Parallel genetic algorithms (PGAs) have been developed to reduce the large execution times that are associated with serial genetic algorithms (SGAs). They have also been used to solve larger problems and to find better solutions. In this paper, a comparative analysis of five different coarse-grained PGAs is conducted using the traveling salesman problem as the basis of this case study. To make ...

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...

This paper analyzes the elastic net approach (Durbin and Willshaw 1987) to the traveling salesman problem of finding the shortest path through a set of cities. The elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities. The tradeoff between these two require­ ments is controlled by a scale parameter K. A global...

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...

This paper mainly investigates the traveling salesman problem under uncertain environment, in which not all the edge weights are deterministically present, but are present with uncertain variables. As a result, five types optimal route models for the uncertain traveling salesman problem, i.e., expected optimal route, α-optimal route, distribution optimal route, expected approximation optimal ro...

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on...

In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a lineariz...

Since the computation of an exact solution is very expensive (under the assumption that P 6= NP ), we are interested in approximate solutions – at least for special cases. Particularly, we look for an Polynomial Time Approximation Scheme (PTAS), i.e., for any fixed error parameter ε > 0, the running time is bounded by a polynomial in n and the costs of the computed tour does not exceed (1+ε) ·O...

In memory ofPaolo Camerini Local search is a well-known and a well·investigated solution approach for the traveling salesman problem. It is not obvious, however, how local search for the TSP has to be implemented efficiently when each city has to be visited within one or more given time windows.1bis is particularly true when parallel computer architectures are available. We consider these quest...