P 1 9 9 1 - 1 1 - 1
IMSDC'gi
M S D
9 1
The 4th
PROCEEDINGS VOL. 1
International
Marine
Systems
Design
Conference
Kobe, Japan
May 26 - 30, 1991
THE SOCIETY OF NAVAL ARCHITECTS OF JAPAN
THE KANSAI SOCIETY OF NAVAL ARCHITECTS, JAPAN
THE SCIENCE COUNSIL OF JAPAN
The Fourth International Marine Systems Design Conference
May 26 - 30, 1991
International Conference Center, Kobe, Japan
The Society of Naval Architects of Japan
The Kansai Society of Naval Architects, Japan
The Science Council of Japan
PREFACE
This volume contains the papers of the IMSDC'91 conference at the
Intemational Conference center in Kobe, Japan on Monday 27th through
Thursday 29th of May 1991.
The IMSDC'91 is the Fourth Intemational Marine Systems Design
Conference, following very successful '82 Conference in London, '85
Conference in Lyngby and '88 Conference in Pittsburgh. Forty seven
papers, including four very valuable invited papers, dealing with subjects in
the field of ship and marine systems design, design applied to the offshore
industry, design of propulsion systems and the theory of design are
presented. The authors come from Australia, Brazil, Bulgaria, Canada,
China, Finland, France, Germany, Hong Kong, Indonesia, Japan, Korea,
Nigeria, Norway, The Netherlands, The United Kingdom and The United
States of America.
The IMSDC'91 conference is arranged by the Society of Naval Architects
of Japan and the Kansai Society of Naval Architects, Japan under the
auspices of the Science Council of Japan.
The Intemational IMSDC'91 Committee
The Japanese Organising Committee
The Japanese Executive Committee
ORGANIZATION
JAPANESE ORGANIZING COMMITTEE
Prof. S. Takezawa (Chairman)
Mr. K. Kai
Mr. K. Toda
Mr. E. Kataoka
Mr. Y. Sasakawa
Mr. H. Matsunari
Mr. M. Uchida
Mr. K. Inaba
Mr. F. Higaki
Mr. M. Kanamori
Mr. S. Fumta
Mr. K. Minamizaki
Mr. Y. Manabe
Mr. A. Miyazaki
Mr. J. Hoshino
Mr. Y. Fujiwara
Mr. H. Miyazaki
Mr. H. Matsuura
Mr. K. Sannomiya
Mr. S. Kuroda
Mr. I. Ohno
Prof. S. Nakamura
Prof. N. Takarada
Prof. T. Koyama
The Society of Naval Architects of Japan
Yokohama National University
The Kansai Society of Naval Architects, Japan
Ministry of Transport
Ship Research Institute
Japan Shipbuilding Industry Foundation
Japanese Shipowner's Association
Nippon Kaiji Kyokai
Shipbuilder's Association of Japan
The Cooperative Association of Japan Shipbuilders
The Shipbuilding Research Association of Japan
Hitachi Zosen Corporation
Ishikawajima-Harima Heavy Industries, Co. Ltd.
Kawasaki Heavy Industries, Ltd.
Mitsubishi Heavy Industries, Ltd.
Mitsui Engineering and Shipbuilding, Co. Ltd.
Namura Shipbuilding Co. Ltd.
NKK Corporation
Oshima Shipbuilding Co. Ltd.
Sanoyas Corporation
Sasebo Heavy Industries, Co. Ltd.
Sumitomo Heavy Industries, Ltd.
Osaka University
Yokohama National University
University of Tokyo
JAPANESE EXECUTIVE COMMITTEE
Prof. S. Nakamura (Chairman)
Prof. K. Taguchi (Vice Chairman)
Prof. N. Takarada (Vice Chairman)
Prof. T. Koyama
Prof. M . Nakato
Prof. Y. Inoue
Prof. N. Fukuchi
Prof. R. Hosoda (Secretary)
Prof. S. Naito (Secretary)
Mr. T. Kaji
Mr. M . Sekihama
Mr. S. Hirano
Mr. M . Nakayama
Mr. S. Namba
Mr. A. Enomoto
Mr. K. Kawasaki
Mr. T. Miyamoto
Osaka University
Fukuyama University
Yokohama National University
University of Tokyo
Hiroshima University
Yokohama National University
Kyushu University
University of Osaka Prefecture
Osaka University
Nippon Kaiji Kyokai
Hitachi Zosen (Corporation
Ishikawajima-Harima Heavy Industries, Co. Ltd.
Kawasaki Heavy Industries, Ltd.
Mitsubishi Heavy Industries, Ltd.
Mitsubishi Heavy Industries, Ltd.
Mitsui Engineering and Shipbuilding Co. Ltd.
NKK Corporation
INTERNATIONAL COMMITTEE
Prof. S. Erichsen (Chairman)
Prof. R. Bhattacharyya
Prof. D. E. Calkins
Prof. C. Gallin
Mr. H. Langenberg
Prof. C. M . Lee
Mr. D. W. Reader
Prof. K. Taguchi
Prof. N. Takarada
The Norwegian Institute of Technology (Norway)
U.S. Naval Academy (U.S.A.)
University of Washington (U.S.A.)
Delft University of Technology (The Netheriands)
Blohm+Voss A/G (Germany)
Pohang University of Science and Technology (Korea)
Lloyd's Register of Shipping (U. K.)
Fukuyama University (Japan)
Yokohama National University (Japan)
SPONSORS
Kobe City
The Japan Shipbuilding Industry Foundation
The Cooperative Association of Japan Shipbuilders
Nippon Kaiji Kyokai
Lloyd's Register of Shipping
Hitachi Zosen Corporation
Ishikawajima-Harima Heavy Industries, Co. Ltd.
Kawasaki Heavy Industries, Ltd.
Mitsui Engineering and Shipbuilding Co. Ltd.
Mitsubishi Heavy Industries, Ltd.
Namura Shipbuilding Co. Ltd.
NKK Corporation
Oshima Shipbuilding Co. Ltd.
Sanoyas Corporation
Sasebo Heavy Industries Co. Ltd.
Sumitomo Heavy Industries, Ltd.
Paper No.
I M S D C ' 9 1
FOURTH INTERNATIONAL MARINE SYSTEMS DESIGN CONFERENCE
C O N T E N T S Page INVITED LECTURE INVITED LECTURE INVITED LECTURE INVITED LECTURE 1-1-1 1-1-2 I- 1-3 II- 1-1 11-1-2 11-1-3' 1-2-1 1-2-2 ' 1-2-3 I- 2-4 II- 2-1
Designing Decisions: Axioms, Models and Marine Applications
by F. Mistree, W. Smith. S. Kamal and B. Bras 1
The New Role of the Classification Societies in the Light of Design, Construction and Operation of Marine Structures
by M. Abe 25
System-Based Passenger Ship Design
by K. Levander 39
The Role of Computer Integrated Manufacturing for the Future Shipbuilding
by T. Koyama 55
Feature Based Small Craft Design for Producibility
by D. E. Calkins and L. A. McCc^ee 61
Computer-Aided Preliminary Design of a High Speed S W A T H Passenger/Car Ferry
by A. Papanikolaou 75
Design Charts for High-Speed catamarans
by K. À. Gr0nnslett et al 91
Trends and Constraints to the Optimum Propulsion System for the V L C C / U L C C ' s of the Nineties
by C. Gallin 97
A Mathematical Model for a Turbocharged 4-Stroke Diesel Engine, Suitable for Simulation of the Dynamic Behaviour of Complete Drive Systems
by Ph. Boot. J. K. Woud and B. J. ter Riet 117
A Digital Computer Model for the Design Integration of Marine Diesel Engine Power Plants
by I. E. Douglas
An Expert System for Fishing Vessel Design
by S. M. Calisal and D. McGreer 131
Design, Construction and Performance of a 21 Tonne S W A T H Fishing Vessel
by H. H. Chun. R. C. McGregor and J. R. MacGregor ***
Rationalized Design of Sailing Yachts
P.K.Pal 141
Development of Wing in Ground Effect Craft "Marine Slider ^ - S K Y - 2 " as a High Speed Marine Boat for Sports and Pleasures
by S. Kubo. T. Kawamura, T. Matsubara, T. Matuoka, A. Higashida. Y. Mizoguchi.
N. Yamaguchi and Y. Oomura 155
Fundamental Design Considerations for the Fuel-Efficiency of Marine Diesel Engine Power Plants
Paper Page No.
11-2-2 Development of Means for Radical Improvement of Prediction of Propeller Excited Vibratory Forces
by H. Tanibayashi, S. Toyama, Y. Saito. M. Takekawa, Y. Okamoto. T. Tanaka. N. Ishii,
T. Hoshino. Y. Ukon and K. Koyama 175
11-2-3 Propeller Induced Excitations and Responses on Large Passenger Vessels in Transient Conditions
by R. Lepeix 185
I- 3-1 C A D / C A M System for Ship Hull Structure
by S. Arase. T. Uto. S. Ueki and F. Ohmae 195
II- 3-1 Hydrodynamic Design of Hull forms
by T. Feng and Y. Tao 207
1-4-1 Designing a Knowledge Based Ship Design System
by H. Stearns. P. Payne and G. Smith 211
I- 4-2 A n Expert System for Use in Concept Design
by M. Welsh and W. Hills 227
II- 4-1 Some Ideas for an Integrated Container Vessel Design
by G. Grossmann 243
11-4-2 Recent Development on Energy-Saving Technology for Actual Ships
by T. Watanabe. A. Shiraki, M. Fukuda. A. Kasahara and Y. Okamoto 253
1-5-1 A Proposal for the Next-Generation Shipbuilding Systems
by K. Kikuchi, M. Hotta. Y. Nagase. M. Tabata and J. Fujita 267
1-5-2 System Integration of Manufacturing Management for Shipbuilding
by K. Horiuchi, M. Nakamura. T. Amemiya and T. Minemura 283
1-5-3 A New Approach to Design System for Shipbuilding
by K. Doi. K. Ito. K. Koga and Y. Nakai 295
I- 5-4 A Computer-Based Compartment Layout Design System Using Entity-Relationship
by K. Y. Ue. Y. C. Kim and W. S. Kang 307
II- 5-1 An Integrated Design and Evaluations Model for Inter-Island Transportation
by P. Sen. I. L. Buxton and T. Achmadi 319
11-5-2 Optimal Choice of Ship Particulars and Port Elements with Queueing Theory in Water Transportation System
by S.Y. Qin and H.X. Pan
1-6-1 Projects, Project Management and Quality Assurance Application and Definitions for the Marine Industry
by C. R. Eichner
1-6-2 Contractual Margins in Relation to Required Performance by S. Erichsen and E. K. Selvig
331
1-5-3 Concept Design Procedure by Systems Approach in Ship Design Evaluation
by B. Abidin 341
351
365
11-6-1 On the Initial Design of a Monohull/Catamaran Ship RIVER S E A
by M. Nakato. H. Nobukawa, Y. Osawa and 0. Matsumoto 373
11-6-2 SWIM -Small Waterplane Interchangeable Monohull
by J. W. Boylston 383
1-7-1 * Standardized Technical Contract Documents - A Chance for Better Predesigns of Shipyards?
by H. Linde
V
Paper Page No.
1-7-2 * Ship's Optimal Design Parameters Sensibility to the Future Exploitation Conditions Forecast
by Z. Alexiev arui I. Kostova * * *
11-7-1 Contra-Rotating Propeller System for Large Merchant Ships
by S. Nishiyama, Y. Sakamoto and R. Fujino 395
11-7-2 How Good is a Container Ship?
by H. Langenberg 413
1-8-1 Some Effects on Ship Structural Design Created by the Increased Application of Higher Tensile Steels
by J. M. Ferguson 429
I- 8-2 An Automated Appraisal in Structural Modelling Using the Framework of Expert System
by 0. Murakawa. K. Mikami, Y. Iwahashi and T. Sakato 445
II- 8-1 Mine Counter-Measures Vessels Based on the S E S Principle
by K. R. Johnsen 453
11-8-2 A Field Measurement of Floating Platform " P O S E I D O N " .
by S. Ando, Y. Okawa and Y. Tsutsui 461
1-9-1 An Empirical Assessment on Reliability of Independent Prismatic Tank Type B Designed by a "Standard"
by H. Emi, M. Oka and N. Yamamoto 475
I- 9-2 Probabilistic Safety Analysis of Jack-up Platforms
by A. Mansour 489
II- 9-1 VITÓRIA RÉGIA - A Low Cost Production Unit for Deep Water
by M. A. L. Petkovic 499
11-9-2 A Computer-Based Approach to Exploit Design Knowledge and Safety Technology in Monitoring Offshore Installations
by G. Langli and B. A. Bremdal 507
4TH INTERNATIONAL MARINE SYSTEMS DESIGN CONFERENCE
DESIGNING DECISIONS:
AXIOMS, MODELS, AND MARINE APPLICATIONS
Farrokh Mistree ^
Saiyid Kamal ^
Warren Smith ^
Bert Bras
1 Professor, Department of Mechanical Engineering. Systems Design Laboratory. University of Houston, Houston, Texas 77204-4792. U S A
2 Naval Architect, Department of Naval Architecture. Department of Defence, Canberra, A C T , Australia. Currently Research Associate, Systems Design Laboratory, University of Houston.
3 Systems Engineer, The M. W. Kellogg Company, Houston, Texas, U S A . Formerly, Research Associate, Systems Design Laboratory, University of Houston.
4 Research Associate, MARIN: Maritime Research Institute Netherlands, Wageningen, The Netherlands. Currently Research Associate, Systems Design Laboratory, University of Houston.
KEYWORDS: Decisions, Designing, Meta-Design, Ship Design, Concurreni Engineering,
Decision-Based Design. Decision Support Problems
ABSTRACT
At present marine design is being influenced by shoner development cycles, greater complexity, more openness and specialization (one of a kind "ship"). Modem, computer-based engineering design requires a hohstic approach that integrates representation, management and subsequent processing of information. Integration is possible through the "standardization" of information management within the design process. Subsequently, enhancing the "communication in design" to bring continuity and uniformity to the transition between different events (and levels) in the design process. We approach standardization from the viewpoint of Decision-Based Design (DBD). The basic premise being "the principal role of an engineer, in the design of an artifact, is to make
decisions".
In this paper, we introduce the fundamental paradigms of DBD, a decision-based design methodology called the Decision Support Problem Technique (DSPT) and fmally some applications of these ideas to marine design. Specifically, we start by providing the background and stating the axioms needed to characterize "decisions" as Decision Support Problems (DSPs). These axioms formalize the minimal requirements that need to be satisfied by the DSPs to exist within the DSPT and the decision models provide the means to implement DBD. An object-oriented knowledge representation scheme, apphcable to the DSPT, is introduced next. This knowledge representation protocol provides the basis for the syntax and semantics of DSPs in terms of transparency, and higher level data abstractions needed to model "decisions" in the design process. Thus, ensuring the applicability of the DSPT across domains, by hiding the details of the solution algorithms, through a mapping between the designers view of the world and the syntax needed to facilitate solution. This mapping is a uniform and structured medium of representation between designers, and between computers and designers. Finally, marine design
applications of Decision Suppon Problems are presented as examples to illustrate the implications of these
developments to ctjrrent design practice.
1. OUR FRAME OF REFERENCE
This paper is a companion to and follows "Decision-Based Design: A Contemporary Paradigm for Ship Design" [1]. For decades ships have been designed using the known "basis ship approach" together with the equally well-known Evans-Buxton-Andrews spiral. The two principal limitations of the spiral are that the process of designing is assumed to be sequential and the opportunity to include life cycle considerations is limited. It is our contention that to increase both the efficiency^ and effectiveness'^ of the
We consider efficiency to be a measure of the swifmcss wilh which information, that can be used by a designer to make a decision, is generated.
Wc consider effectiveness to be a measure of quality of a decision (correctness, completeness, comprehensiveness) lhat is made by a designer.
process of ship design a new paradigm for the process of design is needed. In [ 1 ] we reviewed recent developments in the field of design and offered a contemporary paradigm, Decision-Based Design, for designing ships. This paradigm encompasses systems thinking and embodies the concept of concurrent engineering design for the life cycle.
Taking into account life cycle considerations increases the emphasis on the early stages of project initiation because major design decisions are generally made at this point. Usually, these decisions are based on a predominance of soft information and can have far-reaching effects on the system being designed. Conceptually, it is evident from any perspective that as a design process progresses and decisions are made, the freedom to make changes as one proceeds is reduced and the knowledge about the object of design increases. This is illustrated in Fig. 1. At the same time, there is a transformation in the character of the information
from soft to hard. The essence of concurrent engineering is to "drag" the knowledge curve to tiie left, thereby increasing the ratio of hard to soft information that is available in the early stages of design. This relative improvement in the quality of information should lead to designs that are completed in less time and at less cost than those designed using a traditional sequential process. Compared to traditional engineering design in which synthesis of the product plays the c e n ^ role, the synthesis of the process (which includes desigii, manufacture and support aspects) is the dominant feature in concurrent engineering. With the synthesis of the process at this higher level, the synthesis of the product follows naturally.
Potential Time Savings _. 100%!
INCREASE
KNOWLEDGE Knowledge About Design [Design Freedom DESIGN TIME S C A L E Development of Re<^uirements Conceptual Design Preliminary Design Contract Desnn Detail Design | H H Construction
Fig. 1 The effect of increasing the amount of knowledge about a product at an early stage in the
design process
As evidenced by the recent attention given to concurrent engineering by the United States Department of Defense, the establishment of the Concurrent Engineering Research Center (CERC) at Morgantown, Virginia, and a host of other design research initiatives world wide; design, is in a period of change. The fundamental reason for these changes can be attributed to two singular events; a new emphasis on systems thinking and the pervasive presence of computers. Independent of the approaches or methods used to plan, establish goals and model systems, designers are and will continue to be involved in two primary activities, namely,
processing symbols and making decisions - two activities
that are central to increasing the efficiency and effectiveness of designers and the processes they use.
The characteristics of decisions are then govemed by the characteristics associated with the design of real-life engineering systems. These characteristics may in part be summarized by the following comments.
• Decisions involve information that comes from different sources and disciplines.
• Decisions are govemed by multiple measures of merit and p)erformance.
• A l l the information required to make a decision may
• Some of the information used in making a decision may be hard, that is, based on scientific principles and some information may be soft, that is, based in the designer's judgment and expérience.
• The problem for which a decision is being made is invariably loosely defined and open. Virtually none of the decisions are characterized by a singular, unique solution. The decisions are less than optimal and are called satisficing solutions.
In Decision-Based Design the principal role of an engineer or designer is to make decisions. Decisions help bridge the gap between an idea and reality. In Decision-Based Design, decisions serve as markers to identify the progression of a design from initiation to implementation to termination. In Decision-Based Design they represent a unit of communication; one that has both domain-dependent and domain-independent features. By focusing upon decisions, we have a description of the processes written in a common "language" for teams from the various disciplines - a language that can be used in the process of designing. Our formal definition of the term designing is as follows [2, 3]:
Designing is a process of converting information that characterizes the needs and requirements for a product into knowledge about a product.
In this definition, we use the term product in its most general sense; it may include processes as well.
2 .
THE DECISION SUPPORT PROBLEM
TECHNIQUE
The implementation of Decision-Based Design can take different forms. Our approach is called the Decision Support Problem Technique (DSPT). It is being developed and implemented, at the University of Houston, to provide support for human judgment in designing systems that can be manufactured and maintained. It consists of three principal components: a design philosophy rooted in systems thinking, an approach for identifying and formulating Decision Support Problems (DSPs), and the software. The DSPT consists of two phases, namely, a meta-design phase and a computer-based design phase (see Figure 2).
Meta-Design is a metalevel process of designing systems that includes partitioning the system for function, partitioning the design process into a set of decisions and planning the sequence in which these decisions will be made.
It is noted that during Phase I (meta-design), the product specific decisions themselves are not made or even pursued, but rather, the design process to be implemented in Phase II is itself designed. In Phase II (design), major decisions are modeled as DSPs and solutions to these DSPs sought. In the following the basis for the two phases of the DSPT is established with respect to the underlying axioms and definitions. Additionally, the role of DSPs, decision entities, keywords, descriptors, the representation of the design process and the concept of design templates is also discussed.
2.1 The Basis for Phase I of the DSPT
Phase I of the DSPT is based on the primary axioms of D B D . These axioms help map the design tasks to decisions,
Phase 1: Meta-Desian Phase II: Design
STEP1: IDENTIFY PROBLEM STEPS 3 & 4: STRUCTURE (CHARACTERISTICS AND
DESIGN TYPE) Client problem story
1
Organize domain-dependent information and formulate DSP templates (word and mathematical formulations). t
Tecfinlcal brief STEPS: SOLVE Obtain solutions.
Abstracts Solve the DSPs using appropriate means.
STEP 2: PARTITION AND PLAN STEP 6: POST-SOLUTION Partition each Abstract Into Problem
Stattmantt and identify decision* associated with each problem statement.
Devise plan for solution in terms of the DSPs corresponding to decisions.
Validate solution.
investigate effect on solution of small chamges.
Determine whether Iteration is necessary or makt decision.
