# Optimisation methods for solving a large-scale avionics scheduling problem

Sammanfattning: Modern computer systems in aircraft are based on an integrated modular avionic architecture. In this architecture, software applications share hardware resources on a common avionic platform. Many functions in an aircraft are controlled by software and a failure in such software can have severe consequences. To avoid malfunction, there are many aspects to consider. One aspect is to ensure that the activities in the system get sufficient computing and network communication resources while being completed in time. This thesis contributes to addressing this challenge by studying an avionics scheduling problem proposed by Saab.In this problem, tasks are performed on modules and the messages are sent on a communication network that links the modules. A schedule specifies start times for tasks on modules and the choices of time slots for messages on the communication network. For a schedule to be feasible, constraints must be respected: precedence constraints between tasks, timing constraints on tasks and messages, and communication network constraints involving both tasks and messages. For future platforms, it is expected that large-scale instances need to be solved. The methods introduced in this thesis solve instances with up to 55,000 tasks and 2500 messages.The thesis includes three papers that introduce methods for solving the avionics scheduling problem and one paper that compares techniques to improve the performance of a specific type of decomposition method. The solution methods for the avionics problem differ in how the decomposition is made, how the subproblems are solved, and if the algorithm is guaranteed to find a feasible solution or not, given enough time. Together, the contributions of these papers give an insight into the structure of this type of avionics scheduling problem and how this structure can be exploited to construct efficient exact and matheuristic scheduling methods.Paper A introduces a constraint generation procedure tailored for the avionics scheduling problem. In the constraint generation procedure, a preliminary, possibly infeasible, schedule is constructed by solving a master problem. This schedule is used to define a restriction of the problem, which is solved to find a complete schedule. If no schedule is found within a time-limit, constraints are added to the master problem, which is then solved again. This procedure relies on solving Mixed-Integer Programming (MIP) models. In Paper B, the constraint generation procedure is extended into a matheuristic, where the master problem is solved with a MIP-based adaptive large neighbourhood search. The methods in Paper A and Paper B can solve instances with up to 37,000 tasks and 1700 messages, and 55,000 tasks and 2500 messages, respectively.Logic-Based Benders Decomposition (LBBD) algorithms are treated in Paper C and Paper D. In both papers, a MIP solver is applied to the master problem while a constraint programming solver is used for the subproblem. Paper C addresses the avionics scheduling problem and introduces a new acceleration technique for LBBD. This technique exploits information obtained during cut strengthening to make educated guesses about where feasible solutions might be found. With this technique, the LBBD algorithm outperforms the methods from Paper A and Paper B both with respect to solution time and RAM usage. Paper D investigates cut strengthening for LBBD in a wider context, by evaluating different cut-strengthening algorithms for LBBD on three problems from the literature. The computational evaluation shows that it is advantageous to invest time in finding strong cuts.

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