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Design Optimization:International Journal for Product

& Process Improvement,Vol. 1 No. 3, 1999, pp. 281-292.

# MCB University Press, 1463-5801

Optimizing the process flowfor complex design projects

J.L. RogersNASA Langley Research Center, Hampton, Virginia, USA

C.M. McCulleyLockheed Martin Tactical Aircraft Systems, Fort Worth, Texas, USA

and

C.L. BloebaumDepartment of Mechanical and Aerospace Engineering,

University at Buffalo, Buffalo, New York, USA

Keywords Process management, Genetic algorithms, Multidisciplinary design, Design optimisation

Abstract The design cycle of large, multidisciplinary design projects requires the decompositionof the complex system into design processes and their couplings. Some processes may be groupedinto iterative subcycles. In optimizing such a coupled system, it is essential to determine the bestsequence of the process flow within these subcycles to reduce design cycle time and cost. Manydecomposition approaches assume the capability is available to determine what sequence ofexecution will be imposed during the design cycle. Unfortunately, this is often a complex problemand beyond the capabilities of a design manager. A genetic algorithm can be applied to allow thedesign manager to rapidly examine many combinations for sequencing the process flow in aniterative subcycle and to optimize the sequence based on cost, time, and iteration requirements. Asample test case is presented to show the effects of optimizing the sequence with a geneticalgorithm.

IntroductionMany engineering systems are large and multidisciplinary and require acomplex design cycle. Possible couplings among the design processes must bedetermined before a design cycle begins. After these possible couplings havebeen defined, a design cycle can be decomposed to identify its multilevelstructure. Typically, the processes and their couplings are displayed in theform of a process flow chart such as the one shown in Figure 1. The processesin Figure 1 are representative of a typical conceptual design project.

The design manager's aid for intelligent decomposition (DeMAID) is aknowledge-based software tool for the sequencing of design processes and foridentifying a possible multilevel structure for a design cycle (Rogers, 1989). Theprimary advantage of DeMAID over tools such as process flow charts andprogram evaluation and review technique (PERT) is the ability to group anddisplay the iterative subcycles commonly found in the design cycle. After theiterative subcycles have been determined, their processes should be sequenced

Copyright @ 1999 by MCB University Press. No copyright is asserted in the USA under Title17, US Code. The US Government has a royalty-free license to exercise all rights under thecopyright claimed herein for governmental purposes. All other rights are reserved by thecopyright owner.

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in a manner that will produce a design in the least time and at minimum cost.The original DeMAID software employs a knowledge base to handle this task;however, the knowledge-based approach examines only a limited number ofsequences, providing the user a starting point from which to searchinteractively for the optimum sequence. This paper describes a geneticalgorithm (GA) capability that has been added to DeMAID. This GA examinesa large number of process sequences in each iterative subcycle and optimizesthe sequence based on cost, time, and iteration requirements.

Design structure matrixThe DeMAID software displays the sequence of processes in a design structurematrix (DSM) format (Steward, 1981). Figure 2 contains a sample DSM for therepresentative conceptual design project shown in Figure 1. In the DSM, theprocesses are shown as numbered boxes on the diagonal. The numbers in theboxes correspond to the process numbers in Figure 1. Each process has beenassigned a cost and a time (units depend on the user). Output from a process isshown as a horizontal line that exits a process box, and input is shown as avertical line that enters a process box. The off-diagonal bullets that connect thehorizontal and vertical lines represent couplings between two processes.Couplings in the upper triangle portion of the DSM represent feedforward data(data computed before it is used); couplings in the lower triangle part of thematrix represent feedback data (data required as input before it is computed).Therefore, a feedback implies an iterative process in which an initial estimatemust be made.

AeroModel

AeroAnalysis

Press. &Deflect.

(21) (16)RigidAero

Character

(15)

Flex.Aero

Character

(10)

(5)

(2)

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Stability& Model

Character

AeroElastic

Analysis

Struct.Mode

(7)

(14)

AeroElasticProp.

VehiclePerform.

(22)

MissionPerform.

