A General-Purpose Optimization Engine for Multi ... · A General-Purpose Optimization Engine for Multi-Disciplinary Design Applications ... nature (with a separate ... difficult optimization

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NASA Technical Memorandum 107314

AIAA-96-4163

A General-Purpose Optimization Engine for

Multi-Disciplinary Design Applications

Surya N. Patnaik

Ohio Aerospace Institute

Cleveland, Ohio

Dale A. Hopkins and Laszlo Berke

Lewis Research Center

Cleveland, Ohio

Prepared for the

Sixth Multidisciplinary Analysis and Optimization Symposium

cosponsored by AIAA, NASA, and USAF

Bellevue, Washington, September 4-6, 1996

National Aeronautics and

Space Administration

https://ntrs.nasa.gov/search.jsp?R=19960048016 2018-07-15T23:26:20+00:00Z

GENERALmPURPOSE OPTIMIZATION ENGINE FOR

MULTIDISCIPLINARY DESIGN APPLICATIONS

Surya N. Patnaik,* Dale A. Hopkins, and Lazlo BerkeNational Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

Abstract

A general purpose optimization tool formultidisciplinary applications, which in the literatureis known as COMETBOARDS, is being developedat NASA Lewis Research Center. The modular

organization of COMETBOARDS includes severalanalyzers and state-of-the-art optimization algorithmsalong with their cascading strategy. The codestructure allows quick integration of new analyzersand optimizers. The COMETBOARDS code readsinput information from a number of data files,formulates a design as a set of multidisciplinarynonlinear programming problems, and then solves theresulting problems. COMETBOARDS can be used tosolve a large problem which can be defined throughmultiple disciplines, each of which can be furtherbroken down into several subproblems. Alternatively,a small portion of a large problem can be optimizedin an effort to improve an existing system. Some ofthe other unique features of COMETBOARDSinclude design variable formulation, constraint

formulation, subproblem coupling strategy, globalscaling technique, analysis approximation, use ofeither sequential or parallel computational modes,and so forth. The special features and uniquestrengths of COMETBOARDS assist convergenceand reduce the amount of CPU time used to solve

the difficult optimization problems of aerospaceindustries. COMETBOARDS has been successfullyused to solve a number of problems, includingstructural design of space station components, designof nozzle components of an air-breathing engine,

configuration design of subsonic and supersonicaircraft, mixed flow turbofan engines, wave rotor

topped engines, and so forth. This paper introducesthe COMETBOARDS design tool and its versatility,which is illustrated by citing examples fromstructures, aircraft design, and air-breathingpropulsion engine design.

Introduction

A multidisciplinary optimization engine, whichin the literature is known as COMETBOARDS, is

being developed at NASA Lewis Research Center forthe design of structural components, subsonic andsupersonic aircraft configuration design, and air-breathing propulsion engine design. TheCOMETBOARDS design tool has provision toaccommodate up to ten different disciplines; each ofthese can have a maximum of five subproblems. Thedesign tool in other words can optimize a systemwhich can be defined in terms of fifty optimizationsubproblems. Each subproblem can be defined withits own design variables, constraints, and anobjective function. Computation at the subproblemlevel can be carried out either in sequential or inparallel computational modes. Interdisciplinarycoupling, an important strategy for successfulsolution of the problem, is accomplished throughcoupling at the design variable level and throughlocal and global constraint formulations. On theother hand, by appropriate data specification,COMETBOARDS can also be used to examine the

optimality of a small portion of a much larger designproblem.

The COMETBOARDS system first formulates thedesign as a nonlinear mathematical programmingproblem, reading data from specified input files, andthen solves the resulting problem. Problemformulation can utilize a number of analysis toolsavailable in its 'Analyzers' module. Representativeanalysis tools currently available inCOMETBOARDS include, RPK/NASTRAN 1 for

structural analysis, NASA Engine PerformanceProgram (NEPP) 2 for air-breathing engineperformance analysis, and Flight OptimizationSystems (FLOPS) 3 for aircraft performance analysis.The code allows soft-coupling and quick integrationof new analyzers. COMETBOARDS solution

*Ohio Aerospace Institute, Cleveland, Ohio"This paper is declared a work of the U.S. Governmentand is not subject to copyright protection in the United States."

