Rather than apply system optimization to the detailed system design -- the traditional application of engineering optimization -- our goal here is to apply optimization, trade-off, and verification analysis procedures at both the logical and physical stages of design. i.e.,

• Logical Design.
  Apply optimization and trade-off.

• Physical Design.
  Apply optimization and trade-off.

The key question is not so much what algorithm is appropriate, but "what should the formulation for "optimization and trade-off" analysis look like?

Roughly speaking, the pathway of system development is as follows:

Goals and --> Use Cases --> textual  -----> synthesis of system ----> identification of design
Scenarios                   requirements    structure and system      parameters, objectives,
                                            behavior.                 and constaints.

Step 1. MultiCriteria Optimization

Use multicriteria optimization to find the set of noninferior design solutions.

Regardless of whether a human or a machine does design, the primary design endeavour is one constraint satisfaction (i.e., finding a set of design parameter values that will satisfy all of the constraints), followed by design optimization (i.e., finding the optimal value of one or more design objectives, while remaining feasible).

Step 2. Group Classification in Performance Space

For example, product-lines.

Step 3. Ranking Design Alternatives

Use ranking methods to choose "most desirable option" among noninferior design solutions.

From a mathematical standpoint, the details of each pathway will be affected by the quality of data/information available. Three broad categories of decision making exist: (1) decision making under certainty (i.e., deterministic); (2) decision making under risk; and (3) decision making under uncertainty.

• Production Functions, Economics .... etc.
• For details, see the notes from ENSE 621.

In this section we describe scoring methods and the analytical hierarchy processs (AHP).

The "scoring" and "analytical hierarchy" methods are examples of methods where ideas, feelings and emotions are quantified to provide a numerical scale for assigning priorities among design alternatives.

Both methods are simple to apply, and depend on a preference structure that is obtained "prior" to to the start of the optimization process.

Scoring Method

Scoring methods provide an ordinal ranking of design alternatives. The computational procedure is composed of three simple steps:

1. Weights are assigned to each criterion;
2. The (design) alternatives are are rated against each criterion.
3. The worth (value_j) of "design alternative j" is obtained by computing the weighed sum:

                    i = m
       value_j =  sum [ w_i * a_ij ]
                    i = 1
   

The design alternative with the highest worth (value_j) is selected as the best option.

Example.
See pages 19-20 of Mollaghasemi et al.

Analytical Hierarchy Process (AHP)

The Analytical Hierarchy Process (AHP) was developed in the early 1970s as a means of enabling consistent and rational decisions ~\cite{fisher98,saaty83}. The AHP may be used for quantitative decision making based upon subjective and non-quantifiable criteria.

The problem structure is as follows (Mollaghasemi, pg. 9):

1. Reading Down.
   Reading down each branch, each goal must answer the "how" of its immediately higher goal.

2. Reading Up.
   Reading up each branch, each higher goal answers "why" the goal above it is needed.

3. Reading Across.
   Reading across the goals at a given level under a given goal, the questions are:
   • Are all of the more specific goals "necessary" to accomplish the more general goal?
   • Are the specific goals at this level "sufficient" to accomplish the more general goal?

The purpose of these tests is to ensure a logical flow of reasoning in the hierarchy (albeit, subject to the note below).

Examples

1. Site Selection for a Fed-Ex Package Facility
   See pg. 312 of the ENSE 621 class notes.
2. Selection of a Job
   Based on money, work, and family considerations. See Mollaghasemi, pg's. 37-40.
3. Selection of a School for Study
   See pg's. 520-524 of Taha, 1997.

Criteria for Ranking Design Alternatives

Favorable Properties of a Design Method (from G. Hazelrigg, NSF Program Manager)

The method should:

• Provide a rank ordering of candidate designs.
• Not impose preferences on the designer.
• Permit the comparison of design alternatives under conditions of uncertainty with risky outcomes.
• Be independent of the discipline of engineering.
• Be consistent in its recommendations.
• Make the same recommendation regardless of the order in which the design alternatives are considered.
• Not impose constraints on the design or the design process.
• Be such that the addition of a new design alternative should not make existing alternatives appear less favorable.
• Be such that information is always beneficial.
• Not contradict itself.
• Be validated.

The bottom line:

• All design tools do one of three things:
  • Aid in the creation/definition of design alternatives (i.e., develop the alternative set).
  • Aid in the evaluation of design alternatives (i.e., evaluate expectations).
  • Aid in the selection of a preferred design alternative (determine preferences and apply them to obtain a choice).
• Selection is decision making. It is the same as optimization.
• Optimization theory deals with search techniques, given an objective function and constraints.
• Decision theory deals with proper formulation of the objective function.
• Both are needed to do design.
• Both have been treated extensively in the literature.
• Expectations always involve uncertainty resulting in risk.
• The methods must be valid under conditions of uncertainty and risk.

Common Mistakes:

• Failure to recognize that decisions are being made in design.
• Neglect of uncertainty and risk.
• Trying to assign preferences to things upon which the designer has no preference.
• Failure to recognize the role that preferences play in decision making; attempts to devise methods to "solve the design problem."
• Failure to assign uncertainties only to expectations.
• Failure to use an appropriate utility (objective) function and failure to validate the function used.
• Using the preferences of someone other than the decision maker in a particular design analysis.
• Failure to acknowledge arrow's theorem -- groups generally do not have rational preferences (customer preferences cannot be used to guide design, must rely on demand to account for customers).
• Failure to understand the role of management in engineering design.

So what's important:

• Design research should be scholarly -- acknowledge and reference relevant research results, even if they are 300 years old.
• Design research should not go against relevant accepted extant theory in an ad hoc manner.
• Design research should lead to mathematically sound results.
• Design research should be validated (case studies do not validate such methods).

1. Mollaghasemi M., Pet-Edwards J., "Making Multiple-Objective Decisions," IEEE Computer Society Technical Briefing, IEEE Computer Society Press, Los Alamitos, CA, 1997.
2. Taha H., "Operations Research: An Introduction," International Edition, Prentice-Hall International, Inc., 1997.

Developed in November 2002 by Mark Austin
Copyright © 2002, Mark Austin. All rights reserved. These notes may not be reproduced without expressed written permission of Mark Austin.