Sin ttulo de diapositiva

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International Conference Parallel CFD 2002
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Multicriteria Optimization
International Conference Parallel CFD 2002

• It is of interest in Engineering problems to
  optimize a problem from the optics of many
  criteria.
• Functions normally in conflict, where the global
  optimum for one is not for other.
• In the multicriteria optimization exists a set of
  optimal solutions where an improvement in one of
  the criteria implies the diminishing of another
  this set of solutions is called Pareto Frontier.
• It will be work of the designer, the choose of
  the solution that better fits his requirements or
  necessities, belonging to this Pareto Frontier.

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Disadvantages of Classical Multicriteria Methods

• Many times should be applied an algorithm in
  order to obtain multiple non-dominated solutions.
  (only one solution is found each application).
• They require some information about the handled
  problem (for example, the method of pondering
  coefficients, in order to determine parameters
  that should add a value of one).
• They can be sensitive to the Pareto Front shape
  (they are not capable to find solutions located
  in certain zones like non-convex ones).
• The spread of the Pareto solutions found depends
  on the efficiency of the mono-criteria optimizer.
• They are not appropriate in problems with
  stochasticities or uncertainties.
• They can not handle problems with discrete domain.

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International Conference Parallel CFD 2002
Evolutionary Algorithms

• Can exploit parallelism
• Advantage speed up in calculation time
• ? better exploration and exploitation of search
  space
• Can be coupled with simulation models
• Ability to solve multi-criteria optimisation
  problems
• Potential to cope with constraints
• Can deal with time-varying problems

Mathematical Prospects Evolution for
Optimization Th. Bäck, G. Winter Althaus, B.
Naujoks
from INGENET CASE STUDIES Open Day June 8,
2001 HOW TO IMPROVE ADVANCED DESIGN WITH
EVOLUTIONARY COMPUTING ? von Karman Institute
for Fluid Dynamics Rhode-Saint-Genese, Belgium
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International Conference Parallel CFD 2002
EVOLUTIONARY ALGORITHMS (EAs) are search and
optimisation tools based on stochastics
approaches and the famous Darwin's principle of
survival of the fittest. The robustness of EAs
has been proved in a variety of applications,
including problems that can hardly be solved
through traditionnal optimisation methods. EAs
may equally handle single and multi-objective
which are likely to involve more than one
discipline.
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Solving an Optimization Problem
International Conference Parallel CFD 2002
Test Function F6
Generational Model CHC Algorithm Steady-State
Model
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Solving an Optimization Problem
International Conference Parallel CFD 2002

• The Resolution of an optimization problem with
  genetic algorithms requires the definition of
• CHROMOSOME CODIFICATION (individual or candidate
  to constitute the optimal solution)
• Include the variable information among solutions.
• It should be structured in order to the coherent
  production of individuals through the operators
  of crossover and mutation. (the generated
  population should be consistent with the problem
  definition and also valuable by the objective
  function).
• OBJECTIVE FUNCTION(S) (it can be a mono- or
  multi- criteria context)
• To collect the necessary information for the
  genetic algorithm to search the optimum
  individual. It shall include all the required
  factors asked to the desired solution. It
  measures the adaptation of each individual to the
  environment, or aptitude of the solution.

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Darwinist Process of Genetic Algorithm
International Conference Parallel CFD 2002

• the fitness measures the suitability to the
  environment of each candidate solution
• (evaluation of the fitness function)
• GENETIC OPERATORS
• Selection of the individuals depending on its
  better adaptation to the environment (selection)
  
• Exchange of information among chromosomes
  (crossover)
• Random variation of this information (mutation)
• a new population is generated, and this process
  is iteratively repeated, improving progressively
  the average quality of chromosomes
  (representatives of candidate solutions of the
  problem treated)

create initial population (P)
evaluate initial population (P)
while (NOT termination condition)
P1 probabilistically select
(P) P2 probabilistically cross (P1) P3
probabilistically mute (P2) evaluate
(P3) P4 new population (P,P3) P P4
verify
termination condition
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Genetic Algorithms Basic Operators

• Selection chooses a certain number of individuals
  favoring those with better adaptation to the
  environment which constitute a intermediate
  population
• Crossover exchanges the genotypic information of
  the chromosomes (bits in binary codification),
  producing new individuals
• Mutation modifies randomly the individuals, with
  usually small variations of the genotype
  (exchanges 1s with 0s and vice versa, in binary
  codification).

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Crossover Operators

• Binary encoding
• One-point crossover
• Two point crossover
• Probabilistic multipoint crossover
• Uniform crossover

• Real encoding
• One-point crossover
• Two point crossover
• Probabilistic multipoint crossover
• Arithmetic crossover
• Geometric crossover
• Probabilistic geometric crossover
• Wright heuristic crossover

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International Conference Parallel CFD 2002
Crossover and Mutation
BINARY CODE
One point (Holland)
Two point
Uniform (Syswerda)
Mutation
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Arithmetic crossover Real code
Pt1
P1
I1
I i
I2
Ii1
Ii
I i1
IN
P2
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Selection

• 1. How are the selection probabilities assigned
  to each individual?
• Proportional Selection (Holland 1975)
• (premature convergence, stagnation)
• Scaled Selection (Forrest 1985)
• Ranking Selection (Baker 1985)
• being l number of individuals contained in
  the population
• h min 2 - h max , being its value
  1 lt h max lt 2.
• Uniform Selection

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Selection

• How to select the individuals based in the
  individual probabilities?
• Roulette Wheel Selection RWS (De Jong 1975)
• Stochastic Remainder Selection with replacement
  SRSWR (Brindle 1981, Booker 1982)
• Stochastic Universal Selection SUS
• (J. E. Baker 1987, Grefenstette Baker 1989)

