since the 1970s that the idea of a general algorithmic framework, which can be applied with...
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A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO)
By: Dr. A. H. Kashan
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• 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.
2
Introduction
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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.
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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.
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Concave mirror
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Convex mirrors
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
f
r
Incidentray
Normal
Reflected ray
Principal axis
Principal plane
θ
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Different image characteristics of spherical mirror
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
Concave mirror Convex mirror
f
r
f
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Properties of different mirrors
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
2 1 1
2
rpq
r 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).
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
q HI qm HI HO
p 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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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.
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
2
2 2 22
r r
r HO
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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Conceptual model of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Correction of the artificial spherical aberration
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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
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Correction of the artificial spherical aberration
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Generation of a new solution in OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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Flowchart of OIO
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
See the Flowchart of OIO in the paper
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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
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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bi-objective optimization of a centrifuge pump
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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bi-objective optimization of a centrifuge pump
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A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan
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bi-objective optimization of a centrifuge pump
A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan