Modular Learning and Optimization for Planning of Discrete Event Systems

Optimization of industrial processes, such as manufacturing cells, can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. This is usually referred to as the state explosion problem and is a well-known problem within the control and optimization of automation systems. This thesis proposes two main contributions to improve and to simplify the optimization of these systems. The first is a new method of solving these optimization problems using a compositional optimization approach. This integrates optimization with techniques from compositional supervisory control using modular formal models, dividing the optimization of subsystems into separate subproblems. The second is a modular learning approach that alleviates the need for prior knowledge of the systems and system experts when applying compositional optimization. The key to both techniques is the division of the large system into smaller subsystems and the identification of local behavior in these subsystems, i.e. behavior that is independent of all other subsystems. It is proven in this thesis that this local behavior can be partially optimized individually without affecting the global optimal solution. This is used to reduce the state space in each subsystem, and to construct the global optimal solution compositionally.The thesis also shows that the proposed techniques can be integrated to compute global optimal solutions to large-scale optimization problems, too big to solve based on traditional monolithic models

Compositional optimization of large-scale discrete event systems

Optimization of industrial processes such as manufacturing cells can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. This is usually referred to as the state explosion problem and is a well-known problem within the control and optimization of automation systems.This thesis proposes a new method of solving these optimization problems using a compositional optimization approach. This integrates optimization with techniques from compositional supervisory control, dividing the optimization of subsystems into separate sub-problems. The key to this approach is the identification of local behavior in subsystems, behavior that is independent of all other subsystems. It is proven in this thesis that this local behavior can be optimized individually without affecting the global optimal solution. This is used by the approach, to reduce the state space in each subsystem, and then to utilize these reduced models compositionally when the global optimal solution is computed.Results in this thesis show that compositional optimization efficiently can generate global optimal solutions to large-scale optimization problems, too big to solve based on traditional monolithic models. It is also shown that these techniques can be applied to several industrial applications, e.g. in logistics, manufacturing etc

Time-optimal control of large-scale systems of systems using compositional optimization

Optimization of industrial processes such as manufacturing cells can have great impact on their performance. Finding optimal solutions to these large-scale systems is, however, a complex problem. They typically include multiple subsystems, and the search space generally grows exponentially with each subsystem. In previous work we proposed Compositional Optimization as a method to solve these type of problems. This integrates optimization with techniques from compositional supervisory control, dividing the optimization into separate sub-problems. The main purpose is to mitigate the state explosion problem, but a bonus is that the individual sub-problems can be solved using parallel computation, making the method even more scalable. This paper further improves on compositional optimization with a novel synchronization method, called partial time-weighted synchronization (PTWS), that is specifically designed for time-optimal control of asynchronous systems. The benefit is its ability to combine the behaviour of asynchronous subsystems without introducing additional states or transitions. The method also reduces the search space further by integrating an optimization heuristic that removes many non-optimal or redundant solutions already during synchronization. Results in this paper show that compositional optimization efficiently generates global optimal solutions to large-scale realistic optimization problems, too big to solve when based on traditional monolithic models. It is also shown that the introduction of PTWS drastically decreases the total search space of the optimization compared to previous work

Modular Supervisory Synthesis for Unknown Plant Models Using Active Learning

This paper proposes an approach to synthesize a modular discrete-event supervisor to control a plant, the behavior model of which is unknown, so as to satisfy given specifications. To this end, the Modular Supervisor Learner (MSL) is presented that based on the known specifications and the structure of the system defines the configuration of the supervisors to learn. Then, by actively querying the simulation and interacting with the specification it explores the state-space of the system to learn a set of maximally permissive controllable supervisors

Active Learning of Modular Plant Models

Model-based techniques are these days being embraced by the industry in their development frameworks. While model-based approaches allow for offline verification and validation of the system, and have other advantages over existing methods, they do have their own challenges. One of the challenges is to obtain a model describing the behavior of the system. In this paper we present the Modular Plant Learner (MPL), an algorithm that explores the state-space and constructs a discrete model of a system. The MPL takes as input a hypothesis structure of the system - called the PSH - and using this information, interacts with a simulation of the system to construct a modular discrete-event model. Using an example we show how the algorithm uses the structural information provided - the PSH - to search the state-space in a smart manner, mitigating the state-space explosion problem