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Tournament selection
Pt
I n1
I n2
P1
D.E.
INt
I1
I2
Ii1
Nt
Ii
IN
P2
I n1
I n2
INt
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Example solving with EAs
Search Space
Fitness Function
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Data of the GA

• Population size N6
• Individual Ii(x)
• with x?-2, 2 and i ?1, 2, 3, 4, 5, 6
• Selection operator Tournament (Nt2)
• Crossover rate 50
• Crossover operator Arithmetic (?0.6)
• Mutation rate 12
• Mutation Ii Ii? where ? ?-0.2, 0.2

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P(0)
1.0
0.5
?
-1.5
-2 0 2
-0.48
1.17
-1.0
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Tournament selection
Arithmetic crossover
Mutation
1.0
P1
I1
Not
P(0)
0.8
1.0
0.8
-1.5
Do we cross?
Yes
Do we mutate?
1.17
P2
I2
Yes
-0.084
0.5
0.7
0.5
-0.2 0 0.2
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Tournament selection
Arithmetic crossover
Mutation
0.5
P1
I1
Not
P(0)
-0.088
-0.48
-0.088
-0.48
Do we cross?
Yes
Do we mutate?
-1.0
P2
I2
Not
0.108
0.5
0.108
0.5
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Tournament selection
Arithmetic crossover
Mutation
-1.0
P1
I1P1
Yes
P(0)
-0.04
-1.0
-1.0
-1.5
Do we cross?
Not
Do we mutate?
-0.48
P2
I2P2
Not
-0.48
-0.48
-0.48
-0.48
-0.2 0 0.2
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P(1)
-0.088
-0.084
0.8
-0.48
-0.04
0.108
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International Conference Parallel CFD 2002
The Fundamental Theorem of Genetic Algorithms
Schema is a set of three symbols ,0,1. The
symbol is either a 0 or a 1. Fixed position of
a schema those positions that are a 0 or a 1
(position that is not a ) Order of a schema
O(H) is the total number of fixed positions in
the schema. The length of a schema d(H) is the
distance in number of bits between the first and
last fixed position. Example of schema
(01101010) O(H) 8 d(H) 12 - 1
11. Implicit Parallelism (J. H. Holland) The
number of processed schemas each generation of
genetic algorithm is of O (n 3 ) It shows the
power of genetic algorithms, with n chromosomes a
much greater domain is explored because of the
actuation of genetic operators
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The Fundamental Theorem of Genetic Algorithms
m(H,t) number of times that the schema H is in
the i-th population. (Proportional Selection, one
point crossover, pc crossover probability and pm
mutation probability)
The Theorem shows that schemata with higher
average values of fitness function (f ( H ) / f
med gt 1) , small length (ltlt) and low order
(Oltlt) , called building blocks, grow
exponentially So, independently of the stochastic
character of the operators, it tends to converge
to the optimum, that is constructed by the
generation of the building blocks in the
successive iterations
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International Conference Parallel CFD 2002
NFL Theorem
NFL Theorem (Wolpert Macready, 1995) All
the search algorithms have the same performance
compared to the whole universal set of discrete
functions.
It emphasizes the importance of finding a search
algorithm that can be appropriately adjusted to a
certain problem if a good performance is
desired. Examining the problem from various
strategies can be possible the tuning of the
success of the results.
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Codification Gray Code
The binary code is not homogeneous with respect
to its equivalent decimal number. For example,
the number 7 is followed by the number 8 (in base
ten) But in binary code are 0111 and 1000 ,
diverging the genes in all its positions
Gray Code Representation that allows the
biyective equivalence between phenotype and
genotype for consecutive numbers, with only a bit
or gene of difference
Gray Code operation generator
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International Conference Parallel CFD 2002
EFFORTS MORE IMPORTANTS ON GENETIC ALGORITHMS
AND EVOLUTIONARY ALGORITHMS   - Important
efforts in last 15 years on establishing specific
genetic operators development for specific
problems - Efforts in last years on parameter
self-adaptation of evolutionary algorithms,
specially at Evolutives Strategies  
Progress on performance in multiobjective
evolutionary algorithms
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DESPITE GREAT DIVERSITY OF GENETIC ALGORITHMS
SOME FEW GENERAL CONCLUSSIONS ARE   -  Many
optimization problems only can be solved by
Evolutionary Computation (fiftness with
noise, etc)   -     Hybridization and
paralelization are tools to be always
considered   -    Tournament selection operator
is "often" better than others Two advantages are
the no need to scale values of the objective
function and highly parallelized, easy to get
good balance between exploration and explotation
in the search   Using real encoding produces
"often" faster search algorithms, but exist many
problems where binary encoding is the "natural"
one.

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- Gray encoding "often" is a good choise among
others binary encoding, but not always   - Most
of the Sampling or Recombination operators
developed last years have been established using
real variables (encoding)   - "Some Genetic
Algorithms have certain advantages in certain
circumstances"   Mathematical foundations like
stochastic modeling of evolutionary algorithms as
Markov Chain models are acceptable, and
demonstrate that using elistism is always better
strategie because ensures good convergence
properties towards to the final state of the
evolution
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Any general possible conclussions must be always
formulated as "often" according Wolpert and
Macready ,1995, No Free Lunch theorem So, if
"by chance " the algorithm can align with the
search problem then the algorithm perform well
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NEW CHALLENGES
International Conference Parallel CFD 2002

• Developments on algorithms self-adaptation
  capabilities
• ( intelligent agent software based) increasing
  efficiency and maintaining the robutness of the
  evolutionary algorithms
• (e.g. "flexible evolution " from
  G.Winter,B.Galván and research team of CEANI,
  2001)
•  
• - New generation of evolutionary search
  algorithms using the acknowledge and experience
  gained, but including the potential capabilities
  of all well-known existing Sampling methods, and
  the recent advances in Artificial Intelligence
  (AI)
•  
• Actual ? SelectionSampling Optimization
•  
• Future ? AI Selection Sampling .
  Efficient and Robust Optimization