1American Institute of Aeronautics and Astronautics

techniqueexploitsseveralof its uniquestrengths,whichare availablein its 'Optimizers'module.COMETBOARDSis writtenin Fortran77languageandtestedin CrayandConvexcomputersandinSGIand Sun Unix workstations. SuccessfulCOMETBOARDSsolutionsfor a numberof diverseindustrial problems,from different disciplinescorroboratetherobustnessandversatilityof thedesigntool.With augmentationandimprovement,the researchlevel optimization capability ofCOMETBOARDShasthepotentialof becomingarobustdesigntoolfortheaerospaceindustry.

Thispaperincludesanoverviewof thedesigntool COMETBOARDS.Threeapplications(oneeach,from structures,aircraft design,and air-breathingpropulsionengineconcepts)aregiventoillustrate the versatility and robustnessofCOMETBOARDS.

COMETBOARD$ Design Tool

The modular organization of COMETBOARDS isdepicted in Fig. 1. The key features ofCOMETBOARDS include its multidisciplinarynature (with a separate objective, constraints, andvariables for each discipline, which can be furtherbroken down into several subproblems), substructureoptimization (with coupling strategy available insequential as well as in parallel computationalmodes), state-of-the-art optimization algorithms andtheir cascading 4 strategies, and analysis

approximations by means of linear regressionanalysis and neural network. The COMETBOARDSmodular organization is like a test bed, and a userhas considerable flexibility such as (1) solving aproblem by using available analyzers and optimizersin the code, (2) adding analyzers through soft-coupling into COMETBOARDS and then solvingproblems, (3) checking out the performance of newanalyzers, (4) checking out the performance of anew optimizer utilizing the 40 or so problemsavailable in the COMETBOARDS solved-examples-test-bed; just to mention a few. Space does notpermit the description of the other features andunique strengths of the design toolCOMETBOARDS, some aspects of which can befound in Refs. [5, 6, and 7]. Only the cascadestrategy required to optimize aircraft and engineproblems is described next.

Cascade Optimization Strategy

COMETBOARDS provides for the solution ofdifficult optimization problems by means of acascade strategy. The basic cascade concept is anattempt to solve a complex problem by using morethan one optimizer, when individual optimizers facedifficulties. The cascade concept and its flow

diagram are depicted in Fig. 2. A COMETBOARDSuser has considerable flexibility in developing acascade strategy, by selecting a number ofoptimizers (currently about one dozen differentnonlinear programming algorithms are available),their convergence criteria, analysis approximations,and the amount of random perturbations between

optimizers. Consider for the purpose of illustration,the cascade concept, first optimizer, followed byseveral other optimizers, shown in Fig. 2(a).Individual convergence criteria can be specified foreach optimizer; for example, a coarse stop criteria

may be sufficient for the first optimizer, while a finestop criteria can be stipulated for the last optimizer.Likewise approximate analysis may suffice for thefirst optimizer, reserving an accurate analyzer for thefinal optimizer. The amount of pseudo randomperturbations for design variables between theoptimizers may be specified at the discretion of theuser.

Substructure Optimization Strategy

Design optimization of large structural systemscan be attempted by using the substructuring strategyavailable in COMETBOARDS. In this strategy theoriginal structure is divided into several smallersubstructures. The design of the entire structure canbe accomplished by repeated optimizations of thesubstructures. Substructure optimization can useeither sequential or parallel computational platforms.

The substructure optimization strategy availablein COMETBOARDS is illustrated by considering theexample of the support system of the long spacerstructure of the International Space Station as shownin Fig. 3. The support system, which for analysis isidealized by shell elements, is divided into foursegments and four substructures as depicted in Fig. 3.Substructure (1) includes all shell elements within

segments 3 and 4, substructure (2) includes all shellelements within segments 4 and 1, substructure(3) includes all shell elements within segments 1and 2, and substructure (4) includes all shell

elements within segments 2 and 3. The substructuringprocess incorporates adequate design variablecoupling, which is essential for the success of thestrategy. Notice, for example, the coupling betweenthe first and fourth substructures through theelements in segment 4, which are common to both.

