A polyhedral study of the asymmetric travelling salesman problem with time windows Abstract The asymmetric travelling salesman problem with time windows (ATSP-TW) is a basic model for scheduling and routing applications. In this paper we present a formulation of the problem involving only 0/1-variables associated with the arcs of the underlying digraph. This has the advantage of avoiding additi...

Vehicle routing problem (VRP) is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, to provide the efficient vehicle serving to the customer through different services by visiting the number of cities or stops, the VRP follows the Travelling Salesman Problem (TSP), in which each of vehicle visiting a set of cities such that every city is vis...

There exist a number of problem classes for which obtaining the exact solution becomes exponentially expensive with increasing problem size. The quadratic assignment problem (QAP) or the travelling salesman problem (TSP) are just two examples of such NP-hard problems. In practice, approximate algorithms are employed to obtain a suboptimal solution, where one must face a trade-off between comput...

A rtificial bee Colony algorithm (ABC) is a population based heuristic search technique used for optimization problems. ABC is a very effective optimization technique for continuous optimization problem. Crossover operators have a better exploration property so crossover operators are added to the ABC. This paper presents ABC with different types of real coded crossover operator and its applica...

One of the most important applications of the Asymmetric Hamiltonian Path Problem is in scheduling. In this paper we describe a variant of this problem, and develop both a mathematical programming formulation and simple metaheuristics for solving it. The formulation is based on a transformation of the input data, in such a way that a standard mathematical programming model for the Asymmetric Tr...

We consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints; the problems are online because the set of locations are revealed incrementally over time. We make no probabilistic assumptions whatsoever about the problem data. We consider two main problems: (1) the online Traveling Salesman Problem (TSP) ...