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Desirable Evolution of the Global Optimization
Methods

• Free of parameter
• Incorporation of self-adaptability mechanisms
• Independence of operators
• Independence of the problem

• Dependence of parameter
• Use of fixed operator
• Dependence of the
• problem

Flexible Evolution
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International Conference Parallel CFD 2002
Multicriteria Genetic Algorithm
The genetic operators in this algorithms are
basically the same as in the monocriteria
optimization case, but the selection operator
(how the selection probabilities are assigned to
each individual). There are two necessities in
a multicriteria optimization algorithm
(Goldberg) 2. To maintain a homogeneous
diversity of the population in this frontier.
1. To conduct the search towards to the Pareto
Frontier with a selection criteria based in the
non-domination ranking of the solutions
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Pareto Frontier

• In the set of all possible solutions, the
  non-dominated solutions are those which
  constitute the Pareto frontier
• A solution is non-dominated if
• The solution x is not worse than y in all the
  criteria
• For two minimized criteria, it means that
• x solution is less or equal than y for both.
• 2) The solution x is strictly better than y at
  least in one criteria. For two minimized
  criteria, it means that x solution is less than y
  at least in one of the desired criteria

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International Conference Parallel CFD 2002
Coupling the Optimization Problem with the
Genetic Algorithm

• The fitness function should be evaluated many
  times, so even a little calculation may be a
  considerable amount of time when evaluated
  thousands of times.
• Those operations that can be executed only once
  and are valid for each chromosome, independently
  of the variability of the information they have,
  should be evaluated only once.

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Multicriteria Evolutionary Algorithms

• Some multiobjective evolutionary algorithms
  developed to satisfy both requirements, are VEGA
  (Vector Evaluated Genetic Algorithm), Schaffer
  (1984) MOGA (Multiobjective Genetic Algorithm),
  Fonseca y Fleming (1993) NPGA (Niched Pareto
  Genetic Algorithm), Horn y col. (1994) NSGA
  (Non-Dominated Sorting Genetic Algorithm),
  Srinivas y Deb (1994)
• This algorithms are applied to many engineering
  and scientific problems, showing the potential of
  evolutionary computation in a lot amount of
  fields. However, certain problems they show
  difficulties to obtain optimum results, leaving
  room for improvement

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International Conference Parallel CFD 2002
Recent Proposals in Multicriteria Optimization

• PESA, Corne, Knowles, Oates, 2000
• PESA-II, Corne, Jerram, Knowles, Oates, 2001
• NSGA-II controlled elitism Deb y Goel, 2001
• SPEA2, Zitzler, Laumanns, Thiele, 2001

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Some open questions in multiobjective
evolutionary algorithms remains unresolved, as
how achieve a "well distributed trade-off front",
with adequated diversity as "the decision-maker
likes", and more effort is needed on " how "
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Parallel Genetic Algorithms

• Due to the nature of Evolutionary Algorithms,
  they handle with a population of individuals, and
  the fitness function evaluation is individual
  independent, so they are easily parallelizable.
• Parallel Genetic Algorithms have been applied to
  many kind of different problems, among them
• Classifier systems (Robertson, 1987)
• Functional optimization (Spiessens Manderick,
  1991)
• Combinatorial optimization (Gordon Whitley,
  1993)
• Depending modeling (Flockart, 1995 Araujo et al,
  2000)

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Parallel Genetic Algorithms

• Parallel Genetic Algorithms can be classified in
  four main types
• Global Master-Slave
• Island or Coarse-grained or Distributed Model
• Cellular or Fine-grained or Diffusion Model
• Hybrid or Hierarchical Models
• There are articles which have handled comparison
  between this models. (e.g. Serial and Parallel
  Genetic Algorithms as Function Optimizers, V.
  Gordon, D. Whitley, The Fifth International
  Conference on Genetic Algorithms, 1993, pp.
  177-183, Morgan Kaufmann)
• Some surveys about parallel genetic algorithms
  have been developed, among them we cite A
  Survey of Parallel Genetic Algorithms, E.
  Cantu-Paz (1997), Calculateurs Paralleles,
  Reseaux et Systems Repartis, vol 10, number 2,
  pp. 141-171

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International Conference Parallel CFD 2002
Global Master-Slave Model

• It is a panmitic parallel genetic algorithm (a
  unique whole population).
• Differs from the canonical one, in that some of
  its processes, mainly the evaluation of the
  fitness function, are distributed among some
  processors to be evaluated parallely.
• It is a hardware accelerator, being its
  performance conditioned by the time invested in
  information communication among processors. When
  the total time consumed by the parallel algorithm
  multiplied by the number of processors is
  equivalent to the time taken by the sequential
  genetic algorithm for a fixed number of fitness
  function evaluations, the performance is lineal.
  If it is inferior, the performance is sub-lineal.
• The migration phase can be synchronous (at the
  same time for all the subpopulations) or
  asynchronous (when satisfying certain
  condition/s).
• The steady-state model of genetic algorithm fits
  better with the asynchronous model

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Global Master-Slave Model
International Conference Parallel CFD 2002

Slave Compute fitness
Slave Compute fitness
Slave Compute fitness
MASTER Distribute individuals
Slave Compute fitness
Slave Compute fitness
Slave Compute fitness
Slave Compute fitness
Slave Compute fitness
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Island or Coarse-grained or Distributed Model (I)
International Conference Parallel CFD 2002

