Object-oriented model integration in MIDAS - IEEE Computer Society

OBJECT-ORIENTED MODEL INTEGRATION IN MIDAS M.A.H. Dempster*

Alice M. Ireland1

Department of Mathematics, Statistics & Computing Science and School of Business Adrmnistration Dalhousie University, Halifax, Nova Scotia, Canada B3H 125 *and Balliol College Oxford England OX1 3BJ

tnow a t Department of Accounting Saint Mary’s University Halifax, Nova Scotia, Canada B3H 3C3

ABSTRACT Artificial intelligence researchers have realized the importance of specific domain knowledge in extending the capabilities of rulebased expert systems beyond that of generalized problem solvers [Davis 19841. Similarly, domain-specific research in decision support and model management has led t o more immediately successful systems because the characteristics of individual domains can be exploited t o add power t o the systems. Examples include an actuarial modelling system which is able to formulate and execute problem-solving plans using multiple models sequenced according t o varying problem descriptions [Sivasankaran and Jarke 19851, and a production planning system which formulates linear programs based on object-oriented domain entity descriptions [Binbasioglu and Jarke 19861.

Decision support systems for users without modelling expertise require domain-specific modelling knowledge to translate between conceptual and mathematical problem views. In complez, dynamic decision situations using multiple model types, the system must create and modify individual models to reflect changing domain conditions and assumptions, maintain consistency among different models in the same decision situation and allow communication among models for their complementary use, all without relying on user expertise. This paper describes a system f o r debt decision support which flexibly integrates optimization and simulation modelling and heuristic reasoning f o r non-expert users through an object-oriented, domain-specific knowledge base. Stable domain relationships and mathematical procedures are encapsulated in domain object classes; domain object instances are combined to form common model representations manipulated by operators specific to each model type. The approach is applicable in domains in which stable entities and interactions exist and in which model flexibility results from varying combinations of entities-conditions which are found in many financial and other business modelling situations.

This paper describes the model integration aspects of a system which provides assistance t o non-expert users in the configuration and complimentary use of multiple model types in a limitedbut complex-financial management domain. We address issues of flexibility, consistency, communication and complementarity among two related classes of models using a common objectoriented problem representation in which domain objects encapsulate facts, mathematical relationships and qualitative relationships for common use by all model types. These domain objects act as building blocks for a common representation of each problem situation which is manipulated by operators carrying out configuration, reasoning and solution procedures as required for each model type. The domain-specific approach has allowed us t o take advantage of the structural characteristics of the domain and model types t o produce a flexible modelling environment for naive users.

INTRODUCTION A major goal of decision support systems research is t o provide flexible, dynamic modeling environments for users who are not modelling specialists [Elam and Konsynski 19871. Such an environment must contain application domain knowledge for mapping between user and model problem views, as well as modelling knowledge for flexible model creation, modification, configuration and interpretation. Where multiple model types are used, syatems must recognize when and how t o apply each type, maintain consistent problem descriptions for various models (or recognize and handle inconsistencies), provide for communication among different model types and instances and present a uniform interface shielding the inexperienced user from model creation, instantiation and combination details.

In the following sections we present overviews of the problem domain and the MIDAS (Manager’s Intelligent Debt Advisory System) system architecture, followed by discussions of the system’s knowledge base, the model management features of individual model components and the communication and integration techniques used to handle multiple model types. We conclude with observations gained from the project so far and note directions for our continuing work.

These requirements have only begun to be realized in current model management research. Work on generalized model management systems has provided formal, data-independent model representations and suggestions for generalized manipulation languages [Bonczek et al. 1981, Blanning 1985, Geoffrion 19871 but has not yet focused on practical synthesis, consistency or multiplemodel integration problems. Research on model synthesis [Murphy and Stohr 1986, Dhar and Pople 1987, Dhar and Croker 19881 has successfully illustrated model formulation from fragments for a single model type (linear programming or simulation) but has not considered different model types applied to a common decision situation.