FinalData

(13)

StabilityQualities

(4)

(9)

ControlAnalysis

DynamicAnalysis

(1)

Struct.Analysis

Struct.Model

(18)(3)

DevelopGeometry

(6)

InitialData

(11)Struct.Weight

Weight &Inertia

Analysis

(13)

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ReviseInitialData

(12)

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Figure 1.Process flow chart for aconceptual designproject

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The knowledge base within DeMAID is written with the C language integratedproduction system (CLIPS) (Giarratano and Riley, 1989) and sequences theprocesses to eliminate as many feedbacks as possible. However, in many cases,not all of the feedbacks can be eliminated. If any feedbacks remain, DeMAIDgroups the processes into iterative subcycles such as the one containingprocesses 1-21 in Figure 2. DeMAID has not been used to optimize the sequenceof the processes shown in Figure 2.

In the original version of DeMAID, a knowledge base was used to minimizefeedbacks and group processes into iterative subcycles. No time factors, costfactors, or iteration factors (i.e. the number of iterations required forconvergence) were applied. After the iterative subcycles were identified,DeMAID attempted to minimize the feedbacks within an iterative subcycle. Inmost cases, although more than one sequence could produce the minimumamount of feedbacks, only one sequence was identified.

A large iterative subcycle such as the one shown in Figure 2 can be veryexpensive to converge because the iterative loops defined by the feedbacks arenested, which requires numerous executions of potentially expensiveprocesses. Thus, a new technique is needed that rapidly examines manypossible sequences of processes within a subcycle and selects the best sequencebased on cost, time, and iteration requirements. The GA capability that hasbeen added to DeMAID meets this need.

Coupling strengthsIn the original version of DeMAID, a coupling either existed or did not. Thestrength of the coupling could not be quantified. The most recent version of

Figure 2.Unsequenced DSM for a

conceptual designproject

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DeMAID contains seven levels of coupling strengths: extremely weak, veryweak, weak, nominal, strong, very strong, and extremely strong. Thesestrengths are either supplied by the user or determined through sensitivityanalysis (Bloebaum, 1992; Rogers and Bloebaum, 1994) and quantifiedaccording to rules in the knowledge base. The rules for quantifying are basedon a statistical analysis of the normalized sensitivities.

An iteration factor relates the coupling strengths to the number of iterationsrequired for convergence. The default values are shown in Table I. The usercan override these default values if desired. If coupling strengths are notavailable, the default number of iterations for computational purposes is five(5). The user can interactively move processes along the diagonal to place theweaker couplings, which require fewer iterations for convergence, into thefeedback positions.

Cost and time requirement calculationRules were added to the DeMAID knowledge base to determine the total costand time required for a given design process. Numerous nested iterativeprocesses are evident within the iterative subcycle shown in Figure 2. TheDeMAID software sums the time and cost of each process contained in afeedback loop and multiplies those sums by the iteration factor for thefeedback. For example, in Figure 3, the costs and times for processes 1-4 wouldbe summed, and the sums multiplied by the iteration factor (five, in this case)for the nominal feedback coupling process 4 to process 1. This would yield atime of 500 and a cost of 550. The user defines the units for the cost and thetime.

The drawback to this capability is that it only examines one sequence andmakes no attempt to optimize the sequence based on cost and/or time. Thus, adecision was made to complement the knowledge-based approach in DeMAID

Table I.Relation of couplingstrengths to defaultiterations factors

Coupling strength Default iteration factor

Extremely weak 2Very weak 3Weak 4Nominal 5Strong 6Very strong 7Extremely strong 8

Figure 3.Calculating time andcost requirements

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with a GA. This GA examines a large number of sequences of processes in eachiterative subcycle and optimizes the sequence based on cost, time, and iterationrequirements.

