Automating the Process of Optimization in Spacecraft Design

In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997

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 order 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 customization 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 algorithms 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 problems 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 techniques 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 spacecraft design optimization. 2 Nevertheless, it is not difficult to find in the metaheuristic 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 tendencies of various algorithms,” and proceeds by comparing the perform- [10,11,12,17,23]. Adaptive problem solving ance of several metaheuristics on a scheduling problem. requires a configurable problem solver, They conclude: “If obtaining solutions of higher quality meaning the problem solver possesses control is important, use Simulated Annealing or Greedy Local Search. Detailed parameter tuning is not important for Simulated Annealing and Greedy Local Search pro- 3 The formal statement of the traditional adaptive prob- vided that sufficient amount of computational time is lem solving forumulation and the review of previous available.” work is based on the treatment in [10]. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 decisions that may be resolved in alternative to be values of control points (e.g., a particular ways. Given a configurable problem solver, implementation of an adaptive temperature PS, with several control points, CP1...CPn schedule is one of the possible values for the (where each control point CPi corresponds to a temperature schedule control point for the particular control decision), and a set of values simulated annealing metaheuristic). 4 for each control point, {Mi,1...Mi,k} , a control strategy is an assignment of values to control Several approaches to adaptive problem solv- points that defines the overall behavior of the ing have been discussed in the literature. The problem solver. Let PSSTRAT be the problem first, a syntactic approach, is to preprocess a solver operating under a particular control problem-solving domain into a more efficient strategy. form, based solely on the domain’s syntactic structure. For example, Etzioni’s STATIC The quality of a problem solving strategy is system analyzes a portion of a planning do- defined in terms of the decision-theoretic no- main’s deductive closure to conjecture a set of tion of expected utility. Let U(PSSTRAT,d), be a search control heuristics [3]. Dechter and real valued utility function that is a measure of Pearl describe a class of constraint satisfaction the goodness of the behavior of the problem techniques that preprocess a general class of solver on a specific problem d.5 Then, the ex- problems into a more efficient form [2]. More pected utility can be defined formally over a recent work has focused on recognizing those distribution of problems D: structural properties that influence the effec- tiveness of different heuristic methods = × [4,14,22]. The goal of this approach is to pro- ED[ U ( PS STRAT )]∑ U ( PS STRAT , d ) pr ( d ) d∈ D vide a problem solver with what is essentially The goal of this standard formulation of adap- a big lookup table, specifying which heuristic tive problem solving can be expressed as: strategy to use based on some easily recogniz- given a problem distribution D, find some able syntactic features of a domain. While this control strategy in the space of possible strate- latter approach seems promising, work in this gies that maximizes the expected utility of the area is still preliminary and has focused pri- problem solver. For example, for the problem marily on artificial applications. The disad- of configuring a metaheuristic, say, a genetic vantage of purely syntactic techniques is that algorithm, in a design optimization system, the they ignore a potentially important source of control points include: the population size, the information, the distribution of problems. crossover rate, and the mutation rate, etc. Furthermore, current syntactic approaches to Utility might be defined as the quality of the this problem are specific to a particular, often design generated by the optimizer. unarticulated, utility function (usually problem-solving cost). For example, allowing the Note that a number of approaches to adapting utility function to be a user-specified parame- control points such as the population size of a ter would require a significant and problematic GA [21], have been proposed in the literature. extension of these methods. In our framework, we consider such strategies The second approach to adaptive problem