The thickness of all shell elements within a

segment were grouped to obtain a single activedesign variable. Thus, each substructure has twoactive design variables; namely, substructure(1) contains the third and fourth design variables,substructure (2) contains the fourth and the firstdesign variables, and so forth.

The behavior constraints were separated intolocal and global sets. Separation of behavior

2American Institute of Aeronautics and Astronautics

constraintsinto localandglobalsetsis essentialforconvergenceof thesubstructurestrategy8. Thefirstsetincludedthelocalstressconstraintsassociatedwith each substructure;thesewere reducedbyfollowing the constraintsformulationschemeavailablein thedesigntoolCOMETBOARDS.Theothersetincludedglobaldisplacementconstraintswhichwereconsideredcommonforallsubstructures.

Thefinaloptimumresultsforthesupportsystemwereobtainedafterthreecompletedesigncycles,which totaled solutions of 12 optimizationsubproblems.ThesubstructuredesignsequenceisdepictedinFig.4. Notice,forexample,thereductionin theweightof substructure(1) in Fig.4, betweencycles! and2, andbetweencycles2 and3.In firsttwo cyclesthereis a considerablereductionin theweight,whileconvergenceoccurredduringthenexttwocycles.Othersubproblemcharacteristicsfollowthepatternwithsomedeviations.

Optimumresultsfor theproblemareshowninTableI. Theoptimumweightforthesupportsystemobtainedby usingthe substructuretechniqueis34.71lb; therearethreeactiveconstraints.Theoptimumresult is in goodagreementwith theoptimumsolutionof 34.68lb whichwasobtainedwhentheentirestructurewasdesignedasa singleunit.Likewisethevaluesof thedesignvariablesatthe optimum,shownin TableI, agreedwhensubstructuringand single-stepoptimizationwereused. Bothtechniquesproducedthe samethreeactiveconstraints.

Design Optimization of Supersonic Aircraft Concept

Design optimization of both subsonic andsupersonic aircraft concepts has been attemptedsuccessfully through a soft-coupling of the Flight

Optimi-zation Systems (FLOPS) as the analyzer andCOMETBOARDS as the optimizer. The FLOPSanalyzer through input data specifications can beused to analyze both subsonic and supersonicaircraft. The FLOPS analyzer uses several different

disciplines to predict aircraft performance. Thedifferent disciplines available in a modular forminclude weight, aerodynamics, engine cycleanalysis, propulsion data interpolation, missionperformance, takeoff and landing, noise footprint,and cost. The combined design tool with FLOPS asthe analyzer and COMETBOARDS as the optimizerhas been successfully used to solve a number ofsubsonic and supersonic aircraft problems. Theexample of a supersonic aircraft is given here toillustrate COMETBOARDS capability.

The takeoff gross weight is considered as themerit function of the aircraft problem. Six

independent design variables are considered; theyare (1) engine thrust (in lb), (2) wing size (in sq ft),

(3) engine turbine inlet temperature (in °R),(4) engine overall pressure ratio, (5) bypass ratio,and (6) fan pressure ratio. The six critical behaviorconstraints included are (1) landing approach

velocity, (2) takeoff field length, (3) missedapproach, (4) second segment climb, (5) jetvelocity, and (6) compressor discharge temperature.

The resulting multidisciplinary optimization

problem has distorted design space since bothdesign variables and constraints varied over a verywide range. For example an engine thrust designvariable (which is measured in kip) is immenselydifferent from the bypass ratio variable (which is asmall number). Likewise, landing velocity constraint(in knots) and field length limitation (in thousands offt) differ both in magnitude and in units of measure.The difficult nature of the design problem is furthercompounded because of the statistical and empiricalequations, the smoothing techniques, and so forth,employed in the FLOPS analyzer. In other words, theFLOPS analyzer can be numerically unstable forsome combinations of design variables, especiallyfor a supersonic aircraft. The unique features ofCOMETBOARDS, especially the scaling and thecascade strategy, assisted the convergence of thedifficult problem.

