A Lagrangian Based Approach for the Asymmetric Generalized Traveling Salesman Problem

An Approach for Solving Traveling Salesman Problem

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...

Memetic Algorithm for the Generalized Asymmetric Traveling Salesman Problem

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a new memetic algorithm for GTSP which clearly outperforms the state-of-the-art memetic algorit...

Asymmetric Traveling Salesman Problem

The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

The Asymmetric Traveling Salesman Problem

The Generalized Traveling Salesman Problem: A New Genetic Algorithm Approach

The Generalized Traveling Salesman Problem (GTSP) is a modification of the Traveling Salesman Problem in which nodes are partitioned into clusters and exactly one node from each cluster is visited in a cycle. It has numerous applications, including airplane routing, computer file sequencing, and postal delivery. To produce solutions to this problem, a genetic algorithm (GA) heuristic mimicking ...