Fig. 2 The two phases of the D S P T [4] representation (and processing) of domain relevant design
information. The existence of decisions and their characteristics are embodied in the following Axioms [5]:
Axiom - 1 Existence of Decisions in the DSPT
"The application of the DSPT results in the identification of\ decisions associated with the system (and subsystems that may be relevant)."
Axiom - 2 Type of Decisions in the DSPT
"All decisions identified in the DSPT are categorized as Selection, Compromise, or a combination of these."
The selection decision, in the context of the DSPT, is defined as follows [5]:
Defmition - 1 The Selection Decision
In the DSPT, "the selection decision is the process of\
making a choice between a number of possibilities taking into account a number of measures of merit or attributes."
The emphasis in selection is on the acceptance of certain altematives through the rejection of others. The goal of selection in design is to reduce altematives to a realistic and manageable number based on different measures of merit, called attributes, which represent the functional requirements. The attributes (associated with the altematives) may not all be of equal importance with respect to the decision. Some of the attributes may be quantified using hard information and others may be quantified using soft information.
The compromise decision, in the context of the DSPT, is defined as follows [5]:
Definition - 2 The Compromise Decision
In the DSPT, "the compromise decision reqidres that the
'right' values (or combination) of design variables (e.g., system parameters) be determined, such that, the system is feasible with respect to constraints and system performance
is maximized."
The emphasis in compromise is on modification and change (e.g., dimensional synthesis) by making appropriate trade-offs. The goal of compromise in design is that of modification through iteration based on criteria relevant to the feasibihty and performance of the system. The emphasis on iteration in compromise, which implies that the designer is pursuing a forward progressing process, requires generation, evaluation and alteration of different designs.
The first axiom asserts the existence of decisions and it follows from the view "that the principal role of an engineer, in the design of an artifact, is to make decisions." The second axiom qualifies the type of decisions and establishes that there are only two principal decisions, i.e., the selection and compromise decision. Furthermore, all other decisions can be represented as a combination of these. We refer to these (other than selection or compromise) decisions as
derived decisions.
Axiom-2 is explained using set notation. The set of all primary decisions in the DSPT is denoted as. Decision := {S, C ) ^ where S denotes Selection and C denotes Compromise (as defined in the preceding discussion). A l l derived decisions result from operations on tiiis set. Some derived decisions are illustrated in Fig. 3.
Axiom-1 and Axiom-2 provide the basis for the identification (and categorization) of decisions. Specifically, a decision may be described in terms of Selection and/or Compromise (which are the most basic representation of decisions). The coupled selection-compromise decision (Fig. 3a) is represented by the operator SC (S, Cy* where S and C arc contained in the set Decision. Similarly a coupled selection-selection decision (Fig. 3b) is represented by the operator SS (S, S) where S is contained in the set Decision. A hierarchical decision (Fig. 3c) is represented by CSS (C, SS(S, S)) where SS is as defined above and S and C are contained in the set Decision.
(...,...) indicates a seL
(...) indicates arguments for the operator preceding the left parenthesis. The arguments separated by a "," must be present for the operator to be vahd.
PRIMARY DECISIONS Table 1 Existing keywords and descriptors f N SELECTION C O y P R O U i S E DERIVED DECISIONS ^ SELECT10W » ^ c Ö Ü l P t M M S E j (•) Coupled SelecIion/ConpromEe (b) Coupled Selectlon/Selecllon (e) Hlwarchical Denved Daason
Fig. 3 Examples of derived decisions.
2.2 The Basis for Phase II of the DSPT
The meta-design phase of the DSPT provides a higher level of abstraction (in the form of decisions) for representing the design problem (and associated subproblems). A corollary to Axiom-1 and Axiom-2 links the decisions to DSPs [5].
Corollary to Axiom-1 and Axiom-2
"Decision Support Problems are utilized to provide decision support for the decisions identified (within the DSPT)."
According to the corollary, (principal or derived) decisions are resolved by using decision suppon problems. Thus, once a decision(s) is identified, an appropriate DSP may be used to provide decision support. For instance, the coupled selection-compromise DSP may be used to provide decision suppxjrt for the decision shown in Fig. 3a.
Within the DSPT the nature of Decision Suppon Problems has been qualified through the following axioms [5]:
Axiom - 3 Domain independence of DSP
descriptors and keywords
"The descriptors and keywords used to model DSPs (with the DSPT) need to be domain-independent with respect to processes (e.g., design, maruifacture, maintenance) and discipline (e.g., mechanics, engineering management)."
Axiom - 4 Domain independence of the means to
resolve DSPs
"The techniques used to resolve DSPs (for the DSPT, to provide decision support) need to be domain-independent with respect to processes (e.g., design, manufacture, maintenance) and discipline (e.g., mechanics, engineering numagement)."
Keywords and descriptors are used to provide a mapping of the design problem into a form amenable to solution. The concept of using keywords and descriptors provides the uniformity necessary for the application of DSPs to different domains and, more imponantly, for taking into account interactions between problems representing subsystems. In essence, keywords and descriptors are used to capture domain relevant information into a domain-independent framework. The "solution mechanism" (for the generation and/or evaluation of solutions) operates on the keywords and descriptors to process domain relevant information in a
DSP Keywords Descriptors
Selection Given Feasible Alternatives Identify Attributes
Relative Importance Rate Alternatives with respect
to Attributes Rank Order of preference
Oompromise Given Informatton Find System Variables Satisfy System Constraints Satisfy
System Goals Bounds
Minimize Deviation Function
The keywords and descriptors associated with the selection and compromise DSPs are summarized in Table 1. The role of keywords and descriptors is shown hierarchically in Fig. 4 using the selection D S P as an example. The stmcture shown in Fig. 4 is representative of the typical hierarchy that must exist between the keywords and descriptors of a DSP. Detailed examples of the compromise DSP are given in Sections 4 and 5.
Keywords are used to create the shell of a DSP. They are the "verbs" that segregate domain relevant information, and identify the relationslups between that information. For instance, in the DSPs listed in Table 1, the keyword "Given" is used to group the background or known information. Keywords embody in themselves the "procedural knowledge" [3] about DSPs. For instance, the keyword "Satisfy" in the compromise DSP is used to identify the system constraints, system goals and bounds on system variables (see Section 4). Moreover, "Satisfy" also implies that these constraints, goals and bounds need to be satisfied for a satisfactory design, and that each of these is directiy dependent on one or more system and deviation variables (Usted under the keyword "Find"). Procedural knowledge (or relationships) embodied in keywords is independent of the domain of application and thus enables the DSP to be used across disciplines.
DECISION ENTITY Selecllon^r KEYWORDS Rank D E S C R I P T O R S Amtum
Descriptors are viewed as objects within the D S P formulation and are organized under the relevant keywords. They help transform the problem from its discipline specific description to a discipline independent representation. For instance, to select material (using the selection DSP) based on its strength, color and cost, the material choices arc listed as "altematives" and the selection criteria as "attributes." Descriptors represent the "declarative knowledge" [3] which is used and modified according to the procedural knowledge. Axiom-3 qualifies the representation of design problems using the DSPT. It establishes the fact that the keywords and descriptors needed to formulate DSPs should be domain-independent. This helps abstract the domain of relevance (for the design task) in terms of the design process (as defined by the DSPT) by creating a mapping between the problem domain and the design process.