To examine the robustness of the

COMETBOARDS-FLOPS combined design tool, sixdifferent aircraft design test cases with different

starting points and variable bounds were devised atNASA Langley Research Center. Only five caseswill be given in this paper. All the test problemshave been solved by using NASA Lewis'COMETBOARDS. Optimum solutions for all fivecases are given in Table II. This table reveals thefollowing:

(1) Both COMETBOARDS and anotheroptimizer successfully solved all five test cases.

(2) Optimum solutions obtained by bothCOMETBOARDS and other optimizers were

comparable. The average COMETBOARDS optimumsolution at 666,550.0 lb was about 1 percent lighterthan the other optimizers results at 673,273.0 lb.

(3) Optimum values for the design variablesobtained using COMETBOARDS and otheroptimizers codes compared well with minordifferences. Likewise constraint values agreed wellbetween the two design tools, except for the second

segment climb thrust (SSFOR). WhenCOMETBOARDS was used, SSFOR was at 21.72 Ib,

while the other optimizer resulted in a value of607 lb.

The optimum solution obtained has been verifiedgraphically in Fig. 5. The optimum lies at theintersection of three active constraints, namely,

compressor discharge temperature, jet velocity, andsecond segment climb thrust. With respect to design

3American Institute of Aeronautics and Astronautics

variables, bypass ratio, and fan pressure ratio, theunconstrained minimum condition is achieved

without any active constraint.

Desi_ma of a Mixed flow Turbofan Engine for High-Speed Civil Transport System

Design optimization of air-breathing engines forhigh-speed civil transport applications has beendeveloped through a soft-coupling of the NASAEngine Performance Program (NEPP) with theoptimization tool COMETBOARDS. The combined

COMETBOARDS-NEPP computer simulation is anattempt to optimize the design of multimissionvariable cycle engines with specified hardwarecomponents and configurations with designatedinterconnections. The solution to the nonlinear

engine design problem when attempted through anyone of the dozen robust optimizers available inCOMETBOARDS could provide a feasible optimumsolution for only a portion of the aircraft flight regimebecause of a large number of mission points (definedthrough altitudes, Mach numbers, and power settingcombinations) with diverse constraints (specified on

pressure ratios, temperatures, speed corrections,mass flow rates, etc.) and over all ill-conditioned

design space. Utilization of the unique strengths ofCOMETBOARDS (such as the cascade strategy,global scaling technique, design variables, andconstraint formulations) successfully solved anumber of difficult engine design optimizationproblems.

The COMETBOARDS solution for a 122-

mission-point turbofan engine is given here as thelast numerical example. The 122 mission points forthe mixed flow turbofan (MFTF) engine is depictedin Fig. 6. The design optimization of the MFTFengine required the solution of a sequence of 122optimization subproblems, one for each missionpoint. For each mission point, the thrust of the enginewas considered as the merit function. The followingimportant active design variables were considered:pressure balance in the mixer, R-values for fans andcompressors, fan speed, and so forth. The importantconstraints considered were the following: themaximum speed of the compressor, acceptable surgemargin for the compressor, the dischargetemperatures, the mixer entrance Mach number, andso forth. The most reliable individual optimizationalgorithm available in COMETBOARDS couldprovide feasible results for only a portion of the 122-mission-point flight envelope because of thesequence of a large number of optimizationsubproblems, diverse constraint types, and overall ill-conditioning of the design space. A four optimizercascade strategy could successfully solve the engine

design problem for the entire 122-mission-point flightenvelope. Furthermore, the cascade strategyconverged to the same global solution when begunfrom different design points. The cascade solutionwas normalized with respect to the NEPP results,

which were obtained by using an individualoptimizer and manual interventions. The normalizedsolution, which is shown in Fig. 7, was found to besuperior for most of the 122 mission points, exceptfor a few cases for which both (COMETBOARDSand NEPP) optimum results agreed. For flightsaround mission point 70, COMETBOARDS resultsfor optimum thrust were about 10 percent higher thanthe NEPP solution. In brief, the cascade optimizationstrategy successfully solved the 122- mission-pointmixed-flow turbofan engine design problem.