• Each processor handles with a subpopulation by
  itself
• Subpopulations communicate by certain migrant
  individuals that are transferred from one to
  another subpopulation periodically
• New parameters characterize this model The
  number of subpopulations, the communicating
  structure among them, the migration interval, the
  number of migrants, and the selection of which
  individuals migrate
• They should be correctly assigned for the
  appropriate operation of the optimization
  process. For example, if we need a high selection
  pressure, we can increase the migration frequency
  and/or impose to migrate the best individual
  substituting the worst one of the subpopulation

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Island or Coarse-grained or Distributed Model (II)

• The island model is more than a hardware
  accelerator (so was the global master-slave
  model), and has behavioral differences with the
  panmitic canonical genetic algorithm. This
  differences permit to obtain advantages in many
  cases, inherent not only to the parallelization,
  but also to the algorithm
• Superlinear speedups have been reported, due to
  the nature of the algorithm. E.g.
• Parallel Genetic Algorithms, R. Shonkwiler, pp.
  199-205, Fifth International Conference on
  Genetic Algorithms, 1993, Morgan Kaufmann.
• Puede un algoritmo evolutivo paralelo
  proporcionar ganancia superlineal?, E. Alba, pp.
  89-97, CAEPIA-TTIA 99, Murcia, Spain
• This model is adapted better to a computational
  structure of clusters or multicomputers of
  distributed memory.

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Island or Coarse-grained or Distributed Model
References
International Conference Parallel CFD 2002

• Distributed Genetic Algorithms, R. Tanese,
  pp. 434-440, Third International Conference on
  Genetic Algorithms, 1989, Morgan Kaufmann.
• Punctuated Equilibria A Parallel Genetic
  Algorithm, J.P. Cohoon, S.U. Hedge, W.N. Martin,
  D. Richards, pp. 148-154, Second International
  Conference on Genetic Algorithms, 1987, Laurence
  Erlbaum Associates Eds.
• Parallel Genetic Algorithm for a Hypercube, R.
  Tanese, pp. 177-183, Second International
  Conference on Genetic Algorithms, 1987, Laurence
  Erlbaum Associates Eds.
• The Island Model Genetic Algorithm On
  Separability, Population Size and Convergence,
  D. Whitley, S. Rana, R. Heckendorn, Journal of
  Computing and Information Technology, Volume 7,
  Number 1, 1999

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Island or Coarse-grained or Distributed Model
International Conference Parallel CFD 2002

Subpopulation
Subpopulation
Subpopulation
Subpopulation
Subpopulation
Migration process
Subpopulation
Subpopulation
Subpopulation
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International Conference Parallel CFD 2002
Cellular or Fine-grained or Diffusion Model (I)

• This parallel genetic algorithm model is based in
  the concept of geographic evolution.
• The individuals belonging to the population are
  distributed topologically in a grid (uni-, bi- or
  three-dimensional one), and are restricted to
  reproduce in a small environment of its location.
  
• Normally, each processor controls one or a small
  amount of individuals.

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Cellular or Fine-grained or Diffusion Model (II)

• This model is more than a hardware accelerator
  (so was the global master-slave model), and has
  behavioral differences with the panmitic
  canonical genetic algorithm. This differences
  permit to obtain advantages in many cases,
  inherent not only to the parallelization, but
  also to the algorithm.
• The cellular model is better adapted to a massive
  parallel computational structure SIMD (single
  instruction - multiple data), like the Maspar or
  Connection Machine 200.

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Cellular or Fine-grained or Diffusion Model
References

• Cellular Genetic Algorithms, D. Whitley, pp.
  658, Fifth International Conference on Genetic
  Algorithms, 1993, Morgan Kaufmann.
• Selection in Massively Parallel Genetic
  Algorithms, R. Collins, D. Jefferson, pp.
  249-256, Fourth International Conference on
  Genetic Algorithms, 1991, Morgan Kaufmann.
• Fine-Grained Parallel Genetic Algorithms, B.
  Manderick, P. Spiessens, pp. 428-433, Third
  International Conference on Genetic Algorithms,
  1989, Morgan Kaufmann.

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Cellular or Fine-grained or Diffusion Model
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Example 4 x 22 Population Grid
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Hybrid Models
International Conference Parallel CFD 2002

• This model groups parallel genetic algorithms
  that are combination of the previous models.
• For example, it could be
• An island model, where each of the subpopulations
  is a cellular model.
• An island model, where each of the subpopulations
  is treated as a master-slave model.
• An island model, where each of the subpopulations
  is treated as another island model. (e.g.
  Hierarchical Distributed Genetic Algorithms, F.
  Herrera, M. Lozano, C. Moraga, International
  Journal of Intelligent Systems 14 (1999)
  1099-1121.)
• Etc.

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Hybrid Models Example (Island Master-Slave)
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Subpopulation
Subpopulation
Subpopulation
Subpopulation
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Hybrid Models Example (Island Cellular)
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Subpopulation
Subpopulation
Subpopulation
Subpopulation
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Hybrid ModelsExample (Island Island)
International Conference Parallel CFD 2002
Subpopulation
Subpopulation
Subpopulation
Subpopulation
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Number of Publications of Parallel GAs

• In the GECCO (Genetic and Evolutionary
  Computation Conference) and its
  Late-Breaking-Papers of years 2001 and 2000, over
  a total of 253 genetic algorithm articles, 14
  where about parallel GAs. (5.5)
• In the EUROGEN Conferences, of years 1999, 1997
  and 1995, over a total of 64 genetic algorithm
  articles, 10 where about parallel GAs. (15.6)
• In the ICGA (International Conferences of Genetic
  Algorithms) of years 1985, 1987, 1989 and 1991,
  over a total of 198 genetic algorithm articles,
  17 where about parallel GAs. (8.6)

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Efficient and Accurate Parallel Genetic Algorithms

• A recent and valorous reference in the field of
  parallel genetic algorithms is the book
  Designing Efficient and Accurate Genetic
  Algorithms, by Erick Cantu-Paz, edited by Kluwer
  Academic Publishers, 2000.
• From it can be derived important information,
  among them we can cite
• Migration between subpopulations favors the
  quality and efficiency of the solution.
• Whole connectivity of subpopulations is a good
  strategy in case of lack of processors

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Efficient and Accurate Parallel Genetic Algorithms

• analysis certain models that help to determine
  appropriately parameters such as
• the number of subpopulations, their size and
• their connectivity, oriented specially to the
  design of hybrid
• models
• analysis the effect of the topology in obtained
  results.