Genetic algorithmThe use of GAs has been instrumental in achieving good solutions to discreteoptimization problems that have not been satisfactorily addressed by othermethods (Goldberg, 1989). Because of the discrete nature of the sequencingproblem, this solution technique has proved effective (Syswerda, 1990). The GAsearches a population of design points, coded as finite-length and finite-alphabet strings. Successive populations are produced primarily by theoperations of selection, crossover, and mutation. The selection operatordetermines which members of the population will survive to participate in theproduction of members of the next population. Selection is based on the valueof the fitness function, or the fitness of the individual members, such thatmembers with greater fitness levels tend to survive. Crossover is therecombination of traits of the selected members, called the mating pool, withthe purpose of producing a child with better fitness levels than its parents.Crossover is accomplished by swapping parts of the string into which thedesign points have been coded. The mutation operation prevents the search ofthe design space from becoming too narrow. After the production of a childpopulation, this operator randomizes small parts of the resulting strings, with avery low probability that any given string position will be affected.

Frequently, a binary coding is used with the GA; the values of the designvariables are coded as binary numbers and then concatenated. While thisapproach works well with numerical problems, it is not efficient for thesequencing problem (Altus et al., 1995; McCulley and Bloebaum, 1994, Rogerset al., 1996). The GA portion of DeMAID uses a direct representation of thesequence as a coding of an n-process system, with each integer 1 through nused only once. For example, the string [1 7 2 4 3 5 6 ] represents the seven-process DSM shown in Figure 4, in which the sequence from the top left cornerof the DSM to the bottom right corner is 1, 7, 2, 4, 3, 5 and 6.

Figure 4.Seven-process DSM

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Selection, which requires only the use of the fitness function, is not affected bythis choice of coding. For this study, selection is accomplished by thetournament selection method. To fill the mating pool, two strings are randomlyselected from the parent pool and compared; the one with greater fitness isincluded in the mating pool.

Different crossover and mutation operators must be used because theyoperate directly on the strings. The result after a GA crossover or mutationoperation must be a valid sequence (i.e. no repeated or missing processes), butvalid sequences cannot always be guaranteed with arbitrary switching ofstring information between or within strings. Suppose there are four processesto sequence (1 2 3 4). A three-bit binary string is needed for representation inthe GA. However, a three-bit string represents eight distinct numbers (0 1 2 3 45 6 7). A valid string for (1 2 3 4) is defined as a combination containing only thenumbers (1 2 3 4) with no duplication. There are 24 possible valid sequencecombinations for (1 2 3 4) out of 330 possible sequence combinations for (0 1 2 34 5 6 7). For example, the mating pool contains two valid strings

00101 | 0011100 representing (1 2 3 4)

10000 | 1010011 representing (4 1 2 3)

Applying a crossover after `̀ gene'' 5 (the divider in the above strings) results inthe strings

001011010011 representing (1 3 2 3)

100000011100 representing (4 0 3 4)

Neither of these strings is valid. The first string contains a duplicate process (3)and misses a process (4) and the second string contains a duplicate process (4),a process (0) not a part of the sequence, and misses two processes (1 and 2). Thesame problems are incurred with mutation.

To resolve the problem, crossover is accomplished by the position-based(Syswerda, 1990) method as shown in Figure 5. Several processes (1, 4, 5, and 6in the Figure) are chosen from the first parent and placed in the same positions

Figure 5.Position-based crossover

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in the child string. Then, the processes (2, 3, and 7 in the figure) that were nottaken from the first parent are taken from the second parent to fill the holes inthe child string in the order in which they appear in the second parent. Theresult is a complete string with one and only one copy of each process number.

Mutation is accomplished through the order-based (Syswerda, 1990) method,as shown in Figure 6. Each string position is polled; if a given string position(position 2 in the figure) is selected to undergo mutation, then its content isswapped with a randomly selected position (position 4 in the figure) in the samestring.

In addition to minimizing feedbacks, the fitness function for the GA inDeMAID can be used to determine the minimum cost and time required forconvergence of each subcycle. For each process contained in a feedback loop,the GA sums the time and cost and multiplies those sums by the feedbackiteration factor to obtain the total cost and time to converge a subcycle. Theuser-definable weights determine the relative importance of each of the majorcomponents of the fitness function. The fitness function is

fitness � 1:0

�wtime�time�wcost�cost�4

where time is the total time required to converge the iterative subcycle, cost isthe total cost to converge the iterative subcycle, and wtime and wcost are user-definable weights. The user can specify that the GA find the optimum sequencebased on time alone by setting the wcost to 0.0. With tournament selection, therelative scale of this fitness function is not important. For inclusion in themating pool, only the relation of the values (i.e. whether one fitness function islarger than the other) matters.

