In the context of aerospace engineering, the optimization of processes may often require to solve multi-objective optimization problems, including mixed variables, multi-modal and non-differentiable quantities, possibly involving highly-expensive objective function evaluations. In Air Traffic Management (ATM), the optimization of procedures and protocols becomes even more complicated, due to the involvement of human controllers, which act as final decision points in the control chain. In this article, we propose the use of computational intelligence techniques, such as Agent-Based Modelling and Simulation (ABMS) and Evolutionary Computing (EC), to design a simulation-based distributed architecture to optimize control plans and procedures in the context of ATM. We rely on Agent-Based fast-time simulations to carry out offline what-if analysis of multiple scenarios, also taking into account human-related decisions, during the strategic or pre-tactical phases. The scenarios are constructed using real-world traffic data traces, while multiple optimization variables governed by an EC algorithm allow to explore the search space to identify the best solutions. Our optimization approach relies on ad-hoc multiobjective performance metrics which allow to assess the goodness of the control of aircraft and air traffic regulations. We present experimental results which prove the viability of our approach, comparing them with real-world data traces, and proving their meaningfulness from an Air Traffic Control perspective.

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in their expressive power. This paper proposes a novel framework called Equivariant Subgraph Aggregation Networks (ESAN) to address this issue. Our main observation is that while two graphs may not be distinguishable by an MPNN, they often contain distinguishable subgraphs. Thus, we propose to represent each graph as a set of subgraphs derived by some predefined policy, and to process it using a suitable equivariant architecture. We develop novel variants of the 1-dimensional Weisfeiler-Leman (1-WL) test for graph isomorphism, and prove lower bounds on the expressiveness of ESAN in terms of these new WL variants. We further prove that our approach increases the expressive power of both MPNNs and more expressive architectures. Moreover, we provide theoretical results that describe how design choices such as the subgraph selection policy and equivariant neural architecture affect our architecture's expressive power. To deal with the increased computational cost, we propose a subgraph sampling scheme, which can be viewed as a stochastic version of our framework. A comprehensive set of experiments on real and synthetic datasets demonstrates that our framework improves the expressive power and overall performance of popular GNN architectures.

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In general, graph representation learning methods assume that the test and train data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and realworld dataset experiments showcasing the benefits of representations that are invariant to train/test distribution shifts.