Pre-runtime scheduling of large-scale electronic systems, as those in modern aircraft, can be computationally challenging. In this paper, we study a distributed integrated modular avionic system of practical relevance where the scheduling includes to assign communication messages to time slots and to sequence tasks on modules. For this problem, the challenge is the huge number of tasks to be scheduled and the intricate interaction between the communication and task scheduling. We present a method based on Logic-Based Benders Decomposition (LBBD) to solve this problem. In a master problem, formulated as a mixed-integer program, communication messages are assigned to time slots and in a subproblem, formulated as a constraint program, tasks are scheduled. Our LBBD scheme is accelerated by using cut strengthening, a subproblem relaxation, and components for preprocessing and initialisation of the scheme. The cut strengthening is of the kind that systematically investigates subsets of variables to include in the cut by solving additional subproblems. To further enhance the efficiency of the scheme, we propose a new strategy that extends cut strengthening to also try to construct feasible solutions by using information from solving the additional subproblems. Our computational evaluation is based on publicly available instances with up to 2530 messages and 54,731 tasks. It shows that our method outperforms previous methods for the problem with respect to both solution times and RAM usage. A further evaluation of the different components in the method shows that our new acceleration strategy is important to achieve these results.
Technical report, Department of Mathematics, Linköping University, May 2022