Multidisciplinary Aircraft Conceptual Design Optimisation Using a Hierarchical Asynchronous Parallel Evolutionary Algorithm (HAPEA) University of Sydney L. F. Gonzalez E. J. Whitney K. Srinivas K.C Wong Pole Scientifique - Dassault Aviation- J. Périaux Slide 1: Intro In this lecture I will present some of the reserarhc results on evolutionary techniques at School of Aerospace, Echanical ns nd Mechatronic Engineering, University of Sydney . This research is allsoo incooperation with J.Periaux at the Pole Scientifique. Specifially we will discuss a Hierarchical Aynchronous Evolutionary technique. Presented at the Sixth ADAPTIVE COMPUTING IN DESIGN AND MANUFACTURE(ACDM 2004) APRIL 20th - 22nd, 2004 at ENGINEERS HOUSE, CLIFTON, BRISTOL, UK

Overview PART 1 Multi-Objective Problems Research in Evolution Algorithms for Aeronautical Design Problems (EAs) PART 2 Test Cases and Applications . PART 3

Multi-Criteria Problems Aeronautical design problems normally require a simultaneous optimisation of conflicting objectives and associated number of constraints. They occur when two or more objectives that cannot be combined rationally. For example: Drag at two different values of lift. Drag and thickness. Pitching moment and maximum lift.

…..Multi--Criteria Optimisation A multi-criteria optimisation problem can be formulated as: Minimise: Subject to constraints: Different Approaches: Traditional aggregating functions, and Pareto and Nash.

Pareto Optimality Formally, the Pareto optimal set can be defined as the set of solutions that are non-dominated with respect to all other points in the search space, or that they dominate every other solution in the search space except fellow members of the Pareto optimal set. For two solutions x and y (in minimisation form): . For a problem in M objectives, this is called the 'relationship' operator. In practice we compute an approximation to the continuous set, by assembling .or each player, as can be seen in Figure 2, whereby information is exchanged

Nash Games Player 2 Player 1 A Nash optimisation can be viewed as a competitive game between two players that each greedily optimise their own objective at the expense of the other player. A Nash equilibrium is obtained when no player can improve his own objective at the expense of the other. Epoch Completed? Player 2 Player 1 Migrate and Exchange

The Problem… Problems in aeronautical design optimisation: Traditional optimisation methods will fail to find the real answer in most real engineering applications. Fitness functions of interest are generally multimodal with a number of local minima. Sometimes the optimum shape/s is not obvious to the designer. The fitness function will involve some numerical noise. Most aerodynamic design problems will need to be stated in multi-objective form. Modern aeronautical design uses CFD (Computational Fluid Dynamics) and FEA almost exclusively. CFD has matured enough to use for preliminary design and optimisation. The internal workings of validated in-house solvers are essentially inaccessible from a modification point of view (they are black-boxes). If we consider aerodynamic optimisation we can see how the following issues arise: The use of CFD is almost always present as it has matured enough for preliminary design and optimisation but the internal workings of this solvers are essentially inaccessible for modifications, they can be considered black boxes. Most of the problems have to be stated in multiobjetcive form and the fitness function is generally complex, and multimodal and with many local minima and involve noise

… The Solution…. Why Evolution? Techniques such as Evolution Algorithms can explore large variations in designs. They also handle errors and deceptive sub-optimal solutions with aplomb. They are extremely easy to parallelise, significantly reducing computation time. They can provide optimal solutions for single and multi-objective problems. EAs successively map multiple populations of points, allowing solution diversity. They are capable of finding a number of solutions in a Pareto set or calculating a robust Nash game. The problem is that traditional optimiser fail to find the global answer in this sort of problems, but different applications of Eas have shown potential in this area as they found global solutions and are easy to parallelize reducing their computational time. Lso theEAS can mapo succesive populations and arer vabapbel of finding Pareto set or ansh equoibrium solutions..

What Are Evolution Algorithms? Based on the Darwinian theory of evolution  Populations of individuals evolve and reproduce by means of mutation and crossover operators and compete in a set environment for survival of the fittest. Evolution Crossover Mutation Fittest Computers perform this evolution process as a mathematical simplification. EAs move populations of solutions, rather than ‘cut-and-try’ one to another. EAs applied to sciences, arts and engineering. Aerofoil and wing design, crew scheduling, control loops,etc.

Why EAs? …Test Functions Here our EA solves a two objective problem with two design variables. There are two possible Pareto optimal fronts; one obvious and concave, the other deceptive and convex.