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Computational Fluid Dynamics Applications

• Combinatorial possibilities of CFD and GAs
• Sequential CFD and Sequential GA
• Sequential CFD and Parallel GA
• Parallel CFD and Sequential GA
• Parallel CFD and Parallel GA
• Studies suggest than the maximum performance can
  be obtained with parallel CFD and parallel GA.
  (e.g. Quagliarella, EUROGEN 1995).

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International Conference Parallel CFD 2002

• Some references
• Genetic Algorithms Applications in Computational
  Fluid Dynamics, D. Quagliarella, pp. 417-442,
  Genetic Algorithms in Engineering and Computer
  Science. John Wiley Sons (EUROGEN 1995).
• Parallel Genetic Algorithms for Optimisation in
  CFD, D. Doorly, pp. 251-270, Genetic Algorithms
  in Engineering and Computer Science. John Wiley
  Sons (EUROGEN 1995)
• As examples of applications in Fluid Dynamics
• Unstructured meshes partitioning optimization.
• Optimum airfoil design (direct and inverse
  approximations)

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CFD DOMINANT APPLICATIONS IN AERONAUTICS AND
ENERGY THE EUROPEAN INGENET DATABASE
EXPERIENCE ( J.Periaux and G. Winter 45
mns)
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INGENET INdustrial Design and
Applications using GEnetic Algorithms and
Evolution Strategies NETwork A Thematic
Network of the European Commission
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INGENET NETWORK TO BRING TOGETHER ACADEMIC AND
INDUSTRIES PARTNERS IN ORDER TO EVALUATE AND
COMPARE PERFORMANCES OF ADVANCED EVOLUTIONARY
ALGORITHMS ON SELECTED TEST PROBLEMS OF
INDUSTRIAL INTEREST
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EVOLUTIONARY ALGORITHMS (EAs) INFORMATION
RELEVANT TO INDUSTRIAL APPLICATIONS
DEVELOPMENT AND VALIDATION OF METHODOLOGIES
INVOLVING EAs COMPUTING SELECTED EVOLUTIONARY
MODEL AND INDUSTRIAL ORIENTED TEST CASES
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• OFFERING A BENCHMARK PLATFORM FOR
  APPLICATIONS OF INDUSTRIAL INTEREST working at
  tandem academic and industrial partners
• DEFINITION OF TEST CASES, DATA EVALUATION
• SELECT, DEVELOPE EVOLUTIONARY MODELS
• COMPUTING, VALIDATION,
• PERFORMANCES , SYNTHETIZE
• INSTALLING AN ON-GOING INGENET DATABASE

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International Conference Parallel CFD 2002
  INGENET CASE STUDIES Open Day June 8,
2001   HOW TO IMPROVE ADVANCED DESIGN WITH
EVOLUTIONARY COMPUTING ? von Karman
Institute for Fluid Dynamics Rhode-Saint-Genese,
Belgium 72, Chaussée de Waterloo
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Transonic single-wing optimization case with
inviscid flow
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Transonic single-wing optimization case with
inviscid flow

• SAAB The airfoil shape was modified at 48 wing
  span sections using a linear
  combination of 12 Aerofunctions at
  each section
• CIRA 1 The airfoil shape was modified at 4
  wing span sections using a linear
  combination of 12 Aerofunctions at each
  section. Intermediate sections
  were obtained by linear interpolation.
• CIRA 2 Same shape modification as in CIRA 1 a
  linear twist variation from the
  root to the tip section.

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Transonic single-wing optimization case with
inviscid flow
SAAB

• Flow solver 3D Euler solver
• Optimization Algorithm - Function and gradient
  computation - Gradients computed by means of
  Euler and Adjoint Euler solutions - Constrained
  steepest descend method

CIRA

• Flow solver Non conservative transonic full
  potential solver
• Optimization Algorithm - Genetic algorithm
  (function computations) - Selection 2 step
  random walk - Crossover extended intermediate
  recombination with prob.1 - Mutation carried
  out at word level with prob. 0.05 - Population
  size 32

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Transonic single-wing optimization case with
inviscid flow
CD convergence history
SAAB
CIRA
30 flow solutions
800 flow solutions
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Transonic single-wing optimization case with
inviscid flow
Results with pitching moment constraint CM
-0.132
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Transonic single-wing optimization case with
inviscid flow
CD, CM convergence history
SAAB
CIRA
80 flow solutions
1200 flow solutions
Pareto frontier
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Multi-point 2D airfoil design
Minimisation of an objective function being the
difference between computed/optimised pressure
distribution at two different design points and
pre-defined target pressures for an airfoil The
objective function reads
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Multi-point 2D airfoil design

• Test case bases on a suggestion by T. Labruyere
  (NLR) for the European ECARP project some years
  ago. This test case is currently used for
  validation purposes in three other EC projects.
• The two different design conditions (i1,2) are
  (see table below)
• i1 Typical high-lift airfoil at subsonic
  conditions
• i2 Typical high-speed airfoil at transonic
  conditions

