Title: Particle Swarm Optimisation PSO and Genetic Algorithms GA: An Introduction
1Particle Swarm Optimisation (PSO) and Genetic
Algorithms (GA) An Introduction
- Presented by Saman Halgamuge
- (Material support from Asanga Ratnaweera and
Suhinthan Maheshwararajah)
2Particle Swarm Optimisation.
3Particle Swarm Optimization
- Particle Swarm Optimization (PSO) mimics the
collective intelligent behavior of
unintelligent creatures. - It was developed in 1995 by James Kennedy and
Russell Eberhart Kennedy, J. and Eberhart, R.
(1995). Particle Swarm Optimization,
Proceedings of the 1995 IEEE International
Conference on Neural Networks, pp. 1942-1948,
IEEE Press. (http//dsp.jpl.nasa.gov/members/paym
an/swarm/kennedy95-ijcnn.pdf ) - It has been applied successfully to a wide
variety of search and optimization problems. - In PSO, a swarm of n individuals communicate
either directly or indirectly with one another in
each search directions (gradients).
4Particle Swarm OptimizationThe Anatomy of a
Particle
- A particle (individual) is composed of
- Three vectors
- The x-vector records the current position
(location) of the particle in the search space, - The p-vector records the location of the best
solution found so far by the particle, and - The v-vector contains a gradient (direction) for
which particle will travel in if undisturbed. - fitness value (cost/objective function)
- fitness of the x-vector
Ik X ltxk0,xk1,,xkn-1gt P
ltpk0,pk1,,pkn-1gt V ltvk0,vk1,,vkn-1gt fitness
?
5Searching Process in Swarm Intelligence (PSO)
6Mathematical representation of PSO
xp(t) Position of particle p _at_ iteration t
vp(t) Velocity of particle p _at_ iteration t
pg(t)
pp(t) Local Best Position _at_ iteration t
pg(t) Global Best Position _at_ iteration t
pp(t)
C1 C2 cognitive and Social Component
w inertia weight
vp(t)
Xp(t)
7PSO-How does it work?
Step 1 Initialization randomly choose the
sensor sequence
Step 3 Find the global best particle
Step 4 Perform the search process
Step 2 Fitness evaluation J(µp(T))
Optimal solution is given by the global best
particle at the end of the search process
8How does it work?..
- In PSO, particles never die!
- Particles can be seen as simple agents that fly
through the search space and record (and possibly
communicate) the best solution they have
discovered. - Initially the values of the velocity vectors are
randomly generated with the range -Vmax, Vmax
where Vmax is the maximum value that can be
assigned to any vid. - Once the particle computes the new Xi and
evaluates its new location. If x-fitness is
better than the best x-fitness achieved by the
particle (personal best), personal best will be
updated..
9Particle Swarm OptimizationThe algorithm
1. Initialise particles in the search space at
random. 2. Assign random initial velocities for
each particle. 3. Evaluate the fitness of each
particle according a user defined objective
function. 4. Calculate the new velocities for
each particle. 5. Move the particles. 6. Repeat
steps 3 to 5 until a predefined stopping
criterion is satisfied.
10Particle SwarmControlling Velocities
- When using PSO, it is possible that velocities
can become very large. - Performance can suffer if Vmax is inappropriately
set. - Several methods were developed for controlling
the growth of velocities - A dynamically adjusted inertia factor,
- A dynamically adjusted acceleration coefficients.
- Re-initialisation of stagnated particles..
11Particle Swarm OptimizationRelated Issues
- There are a number of related issues concerning
PSO - Controlling velocities (determining the best
value for Vmax), - Swarm Size,
- Inertia weight factor,
- Robust Settings for (C1 and C2),
12Genetic Algorithms
Genetic algorithms are inspired by Darwin's
theory of evolution.
Genetic Algorithms (GAs) were invented by John
Holland and developed by him and his students and
colleagues. This lead to Holland's book
"Adaptation in Natural and Artificial Systems"
published in 1975.
13Genetic Algorithms Biological background
- All living organisms consist of cells. In each
cell there is the same set of chromosomes. - A chromosome consists of genes, blocks of DNA.
Each gene encodes a particular protein. - Complete set of genetic material (all
chromosomes) is called genome. - Particular set of genes in genome is called
genotype. - The genotype provides (with later development
after birth) basis for the organism's phenotype
(its physical and mental characteristics, such as
eye colour, intelligence etc.)
14Genetic Algorithms
Gene representation
Chromosome 1 0101100100110110 Chromosome 2
1101111000011110
15Crossover operation
Chromosome1 01011 00100110110 Chromosome 2
11011 11000011110 Offspring 1 01011
11000011110 Offspring 2 11011
00100110110
16Outline of the Basic Genetic Algorithm 1.
Generate random population of n chromosomes.
(suitable solutions for the problem) 2.
Evaluate the fitness of each chromosome x in the
population. 3. Create a new population by
repeating following steps (1 to 3) until the new
population is complete. 1. Select two parent
chromosomes from a population according to their
fitness (the better fitness, the bigger chance to
be selected) 2. With a crossover probability
cross over the parents to form new offspring
(children). If no crossover was performed,
children are the exact copies of parents. 3.
With a mutation probability mutate new offspring
at each position in chromosome.
17Outline contd. 4. Place new offspring in the
new population. 5. Use new generated population
for a further run of the algorithm. 6. If the
end condition is satisfied, stop, and return the
best solution in current population. 7. Go to
step 2.
18Parameters of GA
- Crossover probability.
- - how often crossover will be performed. If there
is no crossover - (should be high generally, about 80-95)
- Mutation probability.
- - how often parts of chromosome will be
mutated - (mutation rate should be very low as 0.5-1)
- Population size.
- - how many chromosomes are in population (in
one generation)
19Engine performance optimisation with PSO and GA
Power Output f (CR, ER, ST,IVO, IVD, IVL, EVO,
EVD )
ST - spark timing, ER- equivalence ratio, CR -
compression ratio, IVO - inlet valve open, IVD-
inlet valve duration, EVO - Exhaust valve open,
EVD - Exhaust valve duration , IVL - Inlet valve
lift
Quasi-dimensional engine model is used for engine
power evaluation for a given set of input
parameters Reference A. Ratnaweera, S. K.
Halgamuge and H. C. Watson, Self-Organizing
Hierarchical Particle Swarm Optimizer with time
varying acceleration coefficients, IEEE
Transactions on Evolutionary Computation June
2004, IEEE Press
20Objective function for fitness evaluation
If knock Intensity lt 1
Fitness Power output
else
Fitness Power output x 0.2/ Knock Intensity
Knocking is highly undesirable abnormal
combustion behaviour due to rapid auto ignition
of gas mixture
Note According to engine knock model used in
this study, the engine is considered knocking if
the knock Intensity gt1
21Operating range
measured before top dead centre
22(No Transcript)
23Engine power optimisation
24Reference engines normal operating condition
Optimum operating parameters with PSO
ST - spark timing, ER- equivalence ratio, CR -
compression ratio, IVO - inlet valve open, IVD-
inlet valve duration, EVO - Exhaust valve open,
EVD - Exhaust valve duration, BTDC - before top
dead centre, BBDC - before bottom dead centre,
- all the angles are measured in crank angle
degrees