Axiom-4 may seem self-evident as many solution techniques (e.g., linear programming, nonlinear optimization, expen systems), are applicable to problems from different domains. The purpose of stating this axiom is that when a solution method is adapted (or created) to provide decision suppon its applicability should not be restricted to a specific domain. This condition r.uppien, • ,ts Axiom-3 by stating that decision suppon for a decision ti.at can be modelled using domain-independent constmcts needs to be provided in a domain-independent manner
The role of the two phases of the DSPT in modelling design in general, and designing decisions in particular is presented in the next section.
3 .
MODELING DESIGN DECISIONS
USING THE DSPT
We subscribe to the notion that the principal function of an engineer in general and a design engineer in panicular is to make decisions. In this context, in the earUer sections, we have described our understanding of the nature of designing from a based perspective. We expect our decision-based model to take on different forms to accommodate design of systems in general - designs that are characterized by information from multiple disciplines, different types of designs, and different perspectives within the life cycle. In effect, our model, considered as a system, is open to its environment and we expect it to evolve with time. To facilitate this, oiu* thmst is to make availai'Xe ;ooIs (analogous to the palette of a painter) that a human designer can use at various events of the design time-line. In this section wc describe the environment that provides the "decision-based" tools to the designer.
The fact that decisions are used as the basis for modelling a design process entails that decisions must provide the foundation for the model(s) of the design process. Subsequently, decisions are used to create a domain-independent frame work for computer-based representation and design synthesis. Decisions also help create various levels of abstraction (relevant to different events of the design process). For instance, at a higher level (Phase I) decisions are associated with events and design tasks, and at the a lower level DSPs are mapped into the decisions to provide decision suppon for the design tasks. Hence, decisions become the domain-independent "medium of communication" between the humans (e.g., designers, clients) and computer-based tools (for design analysis and/or design synthesis).
The processes of design, manufacture, maintenance, etc., are modeled in the DSPT using the primary entities:
phases, events, tasks, decisions, and information. This modeling and the use of the DSPT Palette for developing meta-design models or networks is described in detail in [1]. A designer working within the DSPT has the freedom to use submodels or subnetworks of a design process (prescriptive models) created and stored by others and to create models (descriptive models) of his/her intended plan of action using the aforementioned entities. Further issues associated with designing models of design processes are discussed in [6].
The key to modelling a design process is tiie separation of knowledge into two classes [3]. These classes are procedural knowledge and declarative knowledge.
• Procedural knowledge is the knowledge about the process, i.e., knowledge about how to represent (and process) domain information (for design synthesis). • Declarative knowledge is the set of facts represented
(usually) according to the protocol defined by the procedural knowledge. It is the knowledge about the product, i.e., the representation of problem relevant information, facts and background knowledge about the domain.
Procedural knowledge in the Decision Support Problem Technique consists of knowledge for partitioning and planning (Phase I of the DSPT), and, knowledge needed to formulate DSPs (Phase IT), i.e., the definitions of the keywords, descriptors, and the "rules" for their manipulation. For the Decision Suppon Problem Technique declarative knowledge consists of the problem domain infomiation relevant to the two Phases of the design process. It consists of the domain relevant "data" encoded within the DSP descriptors and the output generated through design synthesis (in terms of die descriptors).
3.1 The Environment for Phase I of the DSPT
-The DSPT Palette
The Decision Suppon Problem Technique palette is described in [1]. It is used to model decision-based design processes and is shown in Fig. 5. It contains symbols or icons for the basic entities described in above. These entities are relationships with one input and one output. A model or network of a process is created by connecting entities in a systematic fashion. A n extensive example using the palette in the design of a frigate is given in [1].
3 . 2 The Environment for Phase II of the
DSPT-An Object-Oriented Perspective to DSPs, Keywords and Descriptors
In Phase II of the DSPT the focus is on stmcturing and solving DSPs to provide suppon to humans making those decisions identified Phase I. As described in the preceding section, within each DSP the information is organized using the keywords and descriptors. This organization results in a knowledge representation scheme built on layers of data abstraction as shown in F i g . 6. The keywords and descriptors act as the medium of communication between a (specific) designer's view of the world and the independent view of the design process. The domain-independent view of the design process is relevant for both the "communication" of the design between various concemed parties (e.g., clients, designers) and for computer-based design synthesis. The layers of representation, shown in F i g . 6, provide the following advantages:
• Domain-independence of the D S î T descriptors and keywords (as required by Axiom-3 and Axiom-4) is maintained to provide the necessary mapping between
l^l I I K I T
K
[T[>
Phase Evern Task DKliion... Infcyrnaiion^^^^^^^
CompromiseB
Preliminary Selection@]
System Selection O Sysiem VanableGoals / Bounds Constraints
•
AnalyticalRel all onship
Fig. 5 The D S P T palette for modeling processes
the designers view of the world and the syntax needed to facilitate solution.
• The details of the algorithms and other procedures needed for design synthesis are hidden from the designer.
• Depending on the desired level of detail (in Phase II) the design process may be viewed in terms of decisions, DSPs, keywords associated with a DSP, or descriptors associated with the keywords relevant to a DSP.
The computer implementation of these ideas is based on the concepts of Qbject Qriented programming (OOP). In essence, declarative knowledge is represented as objects, and procedural knowledge is embodied in the "class" (and "subclass") definitions needed to create object instances and methods that operate on the objects. Class definitions for objects at various levels have been defined. For instance, the class definitions for the selection and compromise DSP are schematically shown in Fig. 7. The attributes (slots) for these classes may consist of other class definitions, primitive
or complex value types, or even names of methods (operators). For instance, the compromise D S P lets a designer specify a "system constraint" to model the feasibility of the design with respect to the values of the system variables. Tlie class definition for a system constraint is schematically shown in Fig. 8.
The keywords associated with the DSPs become the procedures needed to manipulate data (object instances). For instance, the procedure corresponding to the keyword "Given," for the compromise DSP, is us&i to query relevant reference data. Or, the procedure conesponding to the keyword "Rank," for the selection DSP, is used to rank the "Given" altematives according to the "Identified" attributes.
The key features of the representation scheme are follows:
as
The OOP basis for tiie representation scheme lends to consistency within the computer-based environment. A l l objects, which are instances of a class, inherit similar properties. Compromise DSP Reference data for solution algorithm Reference data to evaluate relationships [Ust of Variables] [Ust of Constraints] Deviation function [List of Goals] Selection DSP Attribute comparison scheme Selection solver [List of Alternatives] [Ust of Attributes] (Sensitivity Analysis Parameters) DESIGN PROCESS Domain-independent representation KEYWORDS Procedural knowledge about the design process
DESCRIPTORS Declarative Iviowiedge about the domain of interest
DESIGNER'S VIEW Domain information
Fig.7 Class definitions for selection and compromise D S P s . System Constraint [List of Variables] Relationship Expression Degree
/ \
Linear Nonlinear < = ^• The fact tiiat objects are embedded within objects helps maintain different "views" for different designers based on the desired level of detail. For instance, this includes looking at DSPs corresponding to decisions, or the set of constraints for a specific compromise DSP, or a specific constraint.