4 solving, the generative approach, is to gener- Note that a method may consist of smaller elements so that a method may be a set of control rules or a combi- ate custom-made heuristics in response to nation of heuristics. careful, automatic, analysis of past problem- 5 We assume that the problem solver runs for a finite solving attempts. Generative approaches con- amount of time and eventually terminates. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 sider not only the structure of the domain, but and face problems with local optima in the also structures that arise from the problem space of control strategies. Furthermore, they solver interacting with specific problems from typically leave it to the user to conjecture the the domain. This approach is exemplified by space of heuristic methods (see [19] for a no- SOAR [16] and PRODIGY/EBL [18]. These table exception). techniques analyze past problem-solving traces and conjecture heuristic control rules in A Generalization of Adaptive Problem Solving response to particular problem solving ineffi- The standard formulation of adaptive problem ciencies. Such approaches can effectively ex- solving described above is applicable when we ploit the idiosyncratic structure of a domain want to generate a problem solver that will through this careful analysis. The limitation of perform well for a particular problem distri- such approaches is that they have typically fo- bution. There are some problems with this cused on generating heuristics in response to formulation, however, that make it inappropri- particular problems and have not addressed ate for our domain of metaheuristic applica- the issue of adapting to a distribution of prob- 6 tion for spacecraft design optimization. lems well . Furthermore, as with the syntactic approaches, thus far they have been directed First, although the strategy found by an adap- towards a specific utility function. tive problem solver may have good expected performance over some distribution of prob- The third approach is the statistical approach. lem instances, there is no guarantee that the These techniques explicitly reason about per- problem solver performs well for any particu- formance of different heuristic strategies lar instance. In the domain of design optimi- across the distribution of problems. These are zation, the objective is often to generate the generally statistical generate-and-test ap- best possible solution for a specific problem proaches that estimated the average perform- instance, so there is a significant incompati- ance of different heuristics from a random set bility in the objective of the problem formula- of training examples and explore an explicit tion. space of heuristics with greedy search techniques. Examples of such systems are COM- Second, the standard adaptive problem solving POSER [11], PALO [12], and the statistical formulation implicitly assumes that only one component of MULTI-TAC [19]. Similar ap- specific configuration of the problem solver proaches have also been investigated in the will be applied to a particular problem in- operations research community [26]. These stance. If the objective is to generate the best techniques are easy to use, apply to a variety possible solution for a problem, then it may be of domains and utility functions, and can pro- worthwhile to try a number of different prob- vide strong statistical guarantees about their lem solver configurations on the problem in- performance. They are limited, however, as stance. In design optimization, it is often they are computationally expensive, require worthwhile to use massive amounts of com- many training examples to identify a strategy, puting resources7 in order to make significant improvements in the quality of the design, 6 While generative approaches can be trained on a which could lead to benefits that far outweigh problem distribution, learning typically occurs only within the context of a single problem. These systems will often learn knowledge which is helpful in a par- 7 CPU cycles are often quite cheap and readily avail- ticular problem but decreases utility overall, necessi- able, given the amount of computation available on idle tating the use of utility analysis techniques. workstations in many engineering organizations. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 the computational resources used to generate Definition: (Adaptive Problem Solving)— the improvement. Let d be a problem instance. Let PSSTRAT be the problem solver operating under a Finally, the problem solver configuration particular control strategy. Let found by the standard adaptive problem solv- U(PSSTRATt,d), be a real valued utility ing formulation is useful when we are given a function that is a measure of the goodness problem instance that is “typical” of the in- of the behavior of the problem solver on d. stances in the distribution for which the prob- The task of adaptive problem solving is to lem solver was configured. This, however, find a control strategy for the problem may be of limited utility if the problem solver solver that maximizes U(PSSTRAT,d). Given is faced with an instance which is significantly a set of problem instances D=d0, d1,...dn, different from previously seen instances. This the task of adaptive problem solving is to is a problem in our domain, since we are de- find a set of control strategies Strat0, signing a generic design optimization tool for Strat1,... StratN, that maximizes: which the distribution is virtually unrestricted. One could argue that if an instance is suffi- ∑U(,) PS d STRATd ciently different from the distribution for d∈ D which the configuration was optimized, then this forms the basis for a new distribution on If we were to treat the set of instances in the which to run the adaptive problem solver definition above as being samples drawn from (where initially, the distribution consists of a distribution, this formulation of adaptive this single, new instance). Of course, if we problem can be seen as a generalization of the allow for the possibility of maintaining multi- standard formulation, without the restriction ple problem solver configurations, one of that which should be selected depending on the Strat0 = Strat1 = StratN. distribution to which a