PROBLEM AND SYSTEM OVERVIEW Our problem domain is corporate debt planning for a Canadian public utility. The organization’s Treasurer must develop and implement borrowing plans to meet forecast cash requirements over a rolling planning horizon (usually 2-5 years) at minimal cost subject t o risk, market and other internally- and externally-

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imposed constraints. Financing sources include domestic and foreign public bond markets, banks, equipment suppliers and local consumers through savings bonds. Constraints arise from external market conditions such as limitations on amounts available from particular souyes, and from internal conditions such as a desire t o smooth cash flows in future operating periods. Finally, the future interest and exchange rates which determine costs are uncertain and subject t o fluctuations of varying degrees depending on future economic conditions and the financial soundness of the corporation as perceived by rating agencies.

is thus a portfolio management problem, in which t h e debt portfolio is the collection of debts used to meet cash requirements over the planning horizon. The problem is highly complex because the planning horizon extends over a number of time periods, many decisions may be required, and borrowing decisions are contingent on previous borrowing decisions and on future interest and foreign exchange rates. It also requires great modelling flexibility t o handle multiple portfolio configurations and the innovative types of debt that are regularly being created in financial marketi and offered as new potential portfolio components.

Total borrowing cost and risk (cost variation) is a product of many interacting conditions and decisions. For example, $100 million needed for five years beginning today could be borrowed at a fixed rate for five years, in which case costs are known for the entire period, or for two years with refinancing after the i d tial term, in which case costs depend on refinancing arrangements and applicable future interest rates. Developing a borrowing plan

Currently, the Treasurer supports borrowing decisions with spreadsheet-based deterministic cost projections for individual debt dternatives. A model is constructed for each possible debt (callable bond, bond with a sinking fund, savings bond, mortgage etc. with a specific issue date, maturity date, interest rate and other costdetermining characteristics) and planning horizon, and costs are calculated using varying interest and exchange rate assumptions.

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Figure 1. M I D A S Architecture

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This has the advantage of modelling flexibility, since any debt can be “custom-modelled” using a new spreadsheet. It also allows the Treasurer to assess the sensitivity t o future rates of one debt’s cost. However, it is limited t o deterministic rate scenario specifications, and it does not capture the full portfolio or contingency aspects of the debt management problem because it models individual decisions without their interactions

First, the user states a borrowing problem in terms of planning horizon, cash requirements, performance goals and available debt types. A scenario-based stochastic programming model, controlled by a modelling assistant module, suggests an optimal but simplified borrowing plan based on a probabilistic “tree” representation of the user’s assessment of future rates. A rule-based refinement module then examines the optimal simplified plan and produces several candidate plans with additional details and decision values rounded t o marketable quantities; these plans are no longer optimal but will each satisfy the stated borrowing requirements. Finally, a second modelling assistant controls the simulation model in testing the candidate plans by projecting their future cash flows, borrowing costs and ending portfolio values for comparison and evaluation. Linking the three components (and planned additional modules for model checking, interpretation and evaluation) is the function of an object-oriented knowledge base, which maintains a consistent portfolio and domain description underlying all model operations. Because the system is highly modular with a flexible interface, it can also be used for subprocesses of the complete planning process such as testing user-defined decision alternatives or a user-defined borrowing plan.

Several more competitive modelling techniques are applicable t o borrowing decisions, particularly when borrowing is regarded as an investment problem with cash flow direct,ions reversed. Stochastic linear programming [Crane 1971, Bradley and Crane 1972, 1975, 1980, Crane, Knoop and Pettigrew 1977, Lane and Hutchinson 19801, mixed integer programming [Shapiro 19871 and dynamic programming [Elton and Gruber 1971, Kalymon 1971, Boyce and Kalotay 1979) have all been applied t o debt or inveatment portfolio management. Stochastic simulation is a wellknown tool for capital budgeting analysis and has been applied t o the analysis of borrowing alternatives [Hertz 1964, Bradley and Crane 1975, Howard 19861. As in other domains, optimization techniques can handle simplified versions of the problem but cannot quickly solve problems in the detail required for actual decisions. On the other hand, simulation can flexibly model many details but cannot suggest optimal solutions, particularly in complex decision situations.