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Multi-point 2D airfoil design
NTUA Multi-point optimization with
GAs Navier-Stokes analysis tool (turb. mod.
with wall functions) Training of fitness with
neural network
ICD Using ES (1,?) with de-randomized mutation
step size Randomly chosen airfoils as starting
conditions No. of analysis steps less than
1000 Results are directly comparable with
EADS-Ms results
EADS-M Parametrization on both pressure
re-design and multi-point Optimization with 8
Bezier points, two of them are not fixed in
x-direction. Test cases have been run with
different numbers of individuals per
generations. Navier-Stokes on (relatively)
coarse meshes Multi-objective GA (FRONTIER
technology) in use
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Multi-point 2D airfoil design
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EADS-M Results Pareto GA 32 x 32
5
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Multi-point 2D airfoil design
NTUA Low-drag profile
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Multi-point 2D airfoil design
NTUA Results
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CIRAThe flow field around the single element
airfoil in cruise conditions is evaluated through
a full potential approximation of the Navier
-Stokes equations, solved using a finite
difference scheme.High lift flow is
evaluated,instead, using an Euler/boundary layer
interaction method. Use of GAs (Genetic
Algorithms)Multi-objective approach Viscous
approach by Euler/boundary layer
coupling B-Spline approach Maximization of cl
at Ma0.2 for two-component airfoil Maximization
of cl at Ma0.2 for three-component
airfoil Maximization of cl at Ma0.2 for
two-component airfoil plus pitch
control Maximization of cl at Ma0.2 and cd,wake
reduction at Ma0.85
Multi-element airfoil optimization in high-lift
conditions
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Multi-element airfoil optimization in high-lift
conditions
CIRA
The initial configuration used for the high-lift
and transonic runs was defined assembling some of
the components reported in the figure. The
N1BT configuration was chosen as base airfoil
for the transonic single-element design point of
the optimization runs reported here.
Configurations N1BC1F and S1N2BC1F were
instead used for high-lift design points.
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Multi-element airfoil optimization in high-lift
conditions
CIRA
cl maximization at M0.2 with atwo-component
airfoil and control on pitching moment
32 individuals evolved for 40 generations 8 bits
used for variable encoding mutation set at bit
level with a probability of 2 extended
intermediate crossover with 100 activation
probability
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Multi-element airfoil optimization in high-lift
conditions
CIRA
cl maximization at M0.2 with atwo-component
airfoil and control on pitching moment
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Optimization of a 3-element high-lift (2D)
configuration
CIRA
cl maximization at M0.2 with a three-component
airfoil
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Optimization of a 3-element high-lift (2D)
configuration
INRIA Optimize the relative position of slat,
flap and airfoil Standard binary coded GA Euler
approach (finite volume, van Leer MUSCL
approach) Re-meshing with linear-spring
method Lift improvement from 4.9 to 5.13 (after
40 generations) Future Additional optimization
of shape
Trieste Star-CD as analysis tool, running on PC
cluster Navier-Stokes with k-? turbulence
model Unstructured grid 120433 grid points,
14530 cells FRONTIER optimizer, parallel
classical GA, 30 ind. x 40 gen. Crossover prob.
0.9, Mutation prob. 0.1 Lift improvements from
2.89 to 3.79 30
NTUA New sensitivity analysis coupled with Gas
and artificial neural networks (RBF networks,
so-called autocatalytic factors) in order reduce
no. of analysis steps Euler method -
unstructured mesh - same as INRIA
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Optimization of a 3-element high-lift (2D)
configuration
Dassault RA16 geometry Problem to solve related
to overlap, angle and gap (no shape changes so
far), i.e. three design variables per slat and
flap (6 in total) GAs with Nash Equilibrium (2
"players" - for slat and flap) Panel method
coupled with boundary layer approach Lift 5.29
(Nash) versus 4.84 (GA) Future Improvement on
solver (Navier-Stokes?) Domain
decomposition Parallel technique
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Optimization of a 3-element high-lift (2D)
configuration
Dassault/LIP6Convergence 600 evaluations Lift
improvement 8
Initial Configuration
Optimal Configuration
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Optimization of a 3-element high-lift (2D)
configuration
INRIA Slat and flap configuration of initial and
optimised shapes
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Drag reduction on a 2D RAE2822 airfoil Direct
optimization
Reduce shock-induced drag for the RAE2822 airfoil
at Ma0.73 and ?2o by running an Euler
approach. Constraint Lift should be equal to
the original lift
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Drag reduction on a 2D RAE2822 airfoil Direct
optimization
EADS-M results Mach number contoursSingle-objec
tive run 56 reduction in drag(generally no
shock means no drag ... !?)
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Drag reduction on a 2D RAE2822 airfoil Direct
optimization
956
656
EADS-M results Multi-objective
optimization GA 32x32 CL,956 0.8360 CD,956
0.00400 (53) CL,656 0.8345 CD,656
0.00392 (55) CL,initial 0.8364 CD,initial
0.00862
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Drag reduction on a 2D RAE2822 airfoil Direct
optimization
INRIA
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Drag reduction on a 2D RAE2822 airfoil Direct
optimization
INRIA
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Reconstruction of a nozzle with multiple models
Optimization of the shape of a convergent-divergen
t nozzle for transonic flow (involving shocks).