“The Central Difficulty” Evolutionary techniques are … still … very … slow! (Often involving hundreds or thousands of separate flow computations) In general the main problem of Eas is as most of us will know, is that they are slow, very slow so we need means to speed up the computational process. Therefore, we need to think about ways of speeding up the process…

Hierarchical Topology-Multiple Models precise model Exploitation We use a technique that finds optimum solutions by using many different models, that greatly accelerates the optimisation process. Interactions of the layers: solutions go up and down the layers. Time-consuming solvers only for the most promising solutions. Asynchronous Parallel Computing Model 2 intermediate model Model 3 approximate model Exploration Hierarchical Topology Evolution Algorithm Evaluator Parallel Computing and Asynchronous Evaluation

Synchronous Evaluation different speed Evolution Strategy Synchromous Evaluator 1 population (n individuals) Single population The whole population is passed to the evaluator. All the individuals of a given generation need to be evaluated before proceeding to the next generation Hierarchical populations ES Each population has to go through a fixed number of generations before migration can take place Since migration is global, the different populations will have to wait for the slowest one before exchanging individuals Sync Sync Sync ES ES ES ES ES ES Sync Sync Sync Sync

Asynchronous Evaluation different speed Single population Individuals are evaluated one by one, and reintegrated in the population : there is no notion of generation That means the ES can run on any number of processors (whereas for a synchronous approach, a population of 20 individuals can run on 20 processors at the most) 1 individual Evolution Strategy Asynchromous Evaluator 1 individual Hierarchical populations ES Since there is no generation, migration can take place anytime after a minimum number of evaluations have been performed There is no bottleneck ES ES Async ES ES ES ES

Asynchronous Evaluation… Fitness functions are computed asynchronously. Only one candidate solution is generated at a time, and only one individual is incorporated at a time rather than an entire population at every generation as is traditional EAs. Solutions can be generated and returned out of order. No need for synchronicity  no possible wait-time bottleneck. No need for the different processors to be of similar speed. Processors can be added or deleted dynamically during the execution. There is no practical upper limit on the number of processors we can use. All desktop computers in an organisation are fair game.

….Asynchronous Evaluation… Offspring are not sent as a complete 'block' to the parallel machines. A candidate is generated at a time, and sent to any idle processor where it is evaluated at its own speed. After evaluation return to optimiser and check if accepted for insertion into the main population or rejected. New selector operator because offspring cannot now be compared one against the other, or even against the main population due to the variable-time evaluation. Recently evaluated offspring are compared to a previously established rolling-benchmark and if successful, we replace (according to some rule) a pre-existing individual in the population. A separate evaluation buffer, which provides a statistical 'background check' on the comparative fitness of the solution.  Buffer size 2 x PopSize We compare it with the selection buffer by assembling at random a small subset called the tournament Q = [q1,q2,q3,…qn] and check that the individual is not dominated by any member of Q. Q =1/2B (Strong selective pressure), Q =1/6B (weak selection pressure). Compare to past individuals (both accepted and rejected) -inserted or not   If accepted us strategy for replacement replace-worst-always method in this paper. Generate candidate Send to idle processor If evaluation completed send back to optimiser Assign fitness Compare to a tournament and if successful replace The approach used in this research, is to ignore any concept of generation based solution.   This approach is similar to work done by Wakunda and Zell [11] and other non-generational approaches, however the selection operator is quite different, as it couples one-by-one (steady-state) function evaluation with a direct multi-objective fitness criterion. Whilst a parent population exists, offspring are not sent as a complete 'block' to the parallel slaves for solution. Instead one candidate is generated at a time, and is sent to any idle processor where it is evaluated at its own speed. When candidates have been evaluated, they are returned to the optimiser and either accepted by insertion into the main population or rejected. This requires a new selection operator because the offspring cannot now be compared one against the other, or even against the main population due to the variable-time evaluation. We compare recently evaluated offspring against a previously established rolling-benchmark and if successful, we replace (according to some rule) a pre-existing individual in the population. We implement this benchmarking via a separate evaluation buffer, which provides a statistical 'background check' on the comparative fitness of the solution. The length of the buffer should represent a reasonable statistical sample size, but need not be too large; approximately twice the population size is more than ample. W hen an individual has had a fitness assigned, it is then compared to past individuals (both accepted and rejected) to determine whether or not it should be inserted into the main population. If it is to be accepted, then some replacement strategy is invoked and it replaces a member of the main population. We exclusively use the replace-worst-always method in this paper. Compare to accepted and rejected individuals –insert into the population

Applications-Test Functions (1) Here our EA solves a two objective problem with two design variables. The optimal Pareto front contains four discontinuous regions.

