In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 Automating the Process of Optimization in Spacecraft Design Alex S. Fukunaga, Steve Chien, Darren Mutz, Robert L. Sherwood, Andre D. Stechert Jet Propulsion Laboratory, MS 525-3660 California Institute of Technology 4800 Oak Grove Drive Pasadena, CA 91109-8099 (818)306-6157 [email protected], [email protected], [email protected], [email protected], [email protected] Abstract – Spacecraft design optimization is a signing values to X to minimize or maximize difficult problem, due to the complexity of an objective function F(X), subject to the con- optimization cost surfaces and the human ex- straints C. pertise in optimization that is necessary in or- der to achieve good results. In this paper, we Spacecraft design optimization is difficult us- propose the use of a set of generic, metaheu- ing current optimization methods because: ristic optimization algorithms (e.g., genetic • Current methods require a significant algorithms, simulated annealing), which is amount of manual customization by the configured for a particular optimization prob- users in order to be successful, and lem by an adaptive problem solver based on • Current methods are not well suited for artificial intelligence and machine learning mixed discrete/continuous, non-smooth, techniques. We describe work in progress on and possibly probabilistic cost surfaces OASIS, a system for adaptive problem solving that can arise in many design optimization based on these principles. problems. TABLE OF CONTENTS We are currently developing the Optimization 1. INTRODUCTION Assistant (OASIS), a tool for automated 2. OPTIMIZATION USING METAHEURISTICS spacecraft design optimization that addresses 3. ADAPTIVE PROBLEM SOLVING these two issues. The goal of OASIS is to fa- 4. OASIS ARCHITECTURE cilitate rapid "what-if" analysis of spacecraft 5. EXAMPLES OF SPACECRAFT DESIGN design by developing a widely applicable, OPTIMIZATION PROBLEMS spacecraft design optimization system that 6. SUMMARY AND CONCLUSIONS maximizes the automation of the optimization process and minimizes the amount of cus- tomization required by the user. 1. INTRODUCTION Many aspects of spacecraft design can be OASIS consists of an integrated suite of global viewed as instances of constrained optimiza- optimization algorithms that are appropriate tion problems. Given a set of decision vari- for non-smooth, possibly probabilistic, mixed ables X and a set of constraints C on X, the discrete/continuous cost surfaces, and an in- constrained optimization is the problem of as- telligent agent that decides how to apply these In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 algorithms to a particular problem. Given a particular spacecraft design optimization Second, many real-world optimization prob- problem, OASIS performs a meta-level opti- lems are black-box optimization problems, in mization in order to: which the structure of the cost function is • Select an appropriate optimization tech- opaque. That is, it is not possible to directly nique to apply to the problem, and analyze the cost surface by analytic means in • Automatically adapt (customize) the tech- order to guide an optimization algorithm. For nique to fit the problem. example, F(X) can be computed by a complex simulation about which the optimization algo- The rest of this paper is organized as follows. rithm has no information (e.g., to evaluate a Section 2 describes the application of meta- candidate spacecraft design, we could simulate heuristic algorithms to optimization, and its its operations using legacy FORTRAN code problems. In Section 3, we define the frame- about which very little is known to the op- work of adaptive problem solving that we timizer except for its I/O specifications). adopt for OASIS and describe related work in Black-box optimization problems are therefore the area. Section 4 presents an overview of the challenging because currently known algo- OASIS system architecture and describes our rithms for black-box optimization are essen- approach to solving the adaptive solving tially "blind" search algorithms—instead of problem task. In Section 5, we describe two being guided by direct analysis of the cost sur- spacecraft design optimization problems face, they must sample the cost surface in or- which are currently being used as testbed ap- der to indirectly obtain useful information plications for OASIS: the NASA New Millen- about the cost surface. nium DS-2 Mars Microprobe and the Neptune Orbiter spacecraft. Recently, there has been much research activ- ity in so-called metaheuristic algorithms such 2. OPTIMIZATION USING METAHEURISTICS as simulated annealing [15], tabu search [7,8] and genetic algorithms [9] for global optimi- Although optimization is a mature field that zation. These are loosely defined, "general- has been studied extensively by researchers, purpose" heuristics for optimization that pro- there are a number of open, fundamental ceed by iteratively sampling a cost surface, problems in the practical application of opti- and they implement various mechanisms for mization techniques. escaping local optima. Although these algo- rithms have been shown to be successful on First, the problem of global optimization on numerous applications with difficult cost sur- difficult cost surfaces is poorly understood. faces, the behavior of these algorithms is still The optimization of smooth, convex cost poorly understood. Successful application of functions is well understood, and efficient al- these metaheuristics1 to a particular problem gorithms for optimization on these surfaces requires: have been developed. However, these tradi- • Selection of the most appropriate metaheu- tional approaches often perform poorly on cost ristic for the problem, and surfaces with many local optima, since they • Intelligent configuration of the metaheu- tend to get stuck on local optima. Unfortu- ristic by selecting appropriate values for nately, many real-world optimization prob- lems have such a "rugged" cost surface and are thus difficult problems for traditional ap- 1 In the rest of the paper, we use the terms metaheuristic proaches to optimization. and metaheuristic algorithm interchangeably. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 various control parameters (e.g., tempera- which shows that over all possible cost sur- ture cooling schedule for simulated an- faces, the expected performances of all opti- nealing). mization algorithms are exactly equal. Al- Currently, successful applications of metaheu- though it is possible that “all problems of in- ristics are often the result of an iterative cycle terest” (in our context, all nontrivial spacecraft in which a researcher or practitioner selects design optimization problems) reflect a par- and adjusts a number of different metaheuris- ticular subset of all possible cost surfaces for tic/control parameter combinations on a which some metaheuristic configuration’s per- problem, observes the results, and repeats this formance dominates that of all others, we process until satisfactory results are obtained. strongly believe that this is not the case. Thus, This process of selecting and configuring a our assumption throughout this paper is that metaheuristic to obtain good results on a to obtain the best performance for a particular given problem is usually time-consuming, and problem instance, it is necessary to select a requires a significant amount of optimization metaheuristic and configure it so that it expertise (which is often very costly to ob- matches the structure of the cost surface of the tain). As a result, in many cases, the cost of instance. successfully applying metaheuristic tech- niques on black-box problems can be pro- 3. ADAPTIVE PROBLEM SOLVING hibitively expensive. A natural approach to alleviating this problem of selecting and configuring a metaheuristic One might wonder whether there is some su- for particular applications is to automate the per-metaheuristic and a perfect configuration process. This is an instance of the more ge- of this super-metaheuristic, which outperforms neric, adaptive problem solving task, which all others for all problems of interest, or has been studied by the artificial intelligence whether it is at least possible to characterize community, where the task is to automatically the performance of metaheuristic configura- configure a problem solving system (such as tions in general. The current conventional an optimization system). In this section, we wisdom in the optimization research commu- give the standard definition of the adaptive nity is that this possibility is extremely un- problem solving task, and review previous ap- likely (although it not likely that this can ever proaches in the literature3. We then discuss a be formally proved, due to the empirical na- 2 generalization of adaptive problem solving, ture of the question). This is supported by which is the framework we will adopt for the related recent theoretical work such as [24], metaheuristic application problem in space- craft design optimization. 2 Nevertheless, it is not difficult to find in the metaheu- ristic literature empirical studies that claim that one Before discussing approaches to adaptive metaheuristic or one configuration is better than an- problem solving, we formally state the stan- other (e.g., [25] boldly claims that “the objective of this dard definition of the task (as proposed by paper is...to study the general