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

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

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

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

work on one or several neighborhood 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 Are inspired by nature’s capability to evolve living beings well adapted to their environment Metaheuristics Evolutionary algorithms Trajectory methods Swarm intelligence Social, political, music, sport, Physics , etc • Society and civilization • Imperialist competitive algorithm • Harmony search • League championship • Algorithm • Optics Inspired Optimization • Tabu search • Variable neighborhood search • Evolution strategies • Genetic programming • Genetic algorithm • Ant colony optimization • Particle swarm optimization • Artificial bee colony • Bacterial foraging • optimization • Group search optimizer A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

The Optics Inspired Optimization (OIO)

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

Physics as a source of inspiration • There are several nature inspired algorithms which adopt their source of inspiration from Physics, e.g., • Light ray optimization • Spiral 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

Background • Opticsis 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

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

Concave mirror Principal axis Incident ray Reflected ray r θ f Principal plane Normal A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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

Convex mirrors Principal axis Incident ray Normal Reflected ray Principal plane f θ r A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

r f f Concave mirror Convexmirror Different image characteristics of spherical mirror A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

HO p r q HI Properties of different mirrors A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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

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

r f HO r f κ 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

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

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

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

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

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

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

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

Correction of the artificial spherical aberration A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

Generation of a new solution in OIO A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

Flowchart of OIO See the Flowchart of OIO in the paper A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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

bi-objective optimization of a centrifuge pump • The polynomial representation for NPSHr is: A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

bi-objective optimization of a centrifuge pump A New Metaheuristic for Optimization: Optics Inspired Optimization (OIO) By: Dr. A. H. Kashan

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