Modeling for Parametric System-Level Design Optimization

System-level design refers to a synthesis, analysis, and optimization process which reasons with the system in a holistic manner. We are developing a model-based approach to support parametric system-level design optimization. In this paper, we describe our modeling methodology based on the Environment Relationship net framework (Ghezzi et al. 1991) to represent a system for the purpose of design optimization. Specifically, we model a reprographic machine system (e.g., printer, photocopier) whose elements include hardware components and software processes. We discuss the issues that arise in modeling this system and the challenges that remain to be addressed. Introduction System-level design refers to a synthesis, analysis, and optimization process which reasons with the system in a holistic manner. The National Science Foundation’s report Research Opportunities in Engineering Design (NSF 1996) observes that: "It is getting harder to improve system performance from advances in individual disciplines. The number of specialists is increasing, while the number of generalists, capable of doing system integration, is decreasing. The need is for more generalists in product design who can understand the big picture, not just some specialized problems." To manage the complexity of the design process, designers recursively decompose functional specifications into subfunctions and focus their efforts on solving the subproblems and then, integrating their solutions. In the process, they often develop detailed designs of a subsystem without paying adequate attention to its dependencies with the rest of the system. With the advent of embedded computer systems that integrate hardware components with software computation elements (e.g., digital signal processors, digital printers), tile choices available for decomposing functionality are far wider than in traditionalsystems, and the complexity of the interactions among the subsystems compliI Copyright (~)1999, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. / .~ sof~warcsubsystcm .~ ] Figure 1: Reprographic machine: an integrated hardware and software system cute their integration. The interactions between the system’s components are often dynamic, i.e., they depend on different tasks performed by the system at run time. Designing the subsystems in isolation without taking into account their dynamic interactions and their inter-dependencies often necessitates backtracking (which lengthens the design cycle) or may lead to non-optimal solution. Our research is targeted at supporting parametric system-level design optimization. Given a configuration of the system, we use a model-based reasoning approach to tune its parameters to optimize specified objectives, such as performance and manufacturing cost. Our methodology for system level parametric design optimization requires a model that incorporates design variables across the system and allows the designer to study and reason about their effects on optimization objectives (Kapadia & Biswas 1999). The model must inCorporate not just a representation each subsystem, but also capture the interactions and dependencies that exist across subsystems. In this paper, we describe our approach for modeling a system whose components span multiple domains using the Enviromnent Relationship net fi’amework (Ghezzi et al. 1991). From: AAAI Technical Report WS-99-05. Compilation copyright © 1999, AAAI (www.aaai.org). All rights reserved. Reprographic machine As a test bed for our design optimization methodology, we use a digital reprographic machine (e.g., printer, photocopier), which is a computer-controlled electromechanical system that produces documents by manipulating images and sheets of paper. Given a configuration for this system, we are interested in tuning its parameters so that the designed machine optimizes job completion times and manufacturing cost, while meeting specified design constraints. Fig. 1 shows a schematic description of the hardware and software subsystems of interest. The hardware subsystem is responsible for transporting sheets of paper in the machine. It prints simplex (one-sided) and duplex (two-sided) sheets. A sheet enters the machine through an input port. An image is transferred (or printed) the sheet as it passes through the transfer component. A simplex sheet passes through without inversion on its way to the output port. A duplex sheet is inverted, routed to the transport along the duplex loop, an image is transferred on its back side (transfer), and the sheet is inverted again, before it is sent, to the output port. Parameters that affect desired optimization criteria include the transit times of the components and capacities of buffers at the input and output (Kapadia, Biswas, ~z Fromherz 1997). To generate a document (i.e., an ordered sequence of simplex and duplex sheets) the transportation and printing of sheets must satisfy behavior constraints, for example, sheets must be manipulated such that they are available at the output in the specified order, and sheets must not collide with each other anywhere in the paper path. Fig. 1 shows a schematic of the software subsystem which comprises the following processes. The accumulate process receives sheet descriptions from an external source. State-of-the-art reprographic machines are equipped with a scheduler (illustrated in Fig. 2) that receives a stream of sheet descriptions, and dynamically determines optimal times at which individual actions must be initiated to produce the desired output by a process of heuristic search (Fromherz & Carlson 1994). The scheduler may employ different online algorithms (e.g., greedy methods, search with limited lookahead, etc.) which trade off the optimality of the schedule generated and computation time. To prevent the scheduler from being overwhelmed by large document descriptions, it may be designed to consider a fixed number of sheets (called its lookahead (L)) for any computation. In general, we expect larger values of lookahead to improve the prospect of determining an optimal schedule because the scheduler has access to additional information while making its decisions. However, the size of the search space explored by the scheduler increases with larger values of lookahead, which increases the software computation time (T) and consequently, the overall job completion time. We assume that T is a function of L, i.e., T = f(L). At the termination of a