THE PRECEDENCE CONSTRAINED TRAVELING SALESMAN PROBLEM

Solving Precedence Constraint Traveling Salesman Problem using Genetic Algorithm

Traveling Salesman Problem (TSP) is an NP-hard Problem, which has so many different real life applications. Precedence Constraint TSP (PCTSP) is one specific type of TSP in which precedence is given to some cities. PCTSP also has numerous applications. Genetic Algorithms [1] are robust and probabilistic search algorithms based on the mechanics of natural selection and survival of fittest. This ...

A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints a Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints

In this article we consider a variant of the classical asymmetric traveling salesman problem (ATSP), namely the ATSP in which precedence constraints require that certain nodes must precede certain other nodes in any feasible directed tour. This problem occurs as a basic model in scheduling and routing and has a wide range of applications varying from helicopter routing 25], sequencing in exible...

The traveling salesman problem

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...

A Heuristic for the Resource-Constrained Traveling Salesman Problem

The Resource-Constrained Traveling Salesman Problem (RCTSP) is formulated as follows. A set of n cities is given (denoted by V ); travelling from city i to city j incurs cost cij as well as resource consumption rij . The objective is to find a minimum cost Hamilton cycle (or tour) that consumes not more than Rmax units of the resource, where Rmax is some constant. The cost (resource consumption...