Modern computer systems in aircraft are often 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. In order to avoid malfunction, there are many aspects to consider. One aspect is to ensure that the activities in the system is done at the right time with the right resources. To analyse if this is possible or not is often called schedulability analysis.

When multiple functions are using the same resources, the schedulability analysis becomes increasingly challenging. This thesis focuses on a pre-runtime scheduling problem of an integrated modular avionic system proposed by our industrial partner Saab. The purpose of this problem is to find a feasible schedule or prove that none exists as part of a schedulability analysis.

For the system that we study, there are two major challenges. One is that task and communication scheduling are integrated and the other is that there is a large amount of tasks to schedule. For the largest instances, there are more than 10 000 tasks on a single module. In order to solve such problems, we have developed a matheuristic. At the core of this matheuristic is a constraint generation procedure designed to handle the challenges of the scheduling problem.

The constraint generation procedure is based on first making a relaxed scheduling decision and then evaluating this in a separate problem where a complete schedule is produced. This yields a decomposition where most technical details are considered in the relaxed problem, and the actual scheduling of tasks is handled in a subproblem. Both the relaxed problem and the subproblem are formulated and solved as mixed integer programs.

The heuristic component of the matheuristic is that the relaxed problem is solved using an adaptive large neighbourhood search method. Instead of solving the relaxed problem as a single mixed integer program, the adaptive large neighbourhood search explores neighbourhoods through solving a series of mixed integer programs. Features of this search method are that it is made over both discrete and continuous variables and it needs to balance feasibility against profitable objective value.

The matheuristic described in this thesis has been implemented in a scheduling tool. This scheduling tool has been applied to instances provided by our industrial partner and to a set of public instances that we have developed. With this tool, we have solved instances with more than 45 000 tasks.