particular instance belongs, new subproblems arise that must be The approaches for the standard formulation solved, including: can now be reevaluated with respect to the • Given a new problem instance, decide new formulation. In general, if we know of a which distribution it belongs to. configuration ConfD that maximizes expected • Deciding when/whether to “split” an ex- utility over a distribution D of problems to isting problem distribution into two or which a particular instance d belongs, then one more distributions when additional prob- would, by definition, expect (in the probabil- lems are added to the distribution. istic sense) that configuration to perform well on the instance. Suppose that our approach to For our problem of metaheuristic application solving the new adaptive problem solving for design optimization, what is needed then is formulation is to search the space of configu- a task formulation that maximizes the per- rations to find a near-optimal control strategy. formance for each particular problem instance, Then, a useful heuristic would be to try ConfD and does not rely on initial assumptions about first. Thus, we can treat solutions to the stan- the problem distribution from which the in- dard formulation as heuristic solutions for our stance is drawn. Our formulation for adaptive formulation of adaptive problem solving. problem solving is therefore the following: In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997

uted design model components together using a methogram, a graphical diagram represent- 4. OASIS ARCHITECTURE ing the data flow of the system. Each node in OASIS (Optimization Assistant) is an inte- the methogram corresponds to a design model grated software architecture for spacecraft de- component, which may be one of 1) a model sign optimization that supports adaptive in a commercial design tool such as IDEAS, problem solving. The three major components NASTRAN, or SPICE, 2) a program written of OASIS are: in C, C++, or FORTRAN, or 3) an embedded methogram (i.e., this allows methograms to • A spacecraft design model, have a hierarchical structure). Inputs to nodes • A suite of configurable metaheuristics, and in the methogram correspond to input pa- • An adaptive problem solver. rameters for the component represented by the node, and outputs from a methogram node We describe each of these in the following correspond to output values computed by the discussion. component. MIDAS is implemented as a CORBA object, and supports a wide variety of Spacecraft Design Model methods that can be used by external client systems (e.g., a GUI) to manipulate the The spacecraft design model is a software methograms. simulation of a spacecraft design. The design model takes as input decision variables to be This last feature of MIDAS (i.e., the CORBA optimized, and outputs an objective function interface that allows client systems to freely value, which is assigned as the result of an ar- manipulate methograms) is particularly useful bitrarily complex computation (i.e., the simu- for the purposes of designing a black-box op- lator is a black-box simulation). timization system, since it essentially provides the optimization system with a uniform inter- Thus, the design model is the component of face for any design model encapsulated in OASIS that is the most domain-specific, and is MIDAS. Therefore, our solution to the prob- provided by the end users, i.e., spacecraft de- lem of supporting a wide range of design signers. In order for an optimization system models is to support an interface to MIDAS. such as OASIS to be useful in practice, it must That is, OASIS is designed to be an optimiza- support a wide range of design models, which tion system that can be used to optimize any may consist of models implemented using MIDAS model. various languages on different platforms. It is not feasible to expect spacecraft designers to Thus, the design model, which constitutes the implement their models in a particular lan- user input to the OASIS sytem, is composed of guage on a particular platform—if such incon- the following: venient constraints were to be imposed, the • A MIDAS methogram that encapsulates optimization system will not be used by the design model, spacecraft designers. • A list of decision variables, as well as ranges of their possible values (may be The Multidisciplinary Integrated Design As- continuous or discrete), and sistant for Spacecraft (MIDAS) [6] is a graphical design environment that allows a user to integrate a system of possibly distrib- In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997

Figure 1—Screen shot of a MIDAS methogram (part of the Neptune Orbiter model)