• LIP6/Dassault
• Hierarchical GAs with Multiple Models and
  Multiple Solvers
• Application of multiple model approach results in
  2/7th of CPU time
• Method is based on the same algorithmic
  principle, i.e. using parallel genetic algorithms
  with a hierarchical topology for the exchanges
  when migration takes place.
• Trying to keep accuracy of fine mesh for running
  analysis on coarser mesh(es) in order to reduce
  computation time.
• Synchronous and asynchronous evaluation of
  individuals
• Space marching for CFD, viscous and inviscid
  approach

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Reconstruction of a nozzle with multiple models
LIP6/Dassault
Goal rebuild a symmetric convergent/divergent
nozzle with 1-D transonic shocked flows Use a
Hierarchical Parallel GA with multiple models
(from most expensive to cheapest) Try to rebuild
the shape of the nozzle by matching the mach
number distribution generated for the target
nozzle with different grid sizes.
Hierarchical models
Target Nozzle
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Reconstruction of a nozzle with multiple models
LIP6/Dassault
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Reconstruction of a nozzle with multiple models
LIP6/Dassault
Multiple models, mixed Viscous/Inviscid
Solvers Inviscid, viscous, and mixed
inviscid/viscous
HGAs with multiple models the best answer to
the lack of speed dilemma in engineering
environment (3 times faster than other
approaches) Using models of different complexity
significantly is speeding up optimization GAs can
handle approximate models within a hierarchical
topology
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Decentralized Nash strategies to coordinate
subdomains using partial volume information
Linear potential flow in a duct is divided into
two sub-domains of a divergent-convergent nozzle
by least-square minimization in portions of the
overlap.
INRIA Convergent-divergent nozzle Full
potenial method as basic analysis tool Domain
decompositions (2 domains with two sub-solutions
in particular) Nash algorithm based on partial
volume integrals GA optimizer used (optimizing
the generation) Future Use more complex models
(high fidelity models)
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Decentralized Nash strategies to coordinate
subdomains using partial volume information
INRIA
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
Dassault/LIP6 Trade-off solution obtained by a
Nash/GA game based on the red/blue split of the
control points in a Bezier representation One
player for CFD and one player for CEM CFD
method transonic full potential CEM method
Time harmonic Maxwell solver Optimal solution
is a non-trivial solution Experiments
involving a PC cluster
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design

• Goal minimize the RCS of an airfoil by
  optimizing the repartition of active antennas
  over the surface of the airfoil
• GA with a repair mechanism and binary
  representationFor a NACA0012 illuminated with a
  0o incident wave repartition of 7 actives
  antennas among 17 sites

Associated polar RCS
Optimal distribution
Dassault/LIP6
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
Goal minimize the RCS for 2 different angular
sectors Pareto GA with a niching mechanism For a
Bi-NACA0012 illuminated by a 45o and 45
incident waves Optimal repartition to minimize
RCS over -55,-35 and 35,55 angular
sectors
Dassault/LIP6
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
Goal minimize the RCS for a multi-element
airfoil For a 3-element airfoil illuminated by a
45o and 45 incident waves Optimal repartition
to minimize RCS over -55,-35 and 35,55
angular sectors
Associated polar RCS
Optimal distribution
Dassault/LIP6
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
INRIA/Dassault
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
INRIA/ Dassault
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
INRIA/ Dassault
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Multi-objective / Multi-disciplinary (CFD/CEM)
Airfoil Design
INRIA/ Dassault
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MULTIOBJECTIVE POWER DISPATCH OPTIMIZATION
SEPTEMBER 2.001
EUROGEN 2001 - ATHENAS
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MULTIOBJECTIVE POWER DISPATCH OPTIM. THE REAL
PROBLEM
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MULTIOBJECTIVE POWER DISPATCH OPTIM. PROBLEM
PROPOSED
FUEL COST AND ENVIROMENTAL IMPACT
MINIMIZATION FOR A SET OF GENERATION UNITS IN A
TIME PERIOD
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MULTIOBJECTIVE POWER DISPATCH OPTIM.
CONFLICTING OBJECTIVES
NOx Emissions
FUEL COST
POLLUTANT EMISSIONS
SO2 Emissions
Particles Emissions
uit 0 or 1 if the unit i for the hour t is off
(0) or on (1)
GCit(Pit) Generation cost of unit i for hour t,
which depends on the load of generation unit i
for hour t (Pit). Si(xit) Start-up cost of unit
i, which depends on the time the unit has been
stopped until that hour (xit). Di Shut-down
cost of unit i, which is a constant
value. Pollutit(Pit) Atmospheric Emission of
unit i for hour t, which depends on the load of
generation unit i for hour t (Pit).
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MULTIOBJECTIVE POWER DISPATCH OPTIM.
CONSTRAINTS CONSIDERED

• Nmax
• 1.- ? Pit Lt
• i1
• Nmax
• 2.- ? Rit ? Rt
• i1
• Nmax
• 3.- ? Pimaxt ? Lt Rt
• i1
• 4.- Pit ? Pimax
• 5.- Pit ? Pimin
• 6.- Loading ramp
• 7.- Minimum up time

NVj Number of nonfulfilments of the constraint
j. SVj Contributions sum of the nonfulfilments
of the constraint j. Aj, Bj Homogeneization
factors for monetary units . rmax. Number of
estimate constraints.

• Lt Load demand of the system for hour t.
• Rt Spinning reserve of the system for hour t.
• Rit Spining reserve of unit i for hour t.
  (Rit Pimax - Pit ).
• Pimax. Available maximum power of unit i.
• Pimin. Available minimum power of unit i.
• Limi Atmospheric Emission Limit of unit i for a
  particulard pollutant

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MULTIOBJECTIVE POWER DISPATCH OPTIM. SOLUTION
METHODOLOGIES

• TRADITIONAL APPROACHES
• Priority list methods (1943-1957)(1990 -)
• Equal incremental cost criterion Steimberg
  Smith (1943), Kirckmayer (1958).
• Kuhn.Tucher approach (1951)
• Dynamic Programming (DP) (1957)
• Nonlinear ProgrammingGauss Seidel Squires
  (1960), Carpentier (1962)
• Lagrange Multipliers Newton-Raphson (1960
  1970)
• Partial enumeration methods (DP based) (1980
  1990)
• Lagrangian Relaxation (1989)
• ARTIFICIAL INTELLIGENCE APPROACHES
• Monte Carlo Optimization (Simulated Annealing)
• Expert Systems
• Neuronal Networks
• Evolutionary Algorithms (EAs)

