Crossover operator plays a crucial role in the efficiency of genetic algorithm (GA). Several crossover operators have been proposed for solving the travelling salesman problem (TSP) in the literature. These operators have paid less attention to the characteristics of the traveling salesman problem, and majority of these operators can only generate feasible solutions. In this paper, a crossover ...

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...

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to th...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. Key-Words: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing. (Forthco...

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into so-called clusters, and the salesman has to visit every cluster exactly once. While the GTSP is a very important combinatorial optimization problem and is well stud...

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to th...

The attempts to use mobile robots in a variety of environments are currently being limited by their navigational capability, thus a set of robots must be configured for one specific environment. The problem of navigating an environment is the fundamental problem in mobile robotic where various methods including exact and heuristic approaches have been proposed to solve the problem. This paper p...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. KeyWords: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing.

Traveling Salesman Problems with Profits (TSPs with Profits) are a generalization of the Traveling Salesman Problem (TSP) where it is not necessary to visit all vertices. With each vertex is associated a profit. The objective is to find a route with a satisfying collected profit (maximized) and travel cost (minimized). Applications of these problems arise in contexts such as traveling salesman ...

The traveling salesman problem (TSP) is one of the most intensively studied problems in computational mathematics and combinatorial optimization. It is also considered as the class of the NPcomplete combinatorial optimization problems. By literatures, many algorithms and approaches have been launched to solve such the TSP. However, no current algorithms that can provide the exactly optimal solu...