This approach replaces spreadsheets with two types of modelling (stochastic programming and stochastic simulation) which are not familiar to the system’s intended user except at a broad conceptual level. Lack of both experience and trained staff able t o build and run such models have together kept these sophisticated techniques from being used in the past. MIDAS is therefore designed t o replace the scarce intermediary by automating model instantiation, solution, modification, sensitivity analysis and presentation of results. The system is implemented primarily in

The approach we have chosen in MIDAS is the complementary use of stochastic linear programming and simulation modelling, extended with rule-based modules. The two models and their extensions support a hierarchical planning process in which borrowing plans are produced and refined in successive stages (Figure 1).

CALLABLE BONDS DESCRIPTIVE ATTRIBUTES:

Market Coupon rate Issue date Term Maturity date Principal amount Call dates Call prices

Create instance OBJECT MAINTENANCE Input attribute values Change attribute values METHODS: Delete instance Display attribute values

0 PT I M I Z AT ION Coefficient lists

0 P TI M I Z AT10 N Calculate coefficients

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Store decision values Display results Graph results

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Financial performance detail lists Performance indicators

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Project cash flows Summarize cash flows Summarize performance Display results Graph results

Figure 2. A Typical Basic Model Object Class

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F i g u r e 3. M I D A S F i n a n c i a l I n s t r u m e n t C l a s s e s

KEE (Fikes and Kehler 1985, Stefik and Bobrow 1986, Filman 19881 and LISP on a Unisys Explorer workstat,ion, with its optimization model solver implemented in FORTRAN and running on a MicroVAX I1 Ethernetted to the Explorer. KNOWLEDGE REPRESENTATION Debt planning domain knowledge in MIDAS is organized within a frame-based representation in which generic object types are defined, specialized and instantiated as nodes in a semantic inheritance network [Minsky 1975, Stefik and Bobrow 1986, htellicorp 19871. Object classes and individuals contain attributes describing their properties and relationships; attributes and their values are inherited downward through the inheritance hierarchy unless overridden. Objects also contain procedures (methods) specifying operations or behaviors; like attributes, these are also inherited unless modified or overridden. This representation allows modular, non-redundant specification of domain entities, relationships

and behaviors. Object-oriented representations have been recommended for model representation and manipulation in a number of contexts [Applegate et al. 1985, Binbasioglu and Jarke 1986, Dolk 19871. Our debt planning objects are classified according to their roles in the modelling process. Model objects represent domain entities whose financial performance (output values) over time determine the feasibility and desirability of a borrowing plan. Basic model objects represent individual debts or investments. Each basic model object (Figure 2) encapsulates descriptive attributes and their values (interest rate, principal amount, issue date, term, maturity date, etc.), as well as model input and output values (LP coefficients, cash flow lists, borrowing cost lists, etc.). Methods in basic model objects calculate values, direct model solvers and present results. Classes for basic model objects are defined economically using the inheritance hierarchy (Figure 3); individual model objects are instantiations of type classes resulting from borrowing plan decisions.

PO RTFO LlOS OBJECT MAINTENANCE METHODS:

Create instance Input members Change members Delete instance Display members

OPTIMIZATION Optimal ending ATTRIBUTES: market value Borrowing costs by period Plan summary

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Format optimization input Solve optimization model instance Store optimization results Display optimization results

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Project cash flows Summarize cash flows Summarize performance Display results Graph results

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Portfolio performance lists

Figure 4. A Typical Composite Model Object 615

path through the tree (called a scenario) specifies a KEEworld [Filman 19881 which represents the domain state (rates, decisions and financial results) if that scenario is realized.

Composite model objects (Figure 4) combine basic model objects into portfolios, supervise coefficient generation for optimization and simulation of portfolios, handle interactions among objects and summarize and present portfolio optimization and simulation results. Composite model object attributes identify portfolio members and summarize portfolio performance over the planning period, while composite model object methods direct portfolio modelling and result summarization. It is these composite model objects which provide the flexibility needed t o configure models for debt portfolios reflecting alternative borrowing plans.

In addition t o the above functions, each model and support object contains methods for directing its own maintenance through input forms, maintaining consistency of attribute values and displaying its own model-generated results. For example, methods are currently being developed for hot screen graphic representation of rate event trees and associated data entry. Additional analytical objects in the knowledge base contain parameters and procedures for controlling the analytical process, all described further in the next two sections.

