The Traveling Salesman Problem (TSP) is maybe the archetypical problem in combinatorial optimization. This problem and its generalizations, vehicle routing problems, have been studied for more than thirty years; two entire monographs are devoted to the subject [34, 26]. Since the TSP is NP-hard, polynomial-time approximation algorithms are usually studied. However, usually the approaches to the...

The Generalized Traveling Salesman Problem (GTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a sim...

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...

In this paper, a novel methodology is proposed to solve a cooperative multi-depot vehicle routing problem. We establish a mathematical model for multi-owner VRP in which each owner (i.e. player) manages single or multiple depots. The basic idea consists of offering an option that owners cooperatively manage the VRP to save their costs. We present cooperative game theory techniques for cost savi...

Consider a complete graph G = (V,E), in which each node is present with probability pi. We are interested in solving combinatorial optimization problems on subsets of nodes present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the strategy of re-optimization, under which the combinatorial optimization problem is solved optimally for ever...

The primary function of a suspension system of a vehicle is to isolate the road excitations experienced by the tires from being transmitted to the passengers. In this paper, we formulate an optimal vehicle suspension design problem with the quarter-car vehicle dynamic model. A new multi-objective genetic algorithm is used for Pareto optimization of a two-degree of freedom vehicle vibration mode...

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is Θ(log n). Moreover, we prove that the same result also holds for graphic, euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the ClarkeWright savings heuristic for the metric Traveling Salesman Problem is Θ(log n). keywor...

In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then we deliver every item by performing a hamiltonian circuit. We are interested in the convex hull of the (arc-)incidence vectors of such couples of hamiltonian circuits. For the gene...