a new metaheuristic for optimization: optics inspired optimization (oio)

A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO)

By: Dr. A. H. Kashan

• Since the 1970s that the idea of a general algorithmic framework, which can be applied with relatively few modifications to different optimization problems, emerged.

• Metaheuristics: methods that combine rules and randomness while imitating natural phenomena.

• These methods are from now on regularly employed in all the sectors of business, industry, engineering.

• Besides all of the interest necessary to application of metaheuristics, occasionally a new metaheuristic algorithm is introduced that uses a novel metaphor as guide for solving optimization problems.

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Introduction

A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

Some examples

• particle swarm optimization algorithm (PSO): models the flocking behavior of birds;• harmony search (HS): models the musical process of searching for a perfect state of

harmony;• bacterial foraging optimization algorithm (BFOA): models foraging as an

optimization process where an animal seeks to maximize energy per unit time spent for foraging;

• artificial bee colony (ABC): models the intelligent behavior of honey bee swarms;• central force optimization (CFO): models the motion of masses moving under the

influence of gravity;• imperialist competitive algorithm (ICA): models the imperialistic competition

between countries;• fire fly algorithm (FA): performs based on the idealization of the flashing

characteristics of fireflies.• League Championship Algorithm (LCA): tries to mimic a championship environment

wherein artificial teams play in an artificial league for several weeks

3 A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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Metaheuristics

Evolutionary algorithms

Trajectory methods

Social, political, music, sport,

Physics , etc

Are inspired by nature’s capability to evolve living

beings well adapted to their environment

Evolution strategies Genetic programmingGenetic algorithm

Swarm intelligence

Tabu searchVariable neighborhood

search

Ant colony optimizationParticle swarm optimizationArtificial bee colony Bacterial foraging

optimization Group search optimizer

Society and civilizationImperialist competitive

algorithmHarmony searchLeague championship

AlgorithmOptics Inspired

Optimization

work on one or severalneighborhood structure(s) imposed on the members

of the search space.

Any attempt to design algorithms or distributed problem-solving

devices inspired by the collective behavior of social insect colonies

and other animal societies


The Optics Inspired Optimization (OIO)

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OIO as an EA

OIO, is a population based algorithmic framework for global optimization over a continuous search space.

A common feature among all population based algorithms is that they attempt to move a population of possible solutions to promising areas of the search space, in terms of the problem’s objective, during seeking the optimum.

mutation

recombination

Fitness evaluation

selection


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Physics as a source of inspiration

There are several nature inspired algorithms which adopt their source of inspiration from Physics, e.g.,Light ray optimizationSpiral Dynamics inspired optimization Central force optimization Electro magnetism like metaheuristic

OIO performs based on the rationale of optical characteristics of concave and convex mirrors


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Background

Optics is a branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

A curved or spherical mirror is a mirror with a curved reflective surface, which may be either convex (bulging outward) or concave (bulging inward).

The behaviour of light reflected by a curved mirror is subject to the laws of reflection: the incident ray, the reflected ray, and the normal all lie on the

same plane. the angle between the incident ray and the normal is equal to the

angle between the reflected ray and the normal.


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Concave mirror

Has a reflecting surface that bulges inward (away from the incident light).

Reflect light inward to focal point. They are used to focus light.

Concave mirrors show different image types depending on the distance between the object and the mirror.

These mirrors are called "converging" because they tend to collect light that falls on them, refocusing parallel incoming rays toward a focus.

Concave mirrors are used in some telescopes.


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Concave mirror


f

r

Normal

Incidentray

Reflected ray

Principal axis

Principal plane

θ

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Convex mirrors

A convex mirror is a curved mirror in which the reflective surface bulges toward the light source.

Convex mirrors reflect light outwards They always form a virtual image, since the focus (f) and

the centre of curvature (r) are both imaginary points "inside" the mirror, which cannot be reached.

A collimated beam of light diverges after reflection from a convex mirror, since the normal to the surface differs with each spot on the mirror.

The image on a convex mirror is always virtual, upright and smaller than the object


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Convex mirrors


f

r

Incidentray

Normal

Reflected ray

Principal axis

Principal plane

θ

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Different image characteristics of spherical mirror


Concave mirror Convex mirror

f

r

f

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Properties of different mirrors


r q

p

HO

HI

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Mirror equations

The spherical mirror model can be used to develop a simple equation for spherical mirrors.

Using triangle relationship and the laws of reflection, it is also possible to develop a quantitative relationship between the object and image distances.

f= the focal length, r= the radius of curvature (r=2f), p= the object position,q= the image position


2 1 12

rpqr p q p r

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Mirror equations

Distances are positive if they lie on the same side of the mirror as the light rays themselves.

If they lie behind the mirror, the distances are negative. Both of r (or f) and q are negative for a convex mirror Only q is negative for a concave mirror just when the

object lies between the vertex and the focal point. Magnification (m) is another property of a spherical

mirror, which determines how much larger or smaller the image is relative to the object.

In practice, this is a simple ratio of the image height (HI) to the object height (HO).


q HI qm HI HOp HO p

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Spherical abberation

To form an image, mirror equation uses only rays that are close to and almost parallel with the principal axis.

Such a situation is physically imposed by assuming that sin(θ) ≈ θ for rays coming from the axis.

Rays that are far from principal axis do not converge to a single point.

The fact that a spherical mirror does not bring all parallel rays to a single point is known as spherical aberration


κf

r

HO

r

f

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Spherical abberation

This defect is most noticeable for light rays striking the outer edges of the mirror

lateral aberration: The extent of the ray divergence from the focus

lateral aberration can be quantized in terms of the distance HO of the light ray from the principal axis of a concave mirror with the radius of curvature r.


