Dynamic programming algorithm for the vehicle routing problem with time windows and EC social legislation

In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a dynamic programming approach for the vehicle routing problem with time windows including the EC social legislation on drivers' driving and working hours. Our algorithm includes all optional rules in these legislations, which are generally ignored in the literature. To include the legislation in the dynamic programming algorithm we propose a break scheduling method that does not increase the time-complexity of the algorithm. This is a remarkable eect that generally does not hold for local search methods, which have proved to be very successful in solving less restricted vehicle routing problems. Computational results show that our method finds solutions to benchmark instances with 18% less vehicles and 5% less travel distance than state of the art approaches. Furthermore, they show that including all optional rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5%\ud regarding the travel distance. Therefore, the optional rules should be exploited in practice

An algorithm for minimum-cost set-point ordering in a cryogenic wind tunnel

An algorithm for minimum cost ordering of set points in a cryogenic wind tunnel is developed. The procedure generates a matrix of dynamic state transition costs, which is evaluated by means of a single-volume lumped model of the cryogenic wind tunnel and the use of some idealized minimum-costs, which is evaluated by means of a single-volume lumped model of the cryogenic wind tunnel and the use of some idealized minimum-cost state-transition control strategies. A branch and bound algorithm is employed to determine the least costly sequence of state transitions from the transition-cost matrix. Some numerical results based on data for the National Transonic Facility are presented which show a strong preference for state transitions that consume to coolant. Results also show that the choice of the terminal set point in an open odering can produce a wide variation in total cost

Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows

We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature