Satellite-based platforms are currently the only feasible way of achieving intercontinental range for quantum communication, enabling thus the future global quantum internet. Recent demonstrations by the Chinese spacecraft Micius have spurred an international space race and enormous interest in the development of both scientific and commercial systems. Research efforts so far have concentrated upon in-orbit demonstrations involving a single satellite and one or two ground stations. Ultimately satellite quantum key distribution should enable secure network communication between multiple nodes, which requires efficient scheduling of communication with the set of ground stations. Here we present a study of how satellite quantum key distribution can service many ground stations taking into account realistic constraints such as geography, operational hours, and most importantly, weather conditions. The objective is to maximise the number of keys a set of ground stations located in the United Kingdom could share while simultaneously reflecting the communication needs of each node and its relevance in the network. The problem is formulated as a mixed-integer linear optimisation program and solved to a desired optimality gap using a state of the art solver. The approach is presented using a simulation run throughout six years to investigate the total number of keys that can be sent to ground stations.

We propose a multistage algorithm for the Vehicle Routing Problem with Time Windows and Synchronised Visits, which is capable of solving large problem instances arising in Home Health Care applications. The algorithm is based on a Constraint Programming formulation of the daily Home Care Scheduling and Routing Problem. It contains visits with hard time windows and pairwise synchronisation to be staffed by carers who have different skills and work custom shift patterns with contractual breaks. In a computational study, we first experiment with a benchmark set from the literature for the Vehicle Routing Problem with Time Windows and Synchronised Visits. Our algorithm reproduced the majority of the best-known solutions, and strictly improved results for several other instances. Most importantly, we demonstrate that the algorithm can effectively solve real scheduling instances obtained from a UK home care provider. Their size significantly surpass similar scheduling problems considered in the literature. The multistage algorithm solved each of these instances in a matter of minutes, and outperformed human planners, scheduling more visits and significantly reducing total travel time.

Any reliable model for scheduling optical space-toground communication must factor in cloud cover conditions due to attenuation of the laser beam by water droplets in the clouds. In this work, we provide two alternative models of uncertainty for cloud cover predictions: a Robust Optimisation model with a polyhedral uncertainty set and a Distributionally Robust Optimisation model with a moment-based ambiguity set. We computationally analyse their performance over a realistic communications system with one satellite and a network of ground stations located in the United Kingdom. The models are solved to schedule satellite operations for six months utilising cloud cover predictions from official weather forecasts.We found that the presented formulations with the treatment of uncertainty outperform in the long term models in which uncertainty is ignored. Both treatments of uncertainty exhibit similar performance. Nonetheless, the novel variant with the polyhedral uncertainty set is considerably faster to solve.

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Stopping exploration of the search space regions that can be proven to contain only inferior solutions is an important acceleration technique in optimization algorithms. This study is focused on the utility of trie-based data structures for indexing discrete sets that allow to detect such a state faster. An empirical evaluation is performed in the context of index operations executed by a label setting algorithm for solving the Elementary Shortest Path Problem with Resource Constraints. Numerical simulations are run to compare a trie with a HATtrie, a variant of a trie, which is considered as the fastest inmemory data structure for storing text in sorted order, further optimized for efficient use of cache in modern processors. Results indicate that a HAT-trie is better suited for indexing sparse multi dimensional data, such as sets with high cardinality, offering superior performance at a lower memory footprint. Therefore, HAT-tries remain practical when tries reach their scalability limits due to an expensive memory allocation pattern. Authors leave a final note on comparing and reporting credible time benchmarks for the Elementary Shortest Path Problem with Resource Constraints.978-1-5090-6017-7/18/$31.00 ©2018 IEEE

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