2

2 2 22

r r

r HO

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Conceptual model of OIO


OIO is optics inspired population based evolutionary algorithm

it is assumed that a number of artificial light points (points in Rn+1 whose mapping in Rn are potential solutions to the problem) are sitting in front of an artificial wavy mirror (function surface) reflecting their images.

OIO treats the surface of the function to be optimized as the reflecting mirror composed of peaks and valleys.

Each peak is treated as a convex reflective surface and each valley is treated as a concave reflective surface.

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In this way, the artificial ray glittered from an artificial light point is reflected back artificially by the function surface, given that the reflecting surface is partially a part of a peak or a part of a valley,

The artificial image point (a new point in which is mapped in as a new solution in the search domain) is formed upright (toward the light point position in the search space) or inverted (outward the light point position in the search space).

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22



108

64

20

-2-4

-6-8

-10-10-8

-6-4

-20

24

68

80

100

120

200

0

140

40

20

160

60

180

10

A new solution in the search space


23 A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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Given an individual solution O in the population, a different solution F (vertex point) is picked randomly from the population.

If F is worse than O, it is assumed that the surface is convex and a new solution is generated upright somewhere toward O, on the line connecting O and F

If F is better than O then it is assumed that the surface is concave and the new solution is generated upright toward or inverted outward O, on the line connecting O and F in the search space

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26



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Correction of the artificial spherical aberration


If for an artificial light point j we come out to we correct the occurred aberration via increasing the length of the artificial mirror radius of curvature. To correct the occurred aberration, we repeatedly do the following steps until getting

, 0.01,k

tj i

2

,2 2

,

( )22 ( ) ( )

kk

k

k k

ttiit

j it t

i j i

rr

r HO

, 0.01.k

tj i

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Correction of the artificial spherical aberration


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Generation of a new solution in OIO


,,

, , ,

2 1 12

k k

k

k k k k k

t ti j it

j it t t t ti j i j i j i i

r pq

r p q p r

, k k

t t tj i j iHO O F

,, ,

,

k

k k

k

tj it t

j i j i tj i

qHI HO

p

, ,, , , ,

, ,

,

( ) ( )( )

( )2

k k k k

k k k k k k k k

k kk k

k

k k

k k

t t t t t tj i j i j i j it t t t t t t t t

j i i j i i j i j i i j it tt t t tj i j ij i j i

tit t t

i j it tj i i

O F q O F qI F HI F HO I F O F

p pO F O F

rF O F

p r

,1

k

Kt t tj k j i

k

I w I

1

1K

tk

k

w

0 1.tkw

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Flowchart of OIO


See the Flowchart of OIO in the paper

http://drkashan.ir/files/pdf/optics%20inspired%20optimization.pdf

http://drkashan.ir/files/pdf/optics%20inspired%20optimization.pdf

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bi-objective optimization of a centrifuge pump

Centrifugal pumps are widely used in process industries for different applications, such as lifting fluid from one level to another.

η and NPSHr are design features of centrifugal pumps The polynomial representation for η is:

2 21 1 1 1 1 1 10.476 0.33 2.027 0.014 0.013 0.0001Hub Shroud Hub Shroud Hub ShroudY

2 22 2 2 220.3595 1.1797 0.5391 0.00787 0.00397 0.00115mid mid midY

2 23 1 2 1 2 1 217.93 2.01 0.5805 0.013 0.00397 0.0002Shroud Shroud ShroudY

2 24 1 1 137.03 1.228 0.352 0.0078 0.0142 0.00062mid Hub mid Hub mid HubY

2 25 1 2 1 2 1 260.5535 0.66962 0.91212 0.004299 0.005978 0.012869Y Y Y Y Y YY

2 26 3 4 3 4 4 357.0403 0.52137 0.97334 0.003361 0.0063741 0.0128Y Y Y Y Y Y Y

2 25 6 5 6 5 60.68350 3.42012 4.39817 2.330201 2.37611 4.706481Y Y Y Y Y Y


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The polynomial representation for NPSHr is:2 2 6

1 1 1 1 1 1 11.62 0.014 0.16 0.005 0.0010 2.2 10Hub Shroud Hub Shroud Hub ShroudY 2 12 2 5

2 1 2 1 2 2 13.426 0.0152 0.0177 0.0005 3.109 10 1.22 10Hub Hub HubY 2 2 5

3 1 1 16.175 0.1292 0.01609 0.001 0.0005 2.83 10mid Hub mid Hub mid HubY 2 11 2 5

4 1 2 1 2 1 22.47 0.159 0.017 0.0010 1.27 10 1.35 10Shroud Shroud ShroudY 2 2

5 1 2 1 2 1 27.5491 3.5231 0.42880 0.46290 0.019501 0.060303Y Y Y Y Y Y Y 2 2

6 3 4 3 4 3 45.9118 1.963 0.6936 0.21291308 0.0801906 0.2316076Y Y Y Y Y Y Y 2 2

5 6 5 6 5 60.3809 0.0652 1.217 0.0704 0.030280 0.1160804NPSHr Y Y Y Y Y Y


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1

1

2

Maximize Minmize

: 30 70

0 30

60 89

40 60

mid

Hub

Shroud

NPSHr

st

1

1

2

Minmize (1 )

: 30 70

0 30

60 89

40 60

i i

mid

Hub

Shroud

w w NPSHr

st


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a new metaheuristic for optimization: optics inspired optimization (oio)

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