The use of standardized method names for all model objects allows us to ignore calculation details which vary with object type, treating the collection of modelling methods as a high-level set of operators for manipulating model objects in accordance with various modelling techniques. Operators which project financial results are similar in function to spreadsheet cell formulas but are procedurally defined in LISP methods.

The object-oriented knowledge base sketched above was derived from user descriptions of the decision domain augmented by financial and modelling experts. It provides structure, control and a common conceptual base for explaining MIDAS’ underlying modelling and reasoning t o the user without being directly visible. Rather, a uniform user interface provides menu-and-mouse control at all stages of system use. Guided by an overall control method, the user uses input-form windows t o enter or change descriptive parameters for a specific problem. High-level LISP methods and/or rule sets for model creation, modification, analysis and interpretation are either system-controlled or requested by the user via menus (depending on the operating mode selected). These in turn call other LISP-code methods t o carry out the details of particular operations on the specific objects involved. Output is presented in tabular, graphic or templatedriven cultural language form as appropriate. Thus, once the naive user has described the problem in detail, the system mimics an intermediary by handling all technical modelling tasks.

Support objects represent domain entities which provide assumptions or constraints affecting the debt planning task. Our support objects include the borrower (borrowing corporation), financial markets (domestic and foreign) and rate event trees. The borrower object stores financial goals, cash requirements and constraint parameters guiding the planning process. Financial market objects have three roles: to provide default values for types of debt issued in particular markets, t o hold market-related constraint values such as maximum allowable borrowing in a period, and t o provide market interest and exchange rates (deterministic or stochastic) consistent with existing rate scenarios as required by mathematical models or rule sets. Uncertainty is represented through rate event trees, which represent branching, probabilistic rate movements over the planning horizon, as forecast outside the system (Figure 5). Each rate

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A more detailed description of the knowledge base is found in Ireland [1988]; a more extensive explanation of rate event trees and MIDAS’ rate models is found in Dempster and Ireland 119871.

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F i g u r e 5 . I n t e r e s t R a t e E v e n t Tree

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portfolio details, obtained as market default values, user input ormodel results are stored uniformly in the debt objects, giving a complete portfolio specification for examination by other system components.

OPTIMIZATION MODEL MANAGEMENT Following Bradley and Crane [1972, 1975, 19801 and Lane and Hutchinson (19801,MIDAS’ optimizationmodelling uses scenariobased stochastic linear programming to minimize the expected debt portfolio value at the end of the planning period subject to cash requirement, maximal debt cost, corporate and market constraints. Decision variables correspond to “debt types” consisting of hypothetical debts for various terms in various markets; decisions a r e amounts of debt issued, held and retired of each type, contingent on realized rate scenarios. All interest is financed through debt so that the ending value reflects total borrowing cost financed at minimal rates. (A formal specification of the model may be found in Dempster and Ireland (19871.)

OPTIMAL SOLUTION REFINEMENT As it is now specified, the optimization model simplifies reality. There are three main types of simplification: no full account is taken of integer valued constraints, integer-valued decisions or sinking funds. To be solved in reasonable time, we have linearized integer valued constraints such as market minimum borrowing constraints (which are either 0 or a minimum value). We have allowed decisions to be continuous even though in practice debt issue amounts for the test corporation are usually in multiples of $25 million. We have also ignored sinking funds as decision variables. (Debts may often be issued with, or without, sinLing funds-i.e., investment funds which build toward the repayment value at the end of the debt term).

Because the system solves a single decision problem (debt portfolio selection), the optimization model’s general form is constant regardless of the particular decision situation. Decision variables and constraints can vary with each model instantiation and are user-controlled at specification time. Model management tasks performed by the system therefore consist of input parameter calculation, input formatting, input tranmission to the MicroVax solver, output reception from the solver and output storage in the knowledge base.