• An output from a methogram node that at runtime. Currently, this consists of a recon- corresponds the user’s objective function figurable genetic algorithm and a reconfigur- value.8 able simulated annealing/local search. These Figure 1 shows part of a MIDAS methogram are briefly described below9: for the Neptune Orbiter model (see Section 5). Genetic Algorithm—A genetic algorithm Metaheuristic Suite works as follows: a population of sample points from the cost surface is generated. In a OASIS includes a set of configurable meta- process analogous to biological evolution, this heuristics, which are generic implementations of metaheuristics that provide an interface for 9 dynamic reconfiguration of their control points The following is a simplified account - there is much overlap between metaheuristics, and their boundaries are unclear (it is often possible to consider one meta- 8 The objective function could either be obtained di- heuristic as a specialization/generalization of another). rectly from one of the existing outputs in the For example, it is possible to think of some instances of methogram, or it could be computed by adding a new local search as a special case of genetic algorithm with node that computes, e.g., a weighted linear combination a population of 1. For clarity, we present metaheuristics of some set of output nodes. using their “canonical” descriptions. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 population is evolved by repeatedly selecting Our approach to adaptive problem solving is (based on relative optimality) members of the to view it as a meta-level heuristic search population for reproduction, and recombin- through the space of possible problem solver ing/mutating to generate a new population. configurations, where candidate configura- The control points of the genetic algorithm tions are evaluated with respect to a utility include: the population size, the methods used measure, and the goal is find a configuration for selection, crossover, and mutation that maximizes this utility measure. In princi- (methods include the algorithm, as well as ple, it is possible to do a brute-force search their control parameters, such as their fre- through the space of possible problem solver quency of application). configurations. This method is clearly intrac- table in general, since the number of configu- Simulated Annealing/Local Search—Local rations is exponential in the number of control search proceeds by generating an initial point points. Consider a problem solver with c con- on the cost surface and repeatedly applying trol points, each with v values; there are cv neighborhood moves (such as random pertur- problem solver configurations. Suppose we bations, greedy moves, etc.) to move to (on are given a problem instance for which the average) increasingly optimal points on the black-box simulation runs to evaluate a single cost surface. Simulated annealing is a gener- candidate design takes an average of t sec- alization of local search inspired by a physical onds. If each run of the problem solver on this metaphor to the process of annealing, in which instance requires n candidate design evalua- moves to less optimal points are taken prob- tions on average, then the expected time re- abilistically, in accordance with a temperature quired to search this space using an unguided, schedule. During the early part of the anneal- brute force search is O(ntcv). ing process, the temperature is high, and moves to less optimal points are taken more Given the enormous computational expense of frequently; as the temperature is decreased, the searching through the space of problem solver probability of rejecting moves to poorer points configurations, one might wonder whether the on the cost surface increases. The control search should/could be avoided altogether. To points of local search/simulated annealing in- avoid search completely, there are two alter- clude methods for temperature schedule and natives. The first is to find a super- the neighborhood move generator. metaheuristic that outperforms all others for all problem instances (and thereby avoid Adaptive Problem Solver adaptive problem solving altogether). As discussed in Section 2, we reject this solution as Given a spacecraft design optimization prob- infeasible. The second alternative is a syntac- lem instance in the form of a design model, tic, “lookup-table” approach: classify the the adaptive problem solver component of problem instance as a member of some class OASIS selects and configures a metaheuristics of problems, then apply the metaheuristic con- from its suite in order to maximize some util- figuration that is known to work well for this ity measure (usually, this is the quality of the class of problems. This method can work very design found by OASIS). In this section, we well if we happen to have studied the class of motivate our approach to adaptive problem problems to which the particular instance be- solving and describe the architecture of the longs, and we have available a good technique OASIS adaptive problem solver. for classifying the instance as a member of the class. This approach, however, is of limited In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 utility if we encounter an instance of a class • If a problem instance i is in the problem that we know nothing about, or if we cannot instance class I, then it is likely that its correctly classify the problem as one that be- cost surface is of type S; longs to a class for which we have a good • If the behavior of a configuration C is metaheuristic configuration.10 Thus, a purely poor, then the instance is likely to be in in- syntactic approach does not suffice. An adap- stance class I; tive problem solver needs to search the space • If the cost surface of the instance belongs of possible metaheuristic configurations—the to class S, then the instance is likely to be challenge is to discover and apply enough in instance class I. heuristic knowledge to the task to make it more tractable. In addition, this class includes any knowledge that can be used to classify a problem instance What types of heuristic knowledge are avail- as belonging to a particular class of problems, able to be either acquired from a human, or including pattern classification heuristics that through knowledge