Each subcycle is passed to the GA for individual optimization. The GAbegins with a randomly generated initial population of a size determined by theuser and proceeds from generation to generation by applying the threepreviously described operations.

The following parameters, their defaults in parentheses, are available:

. Population (100) ± population size.

. Mutation probability (1.0) ± mutation probability in percent.

Figure 6.Order-based mutation

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. Convergence threshold (0.9) ± a test of the average fitness to determine aconverged population.

. Seed (3818969) ± seed for random number generator.

. Max iterations (500) ± maximum number of iterations to find the bestsequence.

. wt. cost (1.0) ± cost weight for fitness function calculation.

. wt. time (1.0) ± time weight for fitness function calculation.

Convergence is achieved when the average fitness of a population rises abovesome user-defined convergence threshold of the best fitness for that population.At that point, the member of the population with the best fitness is chosen asthe optimal. After the GA has completed sequencing all the subcycles, the newDSM displays the changes.

Sample caseThe example below indicates the savings that can be obtained by resequencingthe processes. In the figures, each process is assigned a cost and a time (unitsdepend on the user). The numbers in the left-hand column correspond to theoriginal process numbers assigned by the user. The processes have beenresequenced by DeMAID.

The DSM in Figure 2 is from a conceptual design project. This DSM wasunsequenced and contains 24 feedbacks. Coupling strengths are used toestimate the number of iterations required for convergence. The calculationsshown in Table II represent the time and cost required to converge a solutionfor each feedback iteration. The total design cycle for this DSM requires 21,340time units and 19,640 cost units for completion.

The DSM in Figure 7 contains the same set of processes with the same times,costs, and coupling strengths that are shown in Figure 2. However, theprocesses have been resequenced and optimized by the GA in DeMAID and thenew sequence is different from the sequence in Figure 1 as shown by thenumbers in the left-hand column. This DSM contains six feedback couplings.The calculations shown in Table III represent the time and cost required toconverge a solution for each feedback iteration. The total design cycle for thisDSM has been reduced from 21,340 time units to 3,800 time units and from19,640 cost units to 3,220 cost units by resequencing the processes.

The initial implementation of the GA determined the optimal sequencewithout regard to the fact that, although it may result in higher time or costestimate in the fitness function, in some cases one process must always becompleted before another process can begin. For example, suppose that process9 (CTANALY) in Figure 7 must always occur before process 8 (AEANALY),regardless of how many processes are between process 9 and process 8. Tohandle this requirement, a constraint is added to the fitness function. Thisconstraint adds a substantial penalty to the fitness of each string where process9 appears after process 8. As shown in Figure 8, applying this constraint adds a

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Table II.Time and cost for

iterations for theunsequenced DSM

To process From process Iterations Time Cost

1 2 8 560 4001 6 4 600 8402 8 8 1,680 1,6803 6 2 160 3204 9 7 1,260 1,2605 18 6 2,580 2,4606 11 8 1,760 1,1207 8 6 540 1808 9 2 140 1008 10 8 720 7208 15 4 960 9608 20 7 2,940 2,520

10 17 8 1,760 2,08011 12 5 350 25012 13 3 180 18013 14 6 300 42014 15 8 400 56014 20 4 920 76015 16 6 300 42016 17 7 350 49017 21 8 1,600 1,28017 20 8 560 40018 19 6 540 18019 20 2 180 60

Figure 7.Sequenced DSM for a

conceptual designproject

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new feedback (process 1 to process 9) in this example. This DSM containsseven feedbacks. The calculations shown in Table IV represent the time andcost required to converge a solution for each feedback iteration. By applyingthe constraint, the total design cycle for this DSM has been increased from3,800 time units to 5,060 time units and from 3,220 cost units to 4,120 cost. Eventhough there are increases in both cost and time, the sequence better reflects thereality of the design sequence.