• Generic procedures (operators) arc defined to process information within objects. Ptocedurcs arc executed according to the messages passed to the object, i.e., the object is made capable of performing operations on itself.
• The "local" state of the operators is saved, using objects, to minimize overhead associated with re-calculation, rcallocation or crcation of redundant copies of data.
In the preceding sections we have briefly described how design processes and design decisions arc rcprcsented in a computer. The completion of a model for a specific design task rcsults in a design template. We thercfore define a design template as a domain specific mathematical model based on one or morc DSPs. A design template may be implemented as a black box in a manner that a designer is only concemed with selected inputs and outputs rcgardless of the intemal workings of the model. The mathematical formulations underlying the DSPs arc presented in the next section.
4. MATHEIVIATICAL FORMULATION OF
T H E DSPs
The difference between the compromise DSP and the traditional single objective mathematical formulation is illustrated in Fig. 9 and Fig. 10 for a two dimensional linear problem. In the single objective formulation shown in Fig. 9, the objective is a function of the system variables. The space of feasible solutions is surrounded by the system constraints and bounds of the problem. The objective is ro maximize the value of Z and thereforc the solution will be at vertex A .
In the compromise formulation, the set of system constraints and bounds define the feasible design space, whercas the set of system goals defines the aspiration space (see Fig. 10). For feasibility the system constraints and bounds must be satisfied whercas the system goals arc to be achieved as far as possible. The solution to this problem rcpresents a trade-off between that which is desired (as modeled by the aspiration space) and that which can be achieved (as modeled by the design space). For illustrative purposes assume that tiierc is no point of overlap between the design space and the aspiration space. Further, the Archimedean form (see Section 4.3) has been used and it is assumed that all the goals arc equally prefened. Can the standard single objective form provide a solution? The answer is no and typically a computer will respond with the following message: No feasible solution is available. Why is the answer no? In the standard form there is no provision to model "soft" constraints. The goals of the compromise DSP are akin to soft constraints. Further, no information is available, when the standard form is used, as to what a designer should do to find a feasible solution.
The solution for the compromise DSP shown in Fig. 10 is at venex A . This is the same solution as that obtained for the problem illusn-ated in Fig. 9. The difference is that in this case the best possible solution is identified and it is left to the designer to accept this solution, modify his/her aspirations or increase the feasible design space. The value of the deviation function and the deviation variables are
Objective Function Z - W i A i ( i û + W 2 A 2 Û Û + W3 A3QÜ Direction ol increasing Z Bounds System constraints
Flg. 9 Graphical representation of a two dimensional single objective optimization problem
A i Q Ü * d i - - di+ - G l Aspiralion Space Feasible Design Space A2Qü + te'- ct2+-G2 [)eviation Function
2 - VV3 (di -+ di+) + W3 (dr + (fe+) + W3 (da"* d3*)
Bounds
System constraints
lÊmm System goals
In this case, it is assumed that W i W2 « W3 Flg. 10 Graphical representation of a two dimensional compromise D S P , Archimedean
formulation
useful in assessing the degree by which each of the goals have not been achieved (see Figure 10). This is very useful information for a designer who is in the process of making trade-offs while designing a real-world system.
One of the first and most widely used multiobjective technique is Goal Programming [7, 8]. Goal Programming is itself a development of the 1950's, but it has only been since the mid 1970's that G P has received substantial and widespread attention - but not from engineers involved in the design of artifacts. Those in the engineering design community who explored the use of optimization in design chose to concentrate on Mathematical Programming and consequentiy G P has been virtually ignored.
The term "Goal Programming" is used, by its developers [91, to indicate the search for an "optimal" program (i.e., set of policies to be implemented), for a mathematical model that is composed solely of goals. This does not represent a limitation, in fact any Mathematical Programming model (e.g., linear programming), may find an alternate representation via GP. Further, not only does G P provide an alternative representation, it often provides a representation that is more effective in capturing the nature of real world problems. In our opinion, the compromise DSP is a subset of GP; a subset that is particularly suitable for use in engineering.
In summary, the terms "Compromise Decision Support Problem" and "Goal Programming" are synonymous to the
extent that they refer to multiobjective optimization models; they both share the concept of deviation variables that measure the "goodness" of the solution with respect to the target values of goals. They both share the concept of problem variables, hard and soft goals (called system variables, system constraints and system goals in the compromise DSP formulation). What distinguishes the compromise DSP formulation is the fact that it is tailored to handle common engineering design situations in which physical limitations manifest themselves as system constraints (mostiy inequalities) and bounds. These constraints and bounds are handled separately ft-om the system goals, contrary to the G P formulation in which everything is converted into goals.
Applications of DSPs include the design of ships, damage tolerant structural and mechanical systems, the design of aircraft, mechanisms, thermal energy systems, design using composite materials and data comprcssion. A detailed set of rcfercnces to these applications is prcsented in [10]. DSPs that include the modeling of uncertainty arc introduced in [11, 12,13]. Derived decisions (see Figurc 3) are modeled as coupled DSPs, for example, coupled selection-compromise, compromise-compromise and selection-selection. These constmcts have been used to study interaction between design and manufacturc [14, 15] and between various events in the conceptual phase of the design process [16]. To facilitate hierarchical design the selection DSP needs to be formulated and solved as a compromise DSP [17] (this is important for facilitating concurrcncy in synthesis). This transformation makes it possible to formulate and solve coupled selection-selection DSPs and coupled selection-compromise DSPs [14, 16,18]. In effect the mathematical forms of the coupled DSPs are akin to compromise DSPs. This is briefly explained in Section 4.4.
4.1 Compromise D S P : W o r d Formulation
The compromise DSP is stated in words as follows: G i v e n
A n altemative to be improved through modification. Assumptions used to model the domain of intercst. The system parameters (fixed variables).
The constraints and goals for the design. F i n d
The values of the independent system variables (they describe the physical attributes of an artifact).
The values of the deviation variables (they indicate the extent to which the goals are achieved).
S a t i s f y
The system constraints that must be satisfied for the solution to be feasible.
The system goals that must achieve, to the extent possible, a specified target value.
The lower and upper bouruis on the system variables and bounds on the deviation variables.
M i n i m i z e
The deviation function that is a measure of the deviation of the system performance from that implied by the set of goals and their associated priority levels or relative weights.
4.2 Compromise DSP:
Formulation
Mathematical
Given
n number of system variables p-Kj number of system constraints p equality constraints
q inequality constraints m number of system goals gi(2ü system constraint function
gi(2Ü = C i ( X ) - D i ( 2 ö
flt(di) fimction of deviation variables to be minimized at priority level k for Preemptive case
weight for Archimedean case Wi Find di". di+ i = 1, n i = 1, . . . . m Satisfy
System constraints (linear, nonlinear) giOD = 0 ; i = l , . . . , p gi(2D > 0 ; i = p+1, ....p+q System goals (linear, nonlinear)
Ai(2D + d r - di+ = Gi ; i = 1, . .., m Bounds Xjmin <_ X j i = 1, . .., n d i " , di ^ 0 ; i = 1, . .., m ( d i - . di+ = 0 ; i = 1, . . . , m ) Minimize
Case a: Preemptive (lexicographic minimum) Z = ( f i ( di-, di+),. . ,fk( di-, di+) ) Case b: Archimedean
m
Z = L W i ( di- + di+) ; i=l
E W i = 1; W i ^ 0
The Matiiematical Formulation of the Compromise DSP
We consider the preceding formulation of a compromise DSP to be a hybrid formulation in that it incorporates concepts from both traditional Mathematical Programming and GP, and makes use of some new ones. It is similar to GP in that the multiple objectives arc formulated as system goals (involving both system and deviation variables) and the deviation function is solely a function of the goal deviation variables. This is in contrast to traditional Mathematical Programming wherc multiple objectives arc modeled as a weighted function of the system variables only. The concept of system constraints, however, is rctained
from the traditional constrained optimization formulation.