To modify the optimal solution into a feasible “real-world’’ plan, a rule-based module reviews LP output at user request and modifies it by suggesting alternatives for the optimal simplified decisions. In the initial version of this module, each decision value that violates a real-world requirement (usually defined by parameters in market objects) are first identified and rounded to the nearest acceptable value. Sinking-fund debt is then set up in markets where sinking fund use is required. Finally, the resulting plan is modified to produce alternative plans with and without sinking funds for decisions in which sinking funds are optional. Simple heuristics reduce the number of alternatives by altering decisions in groups by market or by a system-produced significance ranking, and constraints other than cash or cost requirements are checked and maintained during the modification process. Violations of cash requirement constraints (i.e., borrowing too much or too little in a time period) are noted and penalized during plan simulations, described below.

Input parameter calculation and output storage are handled by LISP-code methods in debt objects representing decision variables. Each decision variable object is a debt instance with market, issue date and term attributes specified and a principal amount of $1. Its coefficients (issue costs, interest paid and retirement costs per period) are calculated by methods which use as sub-methods the cost calculation procedures in the simulation (see below). These methods are inherited by the debt instances from their parent debt classes. Other coefficients and parameters are attribute values in borrower and market objects, directly accessed by the input formatter. Input formatting is handled by a single method in an L P control object. Input is set up in a fixed-format standard extending the MPS format to handle stochastic programming (Birge et al. 19871. Input and output communication are also handled by procedures in this object. Parametric investigation of optimization model results is handled by a separate parametric LP object utilizing the LP control object methods successively through messages.

Each feasible plan resulting from the plan refinement heuristics step is represented as a new KEEworld with a unique borrowing plan represented as a portfolio of debt objects (Figure 6). Debt object attributes in each plan/scenario world reflect decisions and results under that plan and scenario. Because each debt object has inherited all required simulation methods, each plan can be completely simulated over the planning horizon and rate event tree to produce a detailed picture of its future behavior.

Output from the LP solver has the form of decision variable values, i.e., amounts of each debt type borrowed, held or repaid. These are stored in a straightforward manner in the debt variable instances as principal amounts and repayment schedule attributes (amounts held are implicit results of issue and repayment amounts). Shadow prices from the solver now used [Gassmann 19871 are not meaningful; when they do become useful (for pruning scenarios from the interest rate event tree), they will be stored as additional attributes in decision variable objects. Meanwhile, parametric analysis using multiple calls to the solver is used to develop a profile of the maximal cost constraint/objective value relationship, with results stored as portfolio parameters.

SIMULATION MANAGEMENT MIDAS’s simulationis a spreadsheet-style projection of cash flows, ending market value and borrowing costs over the planning horizon for each portfolio. It can be done either in a single pass using the mean rate scenarios described in the rate event tree, or in multiple passes using randomly-generated rates based on the underlying rate scenarios. (For details of the rate generation process, see Dempster and Ireland [1987].) Single-pass simulations produce tables of detailed cost and performance figures, while multiple-pass simulations produce distributions for ending value and debt cost. The simulation can be used either following optimization and plan refinement (the process we have described above) or as a stand-alone system for testing the implications of user-defined borrowing alternatives.

The optimization model thus suggests an optimal debt plan in the form of a portfolio of realized decisions (debts) with specified issue dates, markets, terms, principal amounts and features. All

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F i g u r e 6 . A l t e r n a t i v e B o r r o w i n g P l a n s and S c e n a r i o s

The simulation is controlled at the portfolio level through mesiages t o debt object methods (for details see Ireland 119881). Mathematical relationships in the stochastic linear programming model are extended to produce detailed tables of financial results rather than coefficient matrices. Consistency with the optimization model is maintained (a) through the use of common methods for borrowing cost calculation and ending market-value assessment, ( b ) through a penalization procedure in the simulation which mimics recourse (short-term borrowing) penalties in the linear program, and (c) through debt financing of all interest and sinking fund payments as in the optimization model’s cash requirements constraint. New borrowing decisions are generated heuristically using user-specified rules by the simulation whenever additional cash is required (as, for example, when a plan modification results in too little borrowing in a given period); the simulation of course differs from the optimization in not generating optimal borrowing decisions in these cases.