Figure 8.Sequenced DSM for aconceptual designproject with constraint

Table IV.Time and cost foriterations for thesequenced DSM with aconstraint

To process From process Iterations Time Cost

9 8 6 420 30019 20 2 180 6018 19 6 540 18017 18 8 560 40016 17 7 350 49011 12 3 1,890 1,890

9 1 8 1,120 800

Table III.Time and cost foriterations for thesequenced DSM

To process From process Iterations Time Cost

8 9 2 280 20019 20 2 180 6018 19 6 540 18017 18 8 560 40016 17 7 350 49011 12 3 1,890 1,890

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SummaryThe DeMAID is a knowledge-based software tool for sequencing complexdesign processes, grouping iterative subcycles, and identifying a possiblemultilevel structure for a design cycle. The DeMAID software displays theprocesses in a design structure matrix format in which any process thatrequires input and generates output is an element on the diagonal. Off-diagonalelements indicate a coupling between two processes. The knowledge base inDeMAID attempts to eliminate all feedbacks in the design cycle. If allfeedbacks cannot be eliminated, iterative subcycles are identified. In aniterative subcycle, some data must be estimated and iterations are required toobtain a converged solution. The time and cost to converge the solution isdependent on the process execution sequence. Therefore, it is necessary tooptimize the sequence to minimize the time and cost to find the optimumdesign.

In the original version of DeMAID, the optimal sequencing of processes in aniterative subcycle was generated with a knowledge base and only minimizedthe number of feedbacks. The primary drawback to the original method wasthat only a single sequence could be examined at a time. Changes to thesequence were made interactively and then the times and costs were re-evaluated. This process was extremely slow, with no guarantee that areasonable optimum sequence would be found.

To remedy this problem, a genetic algorithm (GA) has been added toDeMAID to examine many possible sequences of the processes in a designcycle. Each process can now have a time and/or cost associated with it. The GAin DeMAID examines the iterative subcycles to determine their time and cost.The GA fitness function is computed by summing the time and cost of eachprocess contained in a feedback iteration and multiplying the respective totalsby the iteration factor required for convergence. This factor is based on thecoupling strength of the feedback coupling forming the iteration. The GAattempts to determine the optimum sequence of each iterative subcycle byminimizing the total time and cost requirements. Constraints can be added topenalize the fitness function where certain processes are not completed beforeother processes begin. This modification increases the likelihood that a morerealistic optimal or near-optimal sequence will be found.

References

Altus, S.S., Kroo, I.M. and Gage, P.J. (1995), `̀ A genetic algorithm for scheduling anddecomposition of multidisciplinary design problems'', ASME Paper 95-141.

Bloebaum, C.L. (1992), `̀ An intelligent decomposition approach for coupled engineering systems'',AIAA Paper 92-4821.

Giarranto, J. and Riley, G. (1989), Expert Systems Principles and Programming, PW-Kent, Boston,MA.

Goldberg, D. (1989), Genetic Algorithms in Search, Optimization, and Machine Learning,Addison-Wesley, New York, NY.

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McCulley, C.M. and Bloebaum, C.L. (1994), `̀ Optimal sequencing for complex cngineeringsystems using genetic algorithms'', AIAA Paper 94-4327.

Rogers, J.L. and Bloebaum, C.L. (1994), `̀ Ordering design tasks based on coupling strengths'',AIAA Paper 94-4326.

Rogers, J.L., McCulley, C.M. and Bloebaum, C.L. (1996), `̀ Integrating a genetic algorithm into aknowledge-based system for ordering complex design processes'', Artificial Intelligence inDesign '96, Kluwer Academic Publishers, Boston, MA, pp. 119-33.

Steward, D.V. (1981), Systems Analysis and Management: Structure, Strategy and Design,Petrocelli Books Inc., New York, NY.

Syswerda, G. (1990), `̀ Schedule optimization using genetic algorithms'', Handbook of GeneticAlgorithms, Van Nostrand Reinhold, New York, NY.