Applications-Test Functions (2) TNK Again, we solve a two objective problem with two design variables and one. The optimal Pareto front contains four discontinuous regions and constraints

Asynchronous Test: One Dimensional Nozzle

Synchronous, Single Population, Viscous model Pop size = 20 7 processors 45mn

Asynchronous, Multiple Models, Viscous only Pop size = 10 7 processors 12mn

CPU Times for HAPEA Method CPU Time No of evaluations Single Pop, Viscous, Traditional EA 45m 27s  12m 8s 2127  1137 Hierarchical Asynchronous 12m 6s  3m 58s 726  112

Real –world applications Constrained aerofoil design for transonic transport aircraft  3% Drag reduction UAV aerofoil design -Drag minimisation for high-speed transit and loiter conditions. -Drag minimisation for high-speed transit and takeoff conditions. Exhaust nozzle design for minimum losses.

Real –world applications … (2) AF/A-18 Flutter model validation. Three element aerofoil reconstruction from surface pressure data. UCAV MDO Whole aircraft multidisciplinary design. Gross weight minimisation and cruise efficiency Maximisation. Coupling with NASA code FLOPS 2 % improvement in Takeoff GW and Cruise Efficiency

Case Studies Multidisciplinary Aircraft Conceptual Design Case Studies.

UCAV Conceptual Design. Problem Definition: Find conceptual design parameters for a UCAV, to minimise two objectives: Gross weight  min(WG) Cruise efficiency  min(1/[MCRUISE.L/DCRUISE]) We have six unknowns: Lower Bound Upper Aspect Ratio 3.1 5.3 Wing Area (sq ft) 600 1400 Wing Thickness 0.02 0.09 Wing Taper Ratio 0.15 0.55 Wing Sweep (deg) 22.0 47.0 Engine Thrust (lbf) 30500 50000

Mission Definition Description Requirement Range [R, Nm] 1000 Cruise 40000 ft, Mach 0.9, 400 nm Release Payload 1800 Lbs Accelerate Mach 1.5, 500 nm 20000 ft Maneuvers at Mach 0.9 Climb Release Payload 1500 Lbs Taxi Descend Takeoff Landing Engine Start and warm up Description Requirement Range [R, Nm] 1000 Cruise Mach Number [Mcruise] 1.6 Cruise Altitude [hcruise, ft] 40000 Ultimate Load Factor [nult] 12 Takeoff Field Length [sto, ft] 7000

Solver The FLOPS (FLight OPtimisation System) solver developed by L. A. (Arnie) McCullers, NASA Langley Research Center was used for evaluating the aircraft configurations. FLOPS is a workstation based code with capabilities for conceptual and preliminary design of advanced concepts. FLOPS is multidisciplinary in nature and contains several analysis modules including: weights, aerodynamics, engine cycle analysis, propulsion, mission performance, takeoff and landing, noise footprint, cost analysis, and program control. FLOPS has capabilities for optimisation but in this case was used only for analysis. Drag is computed using Empirical Drag Estimation Technique (EDET) - Different hierarchical models are being adapted for drag build up using higher fidelity models.

Two Approaches Solved via : Nash theory and Pareto Optimality.

Implementation Nash Approach. Epoch Completed? Nash Approach. -Two hierarchical trees, with two levels, population size of 40. Player 2 Player 1 Migrate and Exchange - Information exchanged (epoch) after 50 function evaluations. Variables split: -Player One: Aspect ratio, wing thickness and wing sweep; Maximises cruise efficiency. -Player Two: Wing area, engine thrust and wing taper; Minimises gross weight. - Run for 600 function evaluations, but converged after 300.

Nash Results

Nash Results (2)

Cruise Efficiency MCRUISE.L/DCRUISE Nash Results (3) Variables Nash Equilibrium Aspect Ratio 5.13 Wing Area (sq ft) 618 Wing Thickness 0.021 Wing Taper Ratio 0.17 Wing Sweep (deg) 28 Engine Thrust (lbf) 33356 Gross Weight (Lbs) 62463 Cruise Efficiency MCRUISE.L/DCRUISE 23.9

Implementation Single population Pareto Optimality Approach - Population size of 40. - Parallel computations, run asynchronously. - Run for 600 function evaluations. 1 individual Asynchromous Evaluator 1 individual

Pareto Optimality Results Best for Obj 1 Nash Equilibrium Compromised solution Best for Obj 2

