Definition The traveling salesman problem (TSP) is the following optimization problem. Given a complete graph G with edge costs, find a Hamiltonian cycle of minimum cost in G. Definition The metric traveling salesman problem (∆-TSP) is the TSP restricted to instances satisfying the triangle inequality Definition The traveling salesman problem (TSP) is the following optimization problem. Given a...

We present a genetic algorithm for solving the traveling salesman problem by genetic algorithms to optimality for traveling salesman problems with up to 442 cities. Mlihlenbein et al. [MGK 88], [MK 89] have proposed a genetic algorithm for the traveling salesman problem, which generates very good but not optimal solutions for traveling salesman problems with 442 and 531 cities. We have improved...

The traveling salesman problem (TSP) describes a salesman who needs to travel through a list of given cities exactly once by taking the shortest possible tour. The problem is NP-Complete since there are no known polynomial time algorithms to solve it. The main motivation to solve this problem is that the applications of Traveling Salesman are immense. It can be used by banks to find an optimal ...

This paper applies the multi-time window traveling salesman problem to not only optimize logistics cost, but also effectively endow users with multiple discrete idle optional time periods meet requirements of just-in-time production. In process solving, firstly, dynamic penalty factor is introduced into objective function and added relax constraints in order construct relaxation model. Secondly...

Abstract: Multiple traveling salesman problems (MTSP) are a typical computationally complex combinatorial optimization problem, which is an extension of the famous traveling salesman problem (TSP). The MTSP can be generalized to a wide variety of routing and scheduling problems. The paper makes the attempt to show how Genetic Algorithm (GA) can be applied to the MTSP with ability constraint. In...

This paper presented a mixed integer programming for integrated scheduling and process planning. The presented process plan included some orders with precedence relations similar to Multiple Traveling Salesman Problem (MTSP), which was categorized as an NP-hard problem. These types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...

The Generalized Traveling Salesman Problem is one of a well known complex combinatorial optimization problems. Equality-Generalized Traveling Salesman Problem is a particular case of it. Themain objective of the problem it is to find a minimum cost tour passing through exactly one node from each cluster of a large-scale undirected graph. Multi-agent approaches are successfully used nowadays for...