On the Use of Equivalence Classes for Optimal and Suboptimal Bin Packing and Bin Covering

Bin packing and bin covering are important optimization problems in many industrial fields, such as packaging, recycling, and food processing. The problem concerns a set of items, each with its own value, that are to be sorted into bins in such a way that the total value of each bin, as measured by the sum of its item values, is not above (for packing) or below (for covering) a given target value. The optimization problem concerns minimizing, for bin packing, or maximizing, for bin covering, the number of bins. This is a combinatorial NP-hard problem, for which true optimal solutions can only be calculated in specific cases, such as when restricted to a small number of items. To get around this problem, many suboptimal approaches exist. This article describes the formulations of the bin packing and covering problems that allow finding the true optimum, for instance, counting hundreds of items using general-purpose MILP-solvers. Also presented are suboptimal solutions that come within less than 10% of the optimum while taking significantly less time to calculate, even ten to 100 times faster, depending on the required accuracy. Note to Practitioners - A typical case for bin covering is in food processing where food items are automatically sorted into trays of similar weight so that the overweight is minimized. Another application is in recycling, where items such as batteries should be put in crates of similar weight, so that the crates do not exceed a target weight due to later manual handling, but, at the same time, we want as few crates as possible. This is a bin packing problem. On an industrial scale, these tasks are fully automated. Though modern software tool\u27s efficiency to solve bin sorting problems has increased significantly in later years, the problems are inherently tough in the sense that the solution time grows exponentially with the number of items. This limits the problem sizes that can be solved to optimality within a reasonable time. Therefore, much research has focused on heuristic rules that give reasonable solving times while not giving the true optimal number of bins. However, in many cases, the true optimal solution is preferable, and sometimes even necessary, so this is an industrially interesting problem. This article describes an approach to solve the bin packing and covering problems to the true optimum that increases the limit of the number of items that can typically be handled. This is done by observing that items of the same value need not be distinguished. Instead, we can formulate packing/covering problems over item values rather than individual items and sort integer numbers of these values into bins, which allows us to solve to optimum for more than 500 items in a reasonable time. In addition, by redefining what we mean by the same value, we can consider more items to have the same value and achieve even better calculation efficiency

Compositional Optimization of Discrete Event Systems

Optimizing the execution of industrial processes such as manufacturing cells or whole assembly plants can have great impact on their performance. However, finding an optimal sequence of tasks in a large-scale system is a complex optimization problem. Most systems are comprised of multiple sub-systems and the search space of the optimization generally grows exponentially with each sub-system. In this paper, we propose the method compositional optimization to mitigate this problem. Compositional optimization integrates methods from optimization and compositional supervisory control theory to exploit the local behavior of the sub-systems, reducing them individually, and then synthesize a globally optimal controller compositionally. The local optimization technique avoids a monolithic model of the system, which can reduce the complexity of the optimization significantly. The potential of compositional optimization is demonstrated using a realistic example, similar to a large scale industrial application, while we also reflect on the limitations and highlight specific system properties that can be exploited by the method

MIDES: A Tool for Supervisor Synthesis via Active Learning

A tool, MIDES, for automatic learning of models and supervisors for discrete event systems is presented. The tool interfaces with a simulation of the target system to learn a behavioral model through interaction. There are several different algorithms to choose from depending on the intended outcome. Moreover, given a set of specifications, the tool learns a supervisor that can help ensure the controlled system guarantees the specifications. Furthermore, the state-space explosion problem is addressed by learning a modular supervisor. In this paper, we introduce the tool, its interfaces, and algorithms. We demonstrate the usefulness through several case studies

On Optimization of Automation Systems: Integrating Modular Learning and Optimization

Compositional Optimization (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 modular learning 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