Due to the ambitious emission targets the international community as well as individual states have set, the development and deployment of electric aircraft will be further pursued in the upcoming years.
However, it is not possible to replace conventional with electric aircraft without equipping airports with the necessary infrastructure. Since extensions of airports are extremely costly, we present a model that determines the optimal selection of airports in Europe for the development of infrastructure to support the operation of electric aircraft, while accommodating the routing of the passenger demand and staying within emission targets.
To identify the most beneficial flight routes based on the electrification status of each airport the passenger demand is defined as a multi-commodity flow and we apply a path-based formulation within a column generation framework. We have gathered real-world data, which are utilized to analyze the model with regards to solvability in relation to the instance size and the established emission limits.

The Traveling Salesman Problem (TSP) is one of the most extensively researched and widely applied combinatorial optimization problems. It is NP-hard even in the symmetric and metric case, mostly considered here. The Lin-Kernighan-Helsgaun (LKH) heuristic has led to many best known solutions in particular for very large instances and often finds an optimal solution for small instances. We propose variations of LKH that perform significantly faster on large instances. LKH repeatedly improves an initially random tour by exchanging edges along alternating circles. Thereby, it respects several criteria designed to quickly find alternating circles that give a feasible improvement of the tour. We relax one of those criteria - the positive gain criterion - carefully leading to improvement steps hitherto undiscovered by LKH. We confirm this improvement experimentally via extensive simulations on various benchmark libraries for TSP. Our computational study shows that for large instances our method is on average 13\% faster than the latest version of LKH while the quality of solutions stays virtually the same.

The standard multicommodity flow problem is defined on a directed graph and possesses origin-destination pairs as commodities. In this presentation, we consider an additional flow with no predefined origin or destination. This is applicable to an air transportation network, where it should be possible to refuel an aircraft for more than one flight regardless of the origin-destination passenger flow, for example when introducing hydrogen-powered aircraft with a lower flight range. Interesting instances of this problem are relatively large and cannot be solved to optimality via generic approaches. Hence, we introduce a new labeling procedure that is based on Dijkstra's shortest path algorithm. The most relevant changes are shifting the labels to the edges and expanding them so that each commodity has its own label. The additional flow, which does not inherit a predefined origin or destination, is then incorporated as precomputed data represented by an additional capacity from each vertex to all other vertices. Computational results showed a speed-up compared to the generic approach.

Hexaly is a new kind of global optimization solver. Its modeling interface is nonlinear and set-oriented. It also supports user-coded functions, thus enabling black-box optimization and simulation optimization. Thus, Hexaly APIs unify modeling concepts from mixed-linear, nonlinear, and constraint programming. Under the hood, Hexaly combines various exact and heuristic optimization methods: spatial branch-and-bound, simplex methods, interior point methods, augmented Lagrangian methods, automatic Dantzig-Wolfe reformulation, column and row generation, propagation methods, local search, direct search, population-based methods, and surrogate modeling techniques.

Regarding performance benchmarks, Hexaly distinguishes itself against the leading solvers in the market, like Gurobi, IBM Cplex, and Google OR Tools, by delivering fast and scalable solutions to problems in the spaces of Supply Chain and Workforce Management like Routing, Scheduling, Packing, Clustering, Matching, Assignment, and Location problems. For example, on notoriously hard problems like the Pickup and Delivery Problem with Time Windows or Flexible Job Shop Scheduling with Setup Times, Hexaly delivers solutions with a gap to the best solutions known in the literature smaller than 1\% in a few minutes of running times on a basic computer.