Conclusions

COMETBOARDS, with its unique strengthsand strategies, has been used successfully to solvea number of problems from structures, aircraft, andair-breathing propulsion engines. SuccessfulCOMETBOARDS solutions for three difficult

examples (i.e., (1) design optimization of a supportsystem solved by using substructuring capability,(2) supersonic aircraft configuration optimization,and (3) mixed flow turbofan thrust optimization)illustrate the versatility of the code. The cascadestrategy of COMETBOARDS was required togenerate solutions for the aircraft and engineproblems. COMETBOARDS, which is written inFortran 77 language with parallel computationalfacility, is available in the Cray-YMP and Unixworkstations. With some enhancements and

modifications, the research level COMETBOARDS,which has been found robust and reliable for

multidisciplinary design applications has thepotential of becoming a useful design tool for

aerospace industry.

References

1. RPK/NASTRAN, COSMIC, University ofGeorgia, Athens, GA.

2. Kiann, J.N.; and Snyder, C.A.: NEPPProgrammers Manual. NASA TM-106575, 1994.

3. McCullers, L.A.: FLOPS: Aircraft ConfigurationOptimization Including Optimized Flight Profiles.NASA CP-2327, 1984.

4. Patnaik, S. N.; Coronets R. M.; and Hopkins, D.A.:A Cascade Optimization Strategy for Solution ofDifficult Multidisciplinary Design Problems.AIAA/ASME/ASCE/AHS/ASC 37th Structures,Structural Dynamics, and Materials Conference,April 15-17, 1996, Salt Lake City, UT.

4American Institute of Aeronautics and Astronautics

5.Guptiil, J.D.; et al.: COMETBOARDSUser'sManual,NASATM-4537,1996.

6.Patnaik,S.N.;et ai.: ComparativeEvaluationofDifferentOptimizationAlgorithmsfor StructuralDesignApplications.Int. Jnl. Num. Meth.OfEngr.,Vol.39,pp.1761-1774,1996.

7.Patnaik,S.N.;Gendy,A.S.;andHopkinsD.A.:DesignOptimizationof LargeStructuralSystems

WithSubstructuringin a ParallelComputationalEnvironment.Computer Systems in Engineering.

Vol. 5, No.4-6, pp. 425--440, 1994.8. Gendy, A..S.; et al.: Issues in Substructure

Optimization.WCSMO-1 ,Structural a n dMultidisciplinary Optimization, pp. 857-862,1995.

Table I.-Optimum Design Of Support System

Design cycle number

0 (initial)1

(a) Weight

3 (optimum)

Substructurin_

Weight,lb

No substructufing

54.35 54.35

34.04

2 34.7434.71

34.68 (optimum)

Substructure(b) Design

Design variables,in.

variables

Optimum design

Initial Substructurin 8I 0.2 0.1277

II 0.2 0.1298

In 0.2 0.1765

IV 0.2 0.0264

No substructuring0.1277

0.1295

0.17660.0263

Table II.-Optimum Design for Five NASA Langley ResearchCenter Supersonic Aircraft Test Cases

Test cases Takeoff gross weight

(normalized)COMETBOARDS Other optimizers

I 0.99997 1.01785

2 1.00004 1.00184

3 1.00005 1.02855

4 0.99996 1.00200

5 0.99997 1.00019

1.0 (666,550.0 lb)Average 1.00019 (673273.0 ib)

5American Institute of Aeronautics and Astronautics

Fig. 1 .--Organization of COMETBOARDS design tool.

Initial First

design optimizer

Initial

design

,,I Optimum',,

I I IFirst I Second I I Last

optimizer I optimizer I IoptimizerI I II I I

start

solution

Next optimizer

design tn sequence

start

Random

Design iterations

(a) (b)

Fig. 2.--Cascade strategy in COMETBOARDS. (a) Cascade concept. (b) Flow diagram.