discovery/machine learn- can be used by a problem instance analysis ing techniques? We identify three general module. classes of knowledge which are applicable in this context: Domain-independent knowledge—This is a • domain-dependent knowledge about the formalization of the knowledge that human behavior of metaheuristics in a given do- optimization experts possess about optimiza- main, tion in general. It includes knowledge about • domain-independent, meta-knowledge the behavior of metaheuristics on particular about optimization, and classes of cost surfaces11, and knowledge • domain-independent, but system- about the behavior of metaheuristics in gen- dependent structural knowledge. eral. Classes of cost surfaces can be defined by attributes such as the number of local minima, Each of these types of knowledge are dis- distance relationships between local minima, cussed below: etc. Examples of heuristics that can be derived from this type of knowledge include: Domain-dependent knowledge—This includes knowledge about the structure of particular • If a surface of class S, configuration C is classes of problems, and the behavior of meta- promising; heuristics on particular problem instances or • If the behavior of a configuration C is classes of instances. Examples of heuristics poor, then, configuration C’ is promising; that can be derive from this type of knowledge • Given some features of the observed be- include: havior of configuration C, it is likely that the cost surface is in class S. • If a problem instance is in the problem instance class I, then configuration C is promising; 11 Note the difference between classes of problem instances, and classes of cost surfaces. Cost surfaces are a more abstract, and classes of cost surfaces can encom- 10 Indeed, the problems of defining useful notions of pass many classes of problems. For instance, the class classes of problem instances, and classifying a problem of cost surfaces that are “bumpy or rugged” includes instance as belonging to some particular class is a cost surfaces from a very large number of classes of challenging pattern recognition problem in itself. problem instances. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997

This class of knowledge may not be as power- able/value ordering heuristics12 in a search al- ful as domain-dependent knowledge by itself, gorithm that searches the space of metaheu- since it is more abstract in nature and more ristic configurations. difficult to apply. For example, analysis of the cost surface is more computationally expen- We are currently investigating several alter- sive than syntactic analysis of the instance, native approaches to representing the knowl- since it requires expensive runs of the black- edge in OASIS. The initial version of the OA- box simulation to evaluate the cost surface. SIS Adaptive Problem Solver uses Bayesian However, human optimization experts who networks [20] as its primary knowledge repre- may not be domain experts for a particular sentation scheme. Bayesian networks were problem that they are given must often rely on chosen primarily due to their clear, probabilis- their body of domain-independent knowledge, tic semantics, the flexibility with which vari- in combination to what domain-dependent ous kinds of inferences could be performed, knowledge they can obtain. The apparent suc- and the ability to seamlessly integrate new cess of these optimization experts indicates knowledge and observations into the knowl- that this type of knowledge can be a very use- edge base either manually (i.e., entered by a ful means of controlling search. human expert) or automatically (using machine learning techniques). Domain-independent, system-dependent structural knowledge—It may be possible to In the initial implementation, the Bayesian exploit the syntactic structure of the problem networks are manually constructed. A number representation in a particular adaptive problem of techniques have recently been developed solver. For instance, in OASIS, for a particular for learning in Bayesian networks [13]; we are problem instance, it may be possible to ana- currently investigating the application of these lyze the structure of its dataflow graph in the techniques. In addition, we are investigating MIDAS methogram to identify, e.g., decision new approaches to machine learning that take variables that affect a relatively large number advantage of the special structure of the adap- of other nodes in the graph. Hence, it may be tive problem solving domain. For example, more important to focus on nodes of high de- unlike most other domains, in which all the gree than a node than a node of low degree. At training data for machine learning is given to a this time, it seems that useful knowledge of learning algorithm by an external source, the this type may be extremely difficult to acquire, adaptive problem solving domain is interest- although this is an area of research that seems ing in that it is possible for the problem solv- particularly interesting from the de- ing system to perform experiments and gener- sign/human-computer interface perspectives, ate new data, using the exact same mecha- since it entails the understanding of how engi- nisms that are used to evaluate metaheuristic neers structure simulations from a graph- configurations. theoretic point of view. An important auxiliary component that is im- The various types of knowledge described portant for the adaptive problem solving proc- above can be applied either directly or indi- ess and applicable at various levels of the rectly (through chains of inference) as vari- OASIS architecture is the hypothesis testing