Increasing Cruise Efficiency Decreasing Gross Weight Comparison Results Variables Pareto Member 0 Member 3 Pareto Member 7 Nash Equilibrium Aspect Ratio 4.76 5.23 5.27 5.13 Wing Area (sq ft) 629.7 743.8 919 618 Wing Thickness (t/c) 0.046 0.050 0.041 0.021 Wing Taper Ratio 0.15 0.16 0.17 Wing Sweep (deg) 28 25 27 Engine Thrust (lbf) 32065 32219 32259 33356 Nash Point Gross Weight (Lbs) 57540 59179 64606 62463 Increasing Cruise Efficiency Decreasing Gross Weight MCRUISE.L/DCRUISE 22.5 25.1 27.5 23.9

Comparison Results (2) Upper Bound Nash Equilibrium Lower Bound Nash Design Lower Bound

Subsonic Transport Design and Optimisation Problem Definition: Find conceptual design parameters for a subsonic medium size transport aircraft . Gross weight  min(WG) The aircraft has two wing-mounted engines, and the number of passengers and crew is fixed to 200 and 8 respectively. The aircraft is designed to cruise at 40000 ft and Mach 0.8. We have six unknowns: Lower Bound Upper Bound Aspect Ratio 7.0 13.1 Wing Area (sq ft) 1927 2872 Wing Thickness 0.091 0.235 Wing Taper Ratio 0.15 0.55 Wing Sweep (deg) 22.0 47.0 Engine Thrust (lbf) 32000 37000

Constraints and Implementation Constraints in this case are minimum takeoff distance, moment coefficient for stability and control and range required. Violation of these constraints is treated with an rejection criteria. Implementation The solution to this problem has been implemented using a single population and parallel asynchronous evaluation, with the optimiser only considering a single objective. After an empirical study, it was found that a small population size of 10 and buffer size of 30 produced acceptable results.

Results The algorithm was allowed to run for 1500 functions evaluations. Broyden-Fletcher-Goldfarb-Shano (BFGS) algorithm --- > a 3.5% improvement Conjugate gradient (CG) based (Polak-Ribiere) algorithm -- > 2.4% improvement Description EA Best BFGS CG_____ Aspect Ratio [ARw] 13.1 13.0 12.8 Engine Thrust [T, lbf] 34,770 38,852 39,021 Wing Area [Sw, sq ft] 1,929 2,142 2,218 Sweep [w, deg] 27.0 28.4 27.32 Thickness [t/c] 0.091 0.112 0.096 Taper Ratio [w] 0.267 0.267 0.267 ---------------------------------------------------------------------------------------------------- Fuel Weight [Wf, lbs] 34,337 37,342 36,092 Gross Weight [Wg , lbs] 216,702 222,154 224,618

Conclusion The new technique with multiple models: Lower the computational expense dilemma in an engineering environment (three times faster) The multi-criteria HAPEA has shown itself to be promising for direct and inverse design optimisation problems. No problem specific knowledge is required  The method appears to be broadly applicable to black-box solvers. As illustrated a variety of optimisation problems including Multi-disciplinary Design Optimisation (MDO) problems can be solved. The process finds traditional classical aerodynamic results for standard problems, as well as interesting compromise solutions. The algorithm may attempt to circumvent convergence difficulties with the solver. In doing all this work, no special hardware has been required – Desktop PCs networked together have been up to the task.

Wing MDO using Potential flow and structural FEA. What Are We Doing Now? A Hybrid EA - Deterministic optimiser. EA + MDO : Evolutionary Algorithms Architecture for Multidisciplinary Design Optimisation We intend to couple the aerodynamic optimisation with: Aerodynamics – Whole wing design using Euler codes. Electromagnetics - Investigating the tradeoff between efficient aerodynamic design and RCS issues. Structures - Especially in three dimensions means we can investigate interesting tradeoffs that may provide weight improvements. And others… Wing MDO using Potential flow and structural FEA.

Questions???

Results So Far… The new technique is approximately three times faster than other similar EA methods. Evaluations CPU Time Traditional 2311 ± 224 152m ± 20m New Technique 504 ± 490 (-78%) 48m ± 24m (-68%) A testbench for single and multiobjective problems has been developed and tested We have successfully coupled the optimisation code to different compressible and incompressible CFD codes and also to some aircraft design codes CFD Aircraft Design HDASS MSES XFOIL Flight Optimisation Software (FLOPS) FLO22 Nsc2ke ADS (In house)

