On Optimization of Automation Systems: Integrating Modular Learning and Optimization (2022)

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compositional Optimization</i> (CompOpt) was recently proposed for optimization of discrete-event systems of systems. A modular optimization model allows CompOpt to divide the optimization into separate sub-problems, mitigating the state space explosion problem. This paper presents the Modular Optimization Learner (MOL), a method that interacts with a simulation of a system to automatically learn these modular optimization models. MOL uses a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modular learning</i> that takes as input a hypothesis structure of the system and uses the provided structural information to split the acquired learning into a set of modules, and to prune parts of the search space. Experiments show that modular learning reduces the state space by many orders of magnitude compared to a monolithic learning, which enables learning of much larger systems. Furthermore, an integrated greedy search heuristic allows MOL to remove many sub-optimal paths in the individual modules, speeding up the subsequent optimization. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Automation systems are becoming increasingly large and complex and the automation of more and more advanced tasks often requires the coordination of multiple subsystems. Optimization can have a great impact on the efficiency of these systems in terms of cost and operation speed. Finding optimal solutions is, however, a difficult task. As the number of tasks and subsystems of the automation system increases, the search space of the optimization problems tends to grow exponentially. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compositional Optimization</i> (CompOpt) is a method specifically designed for the optimization of large-scale automation systems. A challenge with the application of CompOpt is that it takes as input a specific type of optimization model that divides the system into subsystems; like machines, vehicles, etc. Formulating these models requires a high level of expertise and system knowledge. This paper addresses this challenge with an algorithm that learns these models from a simulation of the system. The simulation can be implemented in any software as long as a suitable interface exists or can be constructed. To divide the learning into subsystems, the algorithm uses an initial <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plant structure hypothesis</i> (PSH). This can be viewed as a meta-model that includes known structural information, such as the number of subsystems and which actions that affect each subsystem. The more structural information that is added to PSH, the more efficient the learning and subsequent optimization will be. The purpose of this is to reduce the level of expertise and system knowledge needed in the application of optimization, to simplify the transition to Industry 4.0.