The different models have common parameter values for coefficient and simulation result calculations arising from parameter definition and value storage in common portfolio, debt and support objects. The models share mathematical procedures for common calculations even though calculation results are used for different purposes in the modelling process. All model communication, including communication with rule-based reasoning modules, is through the common objects. Input t o and results from each model or rule set are stored as attribute values available to the entire system. Because underlying objects store intermediate domain states, the optimization, refinement and simulation models are linked in the staged planning process supported by the system. Each stage has a well-defined, complementary function t o perform in adding t o or modifying the knowledge base domain description.

Computational details for the mean path of each scenario simulation are stored in a spreadsheet format in each debt object t o provide an audit trail for subsequent analysis by the user or the system. For sensitivity analysis using simulation, this allows recalculation only of affected scenarios.

CONCLUSIONS Our primary achievement so far is the illustration of a system enabling complementary use of multiple, complex models and rule-based components in a complex domain by a non-expert user. Relying on extensive object-oriented domain and modelling knowledge, the system shields the user from details of modelling while retaining the ability t o flexibly configure debt portfolios in response t o changing assumptions or conditions. It is clear from the work so far that domain-specific knowledge provides a common conceptual structure for organizing and controlling inp u t , computations and results for different modelling techniques applied t o a single problem. For modelling assistance to naive users, generalized model representations will be insufficient without domain representations to map user problem descriptions into model configurations and model results into user views.

MODEL INTEGRATION AND COMMUNICATION The consistency of our modelling environment arises from the use of domain objects as common underlying conceptual and operational modules for all modelling and heuristic reasoning. The debt portfolio, consisting of individual debt objects active during the planning period, ensures model consistency, communication and complimentary use in several speccfic ways:Both types of models are configured or reconfigured simultaneously when a portfolio is created.

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We have found the use of object-oriented programming techniques implemented in KEE/LISP t o be more than adequate t o the task of system development described i n this paper. We expect this observation t o apply t o the continuing development of MIDAS and related planning systems with similar architectures i n the fields of research and development and integrated design/manufacture/maintenance project control on Micro Explorers. Our only caveats concern the plethora of ways of accomplishing any given task on a n Explorer/KEE workstation and the consequent not insubstantial learning times involved. In this computing environment, the tradeoff between elapsed and applied time needed t o optimize system development is nontrivial. T h e MIDAS system as developed so far is weak in the areas of user help, result interpretation and configuration of innovative debt types; also, it does not yet assist in evaluating borrowing plans based on simulation results. We intend t o add these facilities a s the prototype system becomes operational and supported within the test corporation. The other major effort planned for the MIDAS project is enhancement of the user-model interface assistant modules t o provide intelligent user assistance in interpreting and refining model results for both the optimization and simulation components [Dempster and Ireland 19871. Our preliminary design utilizes a combined frame-and rule-based diagnostic approach, so that the underlying representation described i n this paper will continue t o support enhanced power for user modelling assistance.

Our domain-specific approach contrasts with two other directions i n intelligent decision support systems research. I n designing and developing MIDAS, we have not attempted t o build from formalisms t o a working but circumscribed system, cf. Geoffrion [1987]. Neither have we attempted t o provide generalized support for modelling of a particular general class such as activity analysis by linear programming [Murphy and Stohr 19861. Instead, we have chosen a complex, semi-structured domain and induced the required design principles, models, objects and procedures from domain requirements, (formal) structure where it exists, and heuristics where it does not. This has allowed us the freedom t o explore our domain and its modelling support requirements guided by user needs and known modelling requirements; attempts t o formalize or generalize will be as a result of insights we gain through building a fully functioning real-world system. Nevertheless, we conclude by observing that t o date the MIDAS system architecture utilizes object-oriented programming t o incorporate the following general principles for intelligent systems manipulating several comples models via coupled symbolic/numeric computing on distributed hardware:. Use of a hierarchy of domain specific basic and composite model objects t o provide model configuration flexibility. Use of standardized method names for all model objects t o allow the treatment of methods as high-level operators for manipulating model objects. Use of support objects t o encapsulate goals and constraints as defined by both the user and the domain of the system. Use of methods within analytical objects in the form of nested high-level rule sets and LISP procedures t o guide system analysis of composite model objects in order t o meet goals within constraints.

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