(i+1))+d_(π(N)π(1)) 〗…………..(1) If the distance satisfies d_(i,j)=d_(j,i) for 1≤i,j≤N, it is the symmetric TSP. The vertices of the graph are cities and the graph edges are connections between cities.
The overall objective is to serve a set of customers at minimum cost with a fleet of vehicles of finite capacity operating out at a central depot (i.e. each route starts and ends at the depot). In this application, the objective is to minimize the number of routes and for the same number of routes, to minimize the total route time. To be feasible, the routes must also satisfy three different types of constraints. First, each customer has a certain demand, like a quantity of goods to be delivered.
The traveling salesman problem and genetic algorithms From Class I learned that genetic algorithms are search and optimization methods inspired by the evolution and genetic basis that it implies. For the use of an algorithm a set of possible solutions is generated (we will name each of these solutions "individuals")and our problem (called population), this population is mutated and recombined by random actions, as in evolution, they also undergo an assessment to decide which are the most suitable and separate them from the rest, which will be discarded. Throughout this paper I will try to explain how the problem of The Traveling Salesman can be solved by using a Genetic Algorithm (GA). The Traveling Salesman Problem (TSP) is easy to understand,
(O’Connor, 2008) Travel agents are no longer strangers to modern technologies. Travel agents presently use internet for managing reservations, accounting as well as inventory management systems. (Standing and Vasudavan, 1999) It is a very noticeable fact that travel agents nowadays try to maximise their productivity by involving themselves in collaborative product development with their partners. The industry focus on more customer relationship to sustain competitive advantage. Customer competence in the market can be considered as a key resource which helps the industry to attain this.
A salesman visits N cities with given positions and returns finally to his city of origin. Each city is to be visited only once, and the problem is to find the shortest possible route. In the field of the Travelling Salesman Problem (TSP), there are three main versions of TSP studied. The type of problem depends on how the input function is given Euclidian symmetric or asymmetric, or random distance matrixes. The term Euclidian comes from the representation of each city and the distance of the edges between them.
These solutions can be expressed in terms of non-dominated solutions, non-inferior, admissible, or efficient solutions. Therefore, the aim of this paper is to develop a solution method for the proposed problem that search a set of non-dominated solutions. Since problem under study belong to NP-hard class (Ruiz and Marato, 2006), the exact method is not able to provide feasible solutions even for small instances in a reasonable time. This incapacity justifies the need to employ a variety of heuristics and meta-heuristics to solve these problems to optimality or near optimality. In this paper, a genetic algorithm (GA) is proposed to solve our investigated problem.
Genetic Algorithms(GAs) The theory of Genetic Algorithms first was envisaged by Professor John Holland of the University of Michigan in the early 1970s in one of its seminal work. Two main goals of that work were (1) explaining the adaptive processes of the natural system and (2) designing software that maintains the idea of natural systems . The main concept of Genetic Algorithms is the power of evolution using to solve search and optimization problems. Genetic Algorithms are adaptive heuristic search and optimization methods which mimic the evolutionary ideas of natural selection and natural genetics. Moreover, they are part of Evolutionary Algorithms.
There are estimation methods ranging from old classical models to current machine learning methods. These models are purely based on either linear regression or non-linear regression. Such models take only size of the project as input  . One example of such model is COCOMO. COCOMO and SLIM models are also known as empirical models and these are the popular models .