Special emphasis is placed on the bounds on the system variables unlike in traditional Mathematical Programming and GP. In effect the traditional Mathematical Programming formulation is a subset of the compromise DSP - an indication of the generality of the compromise formulation.
4.3 Compromise DSP: System Descriptors
Compromise DSPs have a minimum of two system
variables. In general, a set of " n " design variables is
rcprcsented by
X = ( X i, X 2. . . . X n ) T .
The vector of variables may include ccmtinuous variables and boolean (1 i f T R U E , 0 i f F A L S E ) variables. System variables are, by their naturc, independent of the other
alter the state of the system. System variables that defme the physical attributes of an artifact arc always nonzero and positive.
A system constraint models a limit that is placed on the design. The set of system constraints must be satisfied for the feasibility of the design. Mathematically, system constraints arc functions of system variables only. They arc rigid and no violations are allowed. They rclate the demand placed on the system, D(20. to the capability of the system, C(2Ö, as either
Ci(2D ^ Di(2D or
Ci(2D = Di(X) ; i = 1, .... m.
The set of system constraints may be all linear, nonlinear or some mix of linear and nonlinear functions. In engineering problems the system constraints arc invariably inequalities. However, occasions rcquiring a^uality system constraints may arise. The rcgion of feasibility defined by the system constraints is called the feasible design space.
A set of system goals is used to model the aspiration a designer has for the design. It relates the goal, G i , of the designer to the acmal performance, A i ( X ) . of the system with respect to the goal. Three conditions can occur, namely:
1. Ai(2Ç) ^ G i ; which implies we wish to achieve a value of Ai(20 that is equal to or less than Gi,
2. Ai(X) ^ Gi ; which implies we wish to achieve a value of A[(X) that is equal to or grcaier than Gi, and 3. Ai(20 = Gj ; which implies we would like the value
of Ai(2ü to equal Gj.
The concept of a deviation variable is now introduced as a measure of achievement. Consider the third condition, namely, we would like the value of A•^(K) to equal Gj. The deviation variable is defined as
di = G j - Ai(2g.
The deviation variable di can be negative or positive. In effect a deviation variable rcprcsents the distance (deviation) between the aspiration level and the actual attainment of the goal. Considerable simplification of the solution algorithm is effected i f one can assert that all the variables in the problem being solved are positive. Thercforc, the deviation variable dj is rcplaced by two variables:
di = d i - - d i + ,
wherc d f . dj* = 0 and d i ' , dj* ^ 0. Thercforc, the system goal becomes:
Ai(2D dj- - di+ = G i ; i = l , . . . , m (1) wherc d j - . di+ = 0 and d j - , dj* ^ 0.
The conditions placed on df and dj"*" ensurc that they are non-negative. Further, it follows that the product constraint
(df . di* = 0) ensures that al least one of the deviation
variables for a particular goal will always be zero. If the problem is solved using an algorithm that provides a vertex solution as a matter of course then this condition is automatically satisfied making its inclusion in the formulation redundant. (This is the case with the A L P algorithm [19, 20] tiiat is incorporated in DSIDES. For completeness we have included this constraint in the mathematical form prcsented earlier and for brcvity we have
omitted this constraint from all subsequent formulations prcsented in this paper.)
The difference between a system variable aixl a deviation variable is that the former represents a distance in the i ^ dimension from the origin of the design space, whercas the latter has as its origin the surface of the system goal. The value of the i * deviation variable is determined by the degree to which the i * goal is achieved. It depends upon the value of AiCS) alone (since Gj is fixed by tiie designer) which in tum is dependent upon the system variables X . The set of deviation variables can be all continuous, all boolean or some can be boolean and others continuous. Obviously, both the deviation variables associated with a particular system goal will be of the same type.
Note that a system goal is always expressed as an equality. When considering equation (1) the following will be tme:
if A i <i G i (underachievement) then di" > 0 and di* = 0, if A j 2: G j (overachievement) then dj- = 0 and di+ > 0,
and
if A i = Gi (exact achievement) then dj- = 0 and dj"*" = 0.
How then do we model tiie three conditions listed previously using equation (1)?
• To satisfy Ai(2D ^ G j , we must ensure that the positive deviation di"*- is zero. The negative deviation, di-, will measure how far is the performance of the acmal design from the goal.
• To satisfy Ai(20 ^ G,, the negative deviation, d f , must be made equal to zero. In this case, the degree of overachievement is indicated by the positive deviation,
di*-• To satisfy Ai(X) = G j , both deviations, df and di*, must be zero.
A distinction is made, in the preceding formulation, between an objective and a goal.
• A n objective in Mathematical Programming is a function that we seek to optimize, through changes in the problem variables. The most common forms of objectives are those in which we seek to maximize or minimize, for example.
Minimize Z = A(X).
• A goal is an objective with a right hand side. This right hand side (G) is the "target value" or aspiration level associated witii üie goal, for example,
A(X) = G.
If we state that we wish to minimize the stress at a point in a beam then our wish represents an objective. If instead we state that we wish to achieve a particular value for the factor of safety at a point in the beam, say T = 2, then we have stated a goal.
The objective of a traditional single objective optimization problem requires the maximization or minimization of a certain function. This function is in terms of the system variables. In a compromise DSP formulation each of the objectives is converted into a goal (according to equation (1)) with its corresponding deviation variables. The resulting formulation is similar to a single objective optimization problem but with the following differences:
• The objective is always to minimize a function. • The objective function is expressed using deviation
variables only.
The objective in the compromise DSP formulation is called the deviation function. As indicated earlier tiie deviation variables are associated with system goals and therefore tiieir ranges of values depend on the goal itself resulting in an order of magnitude problem. A solution to the order of magnitude problem is to normalize the achievement AjCS) with respect to the target value Gj before the deviation variables are introduced. If tiiis is not done die deviation variable with the larger numeric value will dominate the solution process.
The following rules are used to formulate the system goals in a way that ensures that all the deviation variables will range within the same values (0 and 1 in this case).
a. To maximize the achievement, Ai(2ü. choose a target value G, greater or equal to the maximum expected value of A^(K), so that die ratio Ai(2D / Gi is always less or equal than 1. For example, i f AjCX) is the reference stress then G j could be the yield strcss. Consider die following:
Ai(20 <• G i ==> A i ( 2 D / G i ^ 1.
Transform the exprcssion into a system goal by adding and subtracting the corresponding deviation variables.