12 Variable ordering heuristics guide the choice of control points to change; value ordering heuristics guide the choice of control point values to try. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 module. Hypothesis testing is a statistical examples are illustrative of the range of differ- problem in which the confidence in the choice ent optimization problems that arise in space- of one belief over another given data is quanti- craft design. fied. When, for example, a metaheuristic is probabilistic in nature (as is the case with ge- The Mars Soil Penetrator Microprobe netic algorithms and simulated annealing), or As part of the NASA New Millennium pro- the black-box simulation is stochastic, then it gram, two microprobes, each consisting of a is important to be able to efficiently, accu- very low-mass aeroshell and penetrator sys- rately test whether one candidate is better than tem, are planned to launch in January, 1999 another (where a candidate can be, e.g., a (attached to the Mars Surveyor lander), to ar- metaheuristic configuration or a particular derive at Mars in December, 1999. The probes sign). [1] have proposed several efficient will ballistically enter the Martian atmosphere methods for computing within given confi- and passively orient themselves to meet peak dence bounds whether one candidate is better heating and impact requirements. Upon im- than another according to some utility meas- pacting the Martian surface, the probes will ure; we are currently investigating: punch through the entry aeroshell and separate • Extensions to these techniques, into a fore- and aftbody system. The forebody • Integration of these techniques within our will reach a depth of 0.5 to 2 meters, while the stochastic metaheuristics, and • aftbody will remain on the surface for com- Applicability to our new formulation of munications. adaptive problem solving. Each penetrator system includes a suite of Finally, we make use of parallelism and dis- highly miniaturized components needed for tributed processing on networks of worksta- future micropenetrator networks: ultra low tions in order to provide the massive compu- temperature batteries, power microelectronics, tational requirements of adaptive problem and advanced micro-controller, a microtele- solving. Currently, processes are distributed communications system and a science payload using the Parallel Virtual Machines message package (a microlaser system for detecting passing package [5] at the black-box simula- subsurface water). tion level. For example, multiple copies of the black-box simulation are distributed and are The optimization of physical design parame- executed in parallel given different decision ters for a soil penetrator based on these Mars variable assignments (i.e., a number of candi- microprobe is the first testbed for the OASIS date designs are evaluated in parallel). system. The microprobe optimization domain in its entirety is very complex, involving a 5. EXAMPLE SPACECRAFT DESIGN OPTI- three-stage simulation: MIZATION PROBLEMS • Separation analysis (i.e., separation from In this section, we describe two specific the Mars Surveyor), spacecraft design optimization problems to • Aerodynamical simulation, which we are currently applying the OASIS • Soil impact and penetration. system. The first is a low-level optimization of the physical dimensions of a soil penetrator To illustrate the utility of adaptive problem microprobe. The second is a system-level op- solving, we now briefly describe current work timization of the configuration of the commu- on a simplified version of the soil penetration nication system of an orbiter spacecraft. These stage. In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997

Figure 2—Sample points from cost surface for soil penetrator microprobe model. Plot of ratio of depth of penetration to length of penetrator. Soil number = 13 (soft soil)

to penetrate harder targets (the penetrator Given a number of parameters describing the could bounce off the target, for example). initial conditions including the angle of attack of the penetrator, the impact velocity, and the Figures 2 and 3 show plots of sample points hardness of the target surface, the optimization from the cost surface of this simplified pene- problem is to select the total length and outer tration problem for two different soil numbers, diameter of the penetrator, where the objective soillNum=7 (hard), and soilNum=13 (soft). is to maximize the ratio of the depth of pene- The cost surface for soilNum=13 is a rela- tration to the length of the penetrator. We tively smooth surface, while the cost surface maximize this ratio, rather than simply maxi- for soilNum=7 is a much more rugged surface mizing the depth of penetration, since for the Because of the larger number of discontinui- Mars microprobe science mission, the depth of ties in the cost surface for soilNum=7, optimi- penetration should ideally penetrate at least zation algorithms are more likely to get stuck the length of the entire penetrator). in local maxima in this cost surface. We would expect that a greedy metaheuristic One of the initial condition parameters that would be very successful for the soft surface, has a significant impact on the structure of the while a successful metaheuristic for the hard cost surface for this optimization problem