• Evolutionary Programming (1966)
• Evolution Strategies (1973)
• Genetic Algorithms (1975, 1989)
• Flexible Evolution (2001)

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MULTIOBJECTIVE POWER DISPATCH OPTIM. SELECTED
APPROACH
EVOLUTIONARY ALGORITHMS
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MULTIOBJECTIVE POWER DISPATCH OPTIM. FLEXIBLE
EVOLUTION
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MULTIOBJECTIVE POWER DISPATCH OPTIM.
EVOLUTIONARY METHOD
MODIFIED STRENGHT PARETO EVOLUTIONARY ALGORITHM
(MSPEA)
Population t
Pareto set
Elitism (?)
P0.6
P0.4
Updating Pareto set
Population t1
Non dominated solutions
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MULTIOBJECTIVE POWER DISPATCH OPTIM. MSPEA
FLEXIBLE EVOLUTION
FLEXIBLE STRENGHT PARETO EVOLUTIONARY ALGORITHM
(FSPEA)
Operators used
Multiple Selection Operators
Multiple Sampling Operators
Real Coding
Crossover Operators
Mutation Operators
Others
FSPEA
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MULTIOBJECTIVE POWER DISPATCH OPTIM. INITIAL
DATA OF OUR PROBLEM (I)
Start-up cost (m.u.) a ? (1 - e-c ? t) b
Generation cost (m.u./h) A ? P2 B ? P C
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MULTIOBJECTIVE POWER DISPATCH OPTIM. INITIAL
DATA OF OUR PROBLEM (II)
Atmospheric emission of pollutant i (kg/h) AA ?
Pi2 BB ? Pi CCi
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MULTIOBJECTIVE POWER DISPATCH OPTIM. EXAMPLE OF
RESULTS

• Population size 800 individuals
• Number of generations 200
• Selection Tournament
• Crossover Arithmetic (Pc 0.9)
• Mutation One point (Pm 0.9)

Both Pareto Fronts obtained with the same number
of objective function evaluations

• Population size 800 individuals
• Number of generations 200

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MULTIOBJECTIVE POWER DISPATCH OPTIM. CONCLUSIONS

• With the same test conditions, the Flexible
  Evolution has been more efficient than the
  Genetic Algorithms for this problem (It has been
  able to get a better Pareto Front).
• It has been necessary to carry out some
  correction procedures for the strongest
  constraints, being applied at the beginning of
  the algorithm to help it to converge (defining
  clear rules to repair unfeasible solutions using
  constraints).
• The modifications performed to the Strenght
  Pareto Evolutionary Algorithm have been very
  important to obtain better results. These
  modifications have been using of elitism, a
  fixed probabilistic rule of selection and the
  distance criterion to reduce the number of
  non-dominated stored solutions.
• Its important to emphasize that Flexible
  Evolution learns while the algorithm is running
  and is able to decide itself what type of
  selection and sampling method is the best at
  every moment among all the available ones. So, we
  only have to decide two parameters Population
  size and Number of Generations.

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EUROGEN2001 PARTNER CEANI
International Conference Parallel CFD 2002
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The Control Problem

• Control variables physical localization of each
  diffuser on a three-dimensional aquatic domain.
• State pollutant concentration on each point of
  the discretized domain.
• State equation 3D unsteady convection-diffusion-r
  eaction equation.

It is an optimal control problem with inequality
restrictions over the state and minimization of a
cost function.
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Methodology
Physical placement of sewage farms and diffuser,
and caudal of each diffuser
Pollutant concentration calculation
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Selection Sampling
Evolution Algorithms
Optimal decision set
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International Conference Parallel CFD 2002
Summary of round table discussion(INGENET
OpenDay ,VKI, June 2001 ) Present competitive
environment, crucial industrial needs are to
reduce -         the design cost -         the
time to market.   Optimisation tools are useful
in this purpose, but it is essential that they be
-         accurate -         reliable -        
fast  
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Summary of round table discussion(INGENET
OpenDay ,VKI, June 2001 )
Whereas stochastic methods are generally praised
for their robustness, efficiency (speed) is still
a concern   Effort should be made to reduce the
number of function evaluations and/or the cost of
function evaluations ( e.g. by combining with
inexpensive cost function approximations) The
general opinion is that there is no direct
relation between an application field and a
suitable optimisation strategy  
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Summary of round table discussion(INGENET
OpenDay ,VKI, June 2001 )
Optimization tools should offer a wide variety of
strategies to the users so that they
can experience with them until they find the
most suitable tool for their (class of)
problem(s) A direct consequence of this
observation is that optimization tools require
competent users, in particular for the problem
definition, which is felt to be the critical step
of the optimization procedure   Whereas round
table participants think that there is definitely
still room for completely new ideas in the field,
they feel that the technology is now mature for
the development of user targeted tools, a
movement which is alreday well under way "
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International Conference Parallel CFD 2002
INGENET partners presented and delivered results,
many of them have been even improved during the
course of INGENET   Interested third parties can
now well use these data which are all based on
concise case descriptions for own validation
purposes.          Such a validation exercise
can utilise all data which are based on a variety
of optimisers used by INGENET partners
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Almost all work carried out was performed as
tandem work i.e. two partners were constantly
working together, enhancing by this their
knowledge and achieving synergetic effects   In
most cases industries were closely coupled to
academic organisations or, in other words,
applyers with developers
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INGENET Partners reported on their experience
and expertise gained on the
INGENET-inherent EUROGEN conferences with the
major impact that knowledge dissemination on
multi-disciplinary applications led to
an improved understanding, better knowledge
and an enormous cross-fertilisation
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The latter was even improved by links to other
projects (e.g. FLOWnet, AEROSHAPE) which in
turn used some of the INGENET cases for enhanced
optimisation underlining the importance of
INGENET and pointing out how well INGENET was
recognised in the scientific community
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