computation, the scheduler may initiate the execution of all tile actions computed in the schedule. Conversely, it may sheet description I"~ scheduler/\ I ordered sequence of sheet descriptions sheet descriptio~ 2-~ l and their execution sheet de,~criplion a,"" t / times Figure 2: Schedule computation task commit itself to only a predefined number of actions (we call this the commitment parameter (C)). This policy of non-commitment affords it greater flexibility; if more information about the document arrives later that makes an alternative schedule look more promising, the scheduler can reschedule the uncommitted sheets accordingly. The command process communicates control commands to the hardware subsystem for the actions committed to by the scheduler. Table 1 shows an optimal schedule 1 for the document description consisting of one simplex sheet followed by two duplex sheets, and then a simplex sheet (i.e., st, d2, d3, s4) which is completed in 14 time units. While generating this schedule, we assumed the following parameter values: printing an image on to a sheet requires one time unit, inverting a sheet takes two units, transporting a sheet along the duplex loop requires three units, bypassing inversion is instantaneous, software computation takes one unit, lookahead is two, and the commitment parameter is one. The job’s completion time is a function of the system parameters (both hardware and software) and the schedule for the job. Optimizing the behavior of this system is particularly difficult because there is no predefined function that maps the job completion time to the design variables for any job. In (Kapadia & Biswas 1999), we have presented model-based reasoning techniques that start from a compositional model of the reprographic machine system and determine this mapping for a given job. Modeling for optimization A model of a system is a representation that is tailored towards addressing a specific set of tasks to be performed on the system. Creating a model for design optimization first requires that the designer must identify design variables and system optimization objectives. The model of system behavior must incorporate the design variables as system parameters and allow the designer to study and reason about their effects on optimization objectives. The designer must determine a level of detail for modeling that is appropriate for the design task. It may be necessary to combine different kinds of knowledge into a single model, e.g., a model may incorporate quantitative and qualitative relations among its parameters. Creating a veridical model of the system at the desired level of detail, is a difficult problem that requires considerable insight, experience 1An optimal schedule for a job description is one that completes the job in the shortest time. Component/Process Place Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 accumulate P2 81 d2 d3 84 schedule P4 d2 d3 81,84 command P5 d2 d3 81 84 sheet in P6 d2 d3 81 84 transfer P7 d2 d3 81 d2 d3 84 invert PS d2 d3 81 d2 d3 84 transport P9 d2 d3 sheet out PlO 81 d2 d3 84 Table 1: Integrated hardware and software behavior for the job sequence st, d2, d3, sa ’ , and, often, trial and error. Compositional modeling approaches, particularly those that model the behavior of the system from domain principles and component descriptions, help to simplify this problem (Fromherz Saraswat 1995). Furthermore, the model must facilitate the performance of tasks that are used for design optimization, e.g., behavior generation and analysis. Behavior generation for a system which combines subsystems from disparate domains must support the study of the interactions that occur among these subsystems. Behavior analysis must be holistic, i.e., it must permit reasoning about the effects of design variables on optimization objectives in a system-wide manner. Abstract models of components and processes. (DeKleer & Brown 1984) model the behavior of a physical system in terms of material, components, and conduits. In our application, the system’s components span the electromechanical hardware and the software domain, and we are interested tracking the movements of sheets and data in tile system at discrete time points. For each component (as shown in Fig. 3), we model its structure (i.e., input and output ports) and, with the demands of our application in mind, its temporal behavior defined "in terms of spatial locations and time stamps of material and data (i.e., the time it takes for the material to flow through tile component from an input port to an output port). (Gupta &: DeMicheli 1993) model software processes in terms of primitive operations, i.e., assignments, conditional tests, loops, etc. Their software model represents the time reqtfi~ed for the execution of each operation and temporal constraints among the operations.models of components and processes. (DeKleer & Brown 1984) model the behavior of a physical system in terms of material, components, and conduits. In our application, the system’s components span the electromechanical hardware and the software domain, and we are interested tracking the movements of sheets and data in tile system at discrete time points. For each component (as shown in Fig. 3), we model its structure (i.e., input and output ports) and, with the demands of our application in mind, its temporal behavior defined "in terms of spatial locations and time stamps of material and data (i.e., the time it takes for the material to flow through tile component from an input port to an output port). (Gupta &: DeMicheli 1993) model software processes in terms of primitive operations, i.e., assignments, conditional tests, loops, etc. Their software model represents the time reqtfi~ed for the execution of each operation and temporal constraints among the operations. (Thomas, Adams, & Schmidt 1993) choose a more abstract representation for their software subsystems by merging sets of operations into software processes. We select a process level representation where each process, which represents a collection of primitive operations, is modeled as an executable "black box". Data flow through a process is analogous to material flow in a hardware component. The time taken by a software process to perform its specified computation is a function of the nature of the task and the design variables that affect the process. Given that we are primarily interested in tracking the movement of materials and data component/process inputs ! paramnters ! outputs