is surface would require some mechanism to es- the soil number, which indicates the hardness cape local minima. Therefore, to obtain the of the target surface. Intuitively, one would best performance on a similar problem in- expect this to be an important parameter, stance (given a different soil number, for ex- since, for example, it is clearly more difficult ample), one should choose and configure a metaheuristic to exploit this knowledge ap- In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 propriately; this process would benefit from onstration, the focus is on the orbital opera- the application of our adaptive problem solv- tions of Neptune Orbiter. The launch and ing approach. The soil number is therefore a cruise phases of the mission will be included problem parameter that the OASIS adaptive in the optimization once the orbiter problem is problem solver can use as a feature with which well understood. The driving constraints of to classify problem instances (i.e., into prob- the orbiter problem are the optical communi- lems with soft and hard soil numbers). cation aperture, transmit power, and spacecraft mass. The transmit power is a direct input into The Neptune Orbiter the integrated spacecraft design model. The other inputs include the science observation Neptune Orbiter is a mission concept currently time per orbit and the data compression factor. being studied under the Outer Planet Orbital The output of the model that is being maxi- Express program at the Jet Propulsion Labo- mized is the science data volume per orbit. For ratory. The goals of the mission are to put a designs in which the spacecraft mass is greater spacecraft in orbit around Neptune using state- than 260kg, the data volume output is zero. A of-the-art technologies in the areas of tele- spacecraft with a dry mass of greater than communications, propulsion, orbit insertion, 260kg is too heavy to lift on the target launch and autonomous operations. The spacecraft is vehicle. Thus the mass limit bounds the opti- expected to arrive at Neptune (30 a.u.) five mization problem. Currently, we are using years after launch in 2005 using a Delta launch cost models in conjunction with the simulation vehicle. The subsystem requirements include of the orbiter as described above to obtain our 100 kbps data rate, solar electric propulsion, cost function—a quantitative estimate of the solar concentrator power source and a cost of science return (measured in, e.g., volume of less than $400M in FY 94 dollars. science data obtained per dollar cost of the For the initial phase of the optimization dem-

Figure 3—Sample points from cost surface for soil penetrator microprobe model. Plot of ratio of depth of penetration to length of penetrator. Soil number - 7 (hard soil). In Proceedings of IEEE Aerospace Conference, Snowmass, CO, 1997 spacecraft). [4] D. Frost and R. Dechter. “In search of the best constraint satisfaction search,” In Proceedings of National 6. SUMMARY AND CONCLUSION Conf. Artificial Intelligence (AAAI), 1994. Designing a widely applicable tool for space- [5] A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. craft design optimization is a significant tech- Manchek, and V. Sunderam. PVM: Parallel Virtual nical challenge. In this paper, we have pro- Machine - a user's guide and tutorial for networked posed the use of metaheuristic optimization parallel computing. MIT Press, 1994. algorithms, which are customized for particular problem instances by a process of adaptive [6] J. George, J. Peterson, and S. Southard. “Multidisciplinary Integrated Design Assistant for problem solving. By this, we hope to provide a Spacecraft (MIDAS),” In Proceedings of American design optimization tool that can provide Institute of Aeronautics and Astronautics (AIAA), 1995. spacecraft designers with the ability to perform successful design optimization with [7] F. Glover. “Tabu search - part I,” Operations Re- minimal human effort. We have described search Society of America (ORSA) J. Computing, 1:190-206, 1989. OASIS, our current implementation of a system based on these principles, and discussed [8] F. Glover. “Tabu search - part II,” Operations Re- many of the technical issues that have arisen search Society of America (ORSA) J. Computing, 2:4- in its design. Adaptive problem solving for 32, 1990. spacecraft design is a fertile research area with [9] D. Goldberg. Genetic Algorithms in Search, Optimi- significant potential benefits; this paper has zation and Machine Learning. Addison-Wesley, 1989. presented our initial efforts in this area. [10] J. Gratch and S. Chien. “Adaptive problem-solving ACKNOWLEDGMENTS for large-scale scheduling problems: A case study,” Journal of Artificial Intelligence Research, 4:365-396, This work was performed by the Jet Propul- 1996. sion Laboratory, California Institute of Tech- [11] J. Gratch and G. DeJong. “Composer: A probabil- nology, under contract with the National istic solution to the utility problem in speedup learn- Aeronautics and Space Administration. Bob ing,” In Proceedings of National Conf. Artificial Intel- Glaser and Celeste Satter provided the domain ligence (AAAI), 1992. models for the Mars microprobe and Neptune Orbiter, respectively. Thanks to Julia Dunphy [12] R. Greiner and I. Jurisca. “A statistical approach to solving the EBL utility problem,” In Proceedings of and Jose Salcedo for assistance with MIDAS. National Conf. Artificial Intelligence (AAAI), 1992.

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