A i ( 2 0 / G i + df - di+ = 1. (2) In this case, the overachievement variable di+ will always be zero, as indicated earlier. The underachievement deviation, d^-, is then minimized to ensurc that tiie performance of the design will be as close as possible to the desired goal.
b. To minimize the achievement, Ai(2D. die following steps are in taken.
i) Choose a target value Gi less than or equal to the minimum expected value of Ai(X). In this case, the ratio G, / Ai(X) will be less than or equal to one,
\ ( K ) ^ G j = > G,/Ai(X) ^ 1.
Transform the expression into a system goal (note the inversion of G and A) and flip the signs of the deviation variables (to account for the inversion). The deviation variables will vary between 0 and 1 and the equation is given as
G i / A i ( 2 D - dj- + di+ = 1. (3) The underachievement deviation, d f , will be zero as indicated earlier. Minimizing the over-achievement deviation, dj*, will ensure that the performance of die design is as close as possible to the desired goal.
ii) If the target value G , is taken as zero, get an estimate of the maximum value that the achievement Ai(X) can obtain within the bounds set for the system variables, Ai"^(2Ç)- Then divide the inequality by this maximum value and convert into a system goal witii die following result:
The deviation variables will now vary between 0 and 1. Note that the signs of the deviation variables are as in equation (2). In this case, the underachievement deviation, d f , will always be zero. Minimize then the overachievement deviation, dj^, to ensure that the performance of the design will be as close as possible to tiie desired value of zero.
c. If it is desired that AjCSJ = Gi, and
i) i f the target value G\ is approached from below by AjQQ, use equation (2) and minimize (di-+ di+). ii) if tiie target value Gi is approached from above by A[(X), use equation (3) and minimize (df+ &{*"). iii) i f the target value G j is equal to zero, use equation (4) and minimize (di'-f dj+).
Bounds are specific limits placed on the magnitude of each of the system and deviation variables. Each variable has associated with it a lower and an upper bound. Bounds are important for modeüng real-world problems because they provide a means to include die experience-based judgment of a designer in the mathematical formulation. Bounds on the system variables take the form
Xmin < X < X " ! ^ ,
where X " " ' " and represent the set of lower and upper bounds respectively. The bounds on the system variables demarcate the region in which a search is to be made for a feasible solution. In engineering design, the lower bounds are always nonzero and positive, reflecting physical limitations.
Deviation variables are by definition nonnegative and therefore a lower bound of zero is always assigned to them. Upper bounds are not required i f the system goals are normalized as described. We will assume that the system goals will always be normalized and therefore the upper bounds on the deviation variables are not be included in the formulations.
In the compromise D S P formulation the aim is to minimize the difference between that which is desired and that which can be achieved. This is done by minimizing the deviation function, X(^-, d"*")- This function is always written in terms of the deviation variables.
A designer sets an aspiration level for each of the goals. It may be impossible to obtain a design that satisfies all the levels of aspiration. Hence, a compromise solution has to be accepted by the designer. It is desirable, however, to obtain a design whose performance matches the aspiration levels as closely as possible. This, in essence is the objective of a compromise solution. The difference between the goals and achievement is expressed by a combination of appropriate deviation variables, Z(d.-, jl+). This deviation function provides an indication of the extent to which specific goals are achieved.
A l l goals may not be equally important to a designer and the formulations are classified as A r c h i m e d e a n or Preemptive - based on the manner in which importance is assigned to satisficing the goals. The most general form of the deviation function for " m " goals in the Archimedean
Z(A;û'-) = I(Wi-di--i-Wi+di+)
i=l
where the weights W j , W 2 , Wn, reflect tiie level of desire to achieve each of the goals. In this formulation, the weights Wi satisfy the following conditions:
m
I
W i = i=l1 and Wj ^ 0 for all i .
The relationships between the goal (aspiration level), Gj, of the designer and the actual achievement, A^(X), of the goal are summarized in Table 2. It may be difficult to come up with truly credible weights. A systematic approach for determining reasonable weights is to use the schemes presented in [17, 21].
In the Preemptive approach, the difficulty of finding the weights is circumvented by rank ordering the goals. This is probably easier in an industrial environment or in the earher stages of design. The measure of achievement is obtained in terms of the lexicographic minimization of an ordered set of goal deviations, wherein within each set of goals at a particular rank, weights may be used. Goals are ranked lexicographically and an attempt is made to achieve a more important goal before other goals are considered.
The mathematical definition of lexicographic minimum follows (see Ignizio [7,9]).
LEXICOGRAPHIC MINIMUM
Given an ordered array f of nonnegative elements fk's, the solution given by f(') is preferred to f(2) if
fk(l) < fk(2)
and all higher-order elements (i.e., f i , f k - i ) are equal. If no other solution is preferred to f, tiien f is the lexicographic minimum.
As an example, consider two solutions, f^*") and f^^), where f(r) = (0, 10, 400. 56)
f(s) = (0, 11, 12, 20)
In this example, note that f^*") is preferred to f<s). The value 10 corresponding to f^"") is smaller that the value 11 corresponding to Once a prcfercnce is estabhshed then all higher order elements arc assumed to be equivalent. Hence, the deviation function for the Preemptive formulation is written as
Z = (fi(di-,di+) fk(di-,di+) ).
For a four goal problem, the deviation function may look like
Z(ii-,d-^) = ( ( d f + d2-),(d3-),(d4+)}.
Table 2 System goal formulations for Archimedean case
Condition Deviation variables Minimize Weights
A| S G | d f > 0. d 1+ - 0. d r Wf - 0, W,* - W| A| 2 G , d |- - 0, d I* > 0 W f . Wt W | * - 0 A| - G | d |- - 0. d I* - 0 d |- + d I* Wf - W(» - W|
The numerical solution of a Prcemptive formulation requires the use of a special optimization algorithm developed to solve this type of problem. One such algorithm. Multiplex, has been developed by Ignizio [22] and has been incorporated into DSIDES.
4.4 Selection D S P using Compromise D S P Descriptors
The decision support problem rcprcsenting selection is stated as follows:
G i v e n
A set of candidate alternatives. Identify
The principal attributes influencing selection. The relative importance of attributes. Rate
The altematives with rcspect to their attributes. Rank
The altematives in order of preference based on the computed merit function values.
The method of solving a selection DSP is presented in [17, 21].
Assume that there are M altematives and N attributes that influence selection in a particular selection DSP. Then the following need to be determined:
the rating of altemative i with respect to attribute j . die normahzed rating of altemative i with respect to attribute j ; it varies between 0 and 1. There are different ways to effect normahzation. One way for normalizing an attribute rating for altemative i with respect to attribute j is,
Rij =
A . . A . m i n A y _ A j
where Aj"»»" and Aj^Jax represent die lowest and highest possible values of the altemative rating Ajj. The preceding formulation is for the case where the larger value of an attribute rating represents preference. If a smaller value of an attribute rating represents prcference, tiie normalized rating, Rjj, is defined as.
Rij = 1
-A y _ -A j
Ajmax _ AjTiin
Ij is the rclative importance of attribute j ; it is normalized and varies between 0 and 1. For a detailed introduction see Bascaran et al. [17]. MFi is the merit function for altemative i . Therc arc
several methods for modeling tiie merit function. Using a linear model we have,
N
M F i = I i j R i j ; i = 1, . . . , M (5)
For most practical purposes the linear model is sufficient.