Check

No

Yes

I

I

I

Fig. 3.-Support of long spacer structure of lnternational SpaceStation"

0 25 50 75 100 125Number of design iterations

Fig. 4.-Convergence characteristics of sub-structure optimization of support system.

S1 substructure i; Cycle i Completeoptimization cycle i for substructures

0700t//11 0.600

.o_

o.6oo

m 0.430

0.40

0.300 ._ \ ._ \ \._ \ .\ \ ._ _ •3.00 3.25 3.50

3

(a)Fan pressure ratio

70.0_

60.0_

41,500 _ _;'x,_\ _ _ _/

40.0_ _ _ i i i i i-

7.00 8.25 9.50 10.75

8,150Wing area

(c)

12.00

._o 0.0250

0.0230

,=21.5

0.0210O.

0.0190

°0.0170 !_\_,_- _"

2.800 2.900

(b)

3.000 3.1 O0 3.2002950 °R

Turbine inlet temperature

CDT Compressor discharge temperature

TOFL Takeoff field lengthV App Approach velocity

V Jet Jet velocity

X Optimum solution

Fig. 5.mGraphical verification of optimum design of supersonic aircraft. (a) Fan pressure ratio.

(b) Turbine inlet temperature. (c) Wing area.

5.0xl 04

4.0

3.0e""O

,_ 2.0

m

-- • •

• •

1.0-- • •

i•0.00 0.25 0.50

4_

I I I I I I I0.75 1.00 1.25 1.50 1.75 2.00 2.25

Mach number

Fig. 6.--Flight envelope for High-Speed Civil Transport mixed flow

turbofan engine.

2

5EQ.0"0

._

0Z

1.10

1.05

1.00

0.95

Solution

COM ETBOARDS

NEPP optimizer

I I I I25 50 75 100

Number of mission points

Fig. 7.--122 mission points for mixed flow turbofan(MFTF) engine.

I125

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August 1996 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

A General-Purpose Optimization Engine for Multi-Disciplinary

Design Applications

6. AUTHOR(S)

Surya N. Patnaik, Dale A. Hopkins, Laszlo Berke

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

WU-505--63-5B

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REPORT NUMBER

E- 10409

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-107314

AIAA-96-4163

11. SUPPLEMENTARY NOTES

Prepared for the Sixth Multidisciplinary Analysis and Optimization Symposium cosponsored by AIAA, NASA, and

USAF, Bellevue, Washington, September 4-6, 1996. Surya N. Patnaik, Ohio Aerospace Institute, 22800 Cedar Point

Road, Cleveland, Ohio 44142; Dale A. Hopkins and Laszlo Berke, NASA Lewis Research Center. Responsible person,

Dale A. Hopkins, organization code 5210, (216) 433-3260.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 39

This publication is available from the NASA Center for AeroSpace Information, (301) 621--0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS,

is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several

analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick

integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files,

formulates a design as a set of multidisciplinary nonlinear programming problems, and then solves the resulting problems.

COMETBOARDS can be used to solve a large problem which can be defined through multiple disciplines, each of which can

be further broken down into several subproblems. Alternatively, a small portion of a large problem can be optimized in an

effort to improve an existing system. Some of the other unique features of COMETBOARDS include design variable formula-

tion, constraint formulation, subproblem coupling strategy, global scaling technique, analysis approximation, use of either

sequential or parallel computational modes, and so forth. The special features and unique strengths of COMETBOARDS

assist convergence and reduce the amount of CPU time used to solve the difficult optimization problems of aerospace

industries. COMETBOARDS has been successfully used to solve a number of problems, including structural design of space

station components, design of nozzle components of an air-breathing engine, configuration design of subsonic and supersonic

aircraft, mixed flow turbofan engines, wave rotor topped engines, and so forth. This paper introduces the COMETBOARDS

design tool and its versatility, which is illustrated by citing examples from structures, aircraft design, and air-breathing

propulsion engine design.

14. SUBJECT TERMS

Multi-disciplinary optimization; Nonlinear programming algorithms and cascade sub-

structure; Parallel computation

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