10:30 AM - 10:55 AM
The Accelerated Hyperbolic Smoothing Multisource Fermat Weber Method: New Computational Results for Solving Very Large Instances
The work considers the Multisource Fermat-Weber problem. A particular case is the minimum sum-of-distances clustering. Its mathematical modeling leads to a min-sum-min formulation which is a global optimization problem with a bi-level nature, nondifferentiable and with many minimizers. To overcome these hard difficulties, we use the Hyperbolic Smoothing methodology in connection with a partition of observations into two groups: data in frontier and data in gravitational regions, which drastically simplify the computational tasks. For the purpose of illustrating both the reliability and the efficiency of the method, we perform a set of computational experiments making use of traditional instances described in the literature. Apart from consistently presenting similar or even better results when compared to related approaches, the novel technique was able to deal planar location-allocation instances never tackled before, with up to 1243088 cities, more than 1000 times the previous largest one presented in the literature.
The same problem can be defined in spaces with any number of components. In this case, the technique was able to solve even larger problems, up to 1842292 patterns with 16 components.
10:55 AM - 11:20 AM
Aircraft Arrivals Scheduling under Uncertainty
Facing the world-wide steady growth of air traffic, air traffic controllers (ATCs) are more and more challenged to schedule optimally aircraft operations on runways and most importantly landings. The Aircraft Landing Problem (ALP) arises as one consisting in finding the best landing sequence with regard to (a) particular objective(s) and subject to a number of operational constraints. To help ATCs with this task, decision support tools (DSTs) have been designed since the early 90’s. Nevertheless, the most wide-spread landing policy is still First Come First Served (FCFS), even though it has been proved sub-optimal in many deterministic problem statements. Moreover, ALP is a dynamic and stochastic problem by nature. Stochasticity is even more highlighted as DSTs tend to double increase their planning horizon in the near future. We propose a two-stage stochastic program to address the aircraft landing problem under uncertainty, where aircraft predicted arrival times at the near airport area, called TRACON, are assumed to follow known probability distributions. In the first stage, we seek to find an aircraft sequence as well as appropriate target arrival times at TRACON, where the former would minimize runway usage. In the second stage, once the actual arrival times at TRACON are revealed, we decide on target landing times that minimize ATCs’ workload. We use the Julia programming language to model and solve realistic problem instances.
11:20 AM - 11:45 AM
Container vessel voyage planning: Capacity and weight limits to be considered
The container vessel capacity and weight maximum capacities are very important factors which in many papers have either not been properly considered. The limitations explained could significantly change the optimal computed route since the only use of the number of containers discharged and loaded, within ports of the system, is insufficient. It is also necessary to consider the time sequence of those operations within the route. So the obtained route could be vastly different from those that are used in practice. This paper will be a profound examination into the problem from the point of view of practical ships operation.