Appendix-Applications

Publications ADVanced EvolutioN Team (ADVENT ) Selected Publications and Conference Papers 2003 E. Whitney, L. Gonzalez, K. Srinivas, J. Périaux: “Adaptive Evolution Design Without Problem Specific Knowledge ”, Proceedings (to appear) of  EUROGEN 2003, Barcelona, Spain. 2003 E. Whitney, “A Modern Evolutionary Technique for Design and Optimisation in Aeronautics ”, PhD Thesis, School of Aerospace, Mechanical and Mechatronic Engineering, J07 University of Sydney, NSW, 2006 Australia  2003 E. Whitney, L. Gonzalez,  J. Périaux:, and K. Srinivas, “Playing Games with Evolution: Theory and Aeronautical Optimisation Applications”,  ICIAM 2003 -- 5th International Congress on Industrial and Applied Mathematics, Sydney, Australia, July 2003. To appear.  2002 E. Whitney, L. Gonzalez, K. Srinivas, J. Périaux: “Multi-Criteria Aerodynamic Shape Design Problems in CFD using a Modern Evolutionary Algorithm on Distributed Computers”, Proceedings of the Second International Conference on Computational Fluid Dynamics, Sydney, Australia.   2002 J. Périaux:, M. Sefrioui, E. Whitney, L. Gonzalez, K. Srinivas, and J. Wang  “Evolutionary Algorithms, Game Theory and Hierarchical Models in CFD”, Proceedings of the Second International Conference on Computational Fluid Dynamics, Sydney, Australia. 2002 E. Whitney, M. Sefrioui, K. Srinivas, J. Périaux: “Advances in Hierarchical, Parallel Evolutionary Algorithms for Aerodynamic Shape Optimisation”, JSME (Japan Society of Mechanical Engineers) International Journal, Vol. 45, No. 1. 2001 J. Périaux, M. Sefrioui, K. Srinivas, E. Whitney, J. Wang: “Recent Advances in Evolutionary Algorithms for Multicriteria Design Optimisation in Aeronautics”, Kickoff Meeting, MACSI Working Group on Multidisciplinary Optimisation and Inverse Problems, Vienna, Austria. 2001 M. Sefrioui, E. Whitney, J. Périaux, K. Srinivas: “Evolutionary Algorithms for Multi-Objective Design Optimisation”, Proceedings of Coupling of Fluids, Structures and Waves in Aeronautics (CFSWA), A French / Australian workshop, Melbourne, Australia. 2001 J. Périaux, M. Sefrioui, K. Srinivas, E. Whitney, J. Wang: “Advances in Hierarchical Parallel Genetic Algorithms and Game Decision Strategies for Design Optimisation in Aeronautics”, Proceedings of the First French / Finnish Seminar on Innovative Methods for Advanced Technologies, Espoo, Finland. 2000 E. Whitney, K. Srinivas: “Non-Generational Multiobjective Evolution Strategy for Aerofoil Design and Optimisation Problems in CFD”: Proceedings of the First International Conference on Computational Fluid Dynamics, Kyoto, Japan:

Hierarchical Topology-Multiple Models precise model Exploitation Model 2 intermediate model Model 3 approximate model Exploration Interactions of the 3 layers: solutions go up and down the layers. The best ones keep going up until they are completely refined. No need for great precision during exploration. Time-consuming solvers are used only for the most promising solutions. Think of it as a kind of optimisation and population based multigrid.

An Example: Aerofoil Optimisation Property Flt. Cond. 1 Flt Cond.2 Mach 0.75 Reynolds 9 x 106 Lift 0.65 0.715 Constraints: Thickness > 12.1% x/c (RAE 2822) Max thickness position = 20% ® 55% To solve this and other problems standard industrial flow solvers are being used. Aerofoil cd [cl = 0.65 ] [cl = 0.715 ] Traditional Aerofoil RAE2822 0.0147 0.0185 Conventional Optimiser [Nadarajah [1]] 0.0098 (-33.3%) 0.0130 (-29.7%) New Technique 0.0094 (-36.1%) 0.0108 (-41.6%) For a typical 400,000 lb airliner, flying 1,400 hrs/year: 3% drag reduction corresponds to 580,000 lbs (330,000 L) less fuel burned. [1] Nadarajah, S.; Jameson, A, " Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimisation," AIAA 15th Computational Fluid Dynamics Conference, AIAA-2001-2530, Anaheim, CA, June 2001.

Aerofoil Characteristics cl = 0.715 Aerofoil Optimisation (2) Aerofoil Characteristics cl = 0.715 Aerofoil Characteristics cl = 0.65 Delayed drag divergence at high Cl Delayed drag divergence at low Cl Aerofoil Characteristics M¥ = 0.75 Delayed drag rise for increasing lift.

ZDT Test Cases

ZDT1

ZDT2

ZDT3

ZDT4

Constrained Test Cases

BNH

SRN

Two Bar Truss Design A B

Goal Programming- Test Problem P1

Results. Candidate and Target Geometries

Results: Example of Convergence. Mesh Adaptation : Mesh 15