Case study on travelling salesman problem

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Analysis Of The Travelling Salesman Problem

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Analysis Of The Travelling Salesman Problem |

Travelling salesman problem is a problem of combinatorial optimization. The goal of the travelling salesman is to find a cycle in a complete weighted graph, which goes through all its vertices and its cost is minimal. More formally: to find a minimal Hamiltonian circuit in a complete weighted graph. There are many cities in the given country and the travelling salesman has to visit all of them and return to his family in the original city.
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Travelling salesman problem

Step 1 : Solve the problem as an assignment problem. Step 2 : Check for a complete cycle or alternative cycles. If the cycle is complete, Go to Step 4. If not, go to the Step 3.
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The distribution of goods concerns, in a given time period, of a set of customers by a set of vehicles, which are located in one or more depots, are operated by a set of crews drivers and perform their movements by using an appropriate road network. In particular, the solution of VRP calls for the determination of a set of routes, each performed by a single vehicle that starts and ends at its own depot, such that all requirements of the customers are fulfilled, all operational constraints are satisfied, and the global transportation cost is minimized. VRPs are multi-objective in nature and these objectives are conflicting preventing simultaneous optimization in general. It means that one objective is optimized at the cost of other objective. Today, exact VRP methods have a size limit of orders depending on the VRP variant and the time-response requirements.
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