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 Optimization Engineering - Metaheuristic Optimization Algorithms Optimization plays a very important role in science and engineering. Optimization aim is to find out the minimum or maximum value using any objective function or cost function. In optimization different Metaheuristic Algorithms are used to solve complex problems in various fields such as Engineering Problems, Medical Problems, Computer Problems, and different real-life problems that can not be solved using classical methods. Metaheuristic optimization algorithms are classified into two main categories as Single-based optimization algorithms and Population-based optimization algorithms.  Single-based Meta-heuristic algorithms are also known as Trajectory Algorithms. Single-based metaheuristic algorithms provide the single solution in every iteration. Single-based Metaheuristic algorithm examples: Tabu Search, Guided Local Search, Iterated Local Search, Stochastic Local Search, Iterated Local Search, Variable ne...

Water Cycle Algorithm (WCA)  A number of metaheuristic algorithms have been developed to solve various constraints optimization problems. Because according to the No Free Lunch theorem no algorithm alone can not solve various real-world problems. Different problems exist in real life that is complex in nature and hard to solve. Water Cycle Optimization Algorithm is inspired by nature. The water cycle algorithm is a nature-inspired metaheuristics algorithm. Water Cycle Algorithm is basically inspired by the water cycle process in nature. In this video, you will learn how the water cycle algorithm is working step-by-step with examples and its mathematical Model. Water Cycle Algorithm is a metaheuristic optimization method used to solve different constraints-based problems and real-life engineering design problems. Water Cycle is also known as Hydrological Cycle. Water Cycle represents the continuous movement of water below and above the earth's surface. Most Precipitation: Occur as ...

C++ Program to Calculate Area of Rectangle using Objects and Classes. Calculate Area of Rectangle: Area = Length * width Program Output: Source Code  #include<iostream> #include<conio.h> using namespace std; class rectangle { private: int a, b; public: void setdata(int x, int y)  { a = x; b = y; } void area() { int area = a*b; cout<<"\n Area of Rectangle = " <<area; } }; int main() { rectangle r1, r2; //objects r1.setdata(15,40);  //object r1 called setdate() cout<<"\nFor First Rectangle "; r1.area(); // object r1 calls area() r2.setdata(30,60);  //object r1 called setdate() cout<<"\nFor First Rectangle "; r2.area(); // object r1 calls area() getch(); return 0; }

 Programming in C Language: Pointers Define Pointer. A pointer is a variable that stores a memory address. Like all other variables, it also has a name, has to be declared, and occupies some spaces in the memory.  Why Pointer is called Pointer?  It is called a pointer because it points to a particular location in memory by sorting the address of that location. Pointer General Syntax of Declaration data-type * Pointername; Here, Pointername = Name of pointer variable Astric * preceding this name informs the compiler that the variable is declared as a pointer.  Data type = Base type of pointer. For example:          int * iptr;          float * fptr; here iptr is a pointer that should point to a variable of type int. Pointers are also variables so, the compiler will reserve space for t hem and they will also have some address. All pointers irrespective of their base type will occupy the same space in memory since all of...

Firefly Algorithm Firefly algorithm is a swarm-based metaheuristic algorithm that was introduced by Yang. Firefly algorithm is used for solving optimization problems. In this video, you will learn the Firefly algorithm with an example. Firefly Algorithm is inspired by the FLASHING Behavior of Fireflies. For simplicity certain Assumptions used in Firefly Optimization Algorithm: - 1.) Fireflies are attracted to each other. 2) Attractiveness is proportional to BRIGHTNESS. 3.) Less Brighter Firefly is attracted to the Brighter Firefly. 4.) Attractiveness decrease as the distance between 2 fireflies increase. 5.) If the brightness for both is the same, fireflies move randomly. 6.) New Solutions are generated by Random walks & the Attraction of fireflies. Firefly Optimization Algorithm Steps: Initialize Parameters Initialize Population randomly in the search space. Compute Fitness values and select the best solution. Check Stopping Criteria. While Current Iteration = 1:Maximum Iterat...

Manta Ray Foraging Optimization (MRFO) Algorithm  Manta Ray Foraging Optimization (MRFO) Algorithm Example Step 01: Initialize Population Size Suppose, Population Size = 4; Lower Bound = -10; Upper Bound = 10; Maximum Iteration = 4; Suppose Initial Population  1.1  2  0.9  3 Step 02: Compute Fitness Value for each using fitness function. Fitness Values 1.21 4 0.81 9 Step 03: Obtain Best Solution Best solution = Minimum Fitness Value in the current population Best Solution = 0.81 Step 04: Check Stopping Criteria While (Current < Maximum Iteration)  1 < 4   ((True) move to next step )  If stopping criteria is then stop and return the best cost. Step 05: Update Position for each individual. For i = 1 to PopulationSize For i = 1:4 If (rand < 0.5)  THEN Cyclone Foraging Else Chain Foraging End if Step 06: Compute Fitnee Value for Each individual and Select Best Individual. Step 07: Perform Somersault Foraging.  Step 08: Co...

 Grey Wolf Optimization Algorithm Numerical Example Grey Wolf Optimization Algorithm Steps 1.) Initialize Grey Wolf Population. 2.) Initialize a, A, and C. 3.) Calculate the fitness of each search agent. 4.) 𝑿_𝜶 = best search agent 5.) 𝑿_𝜷 = second-best search agent 6.) 𝑿_𝜹 = third best search agent. 7.) while (t<Max number of iteration) 8.) For each search agent       update the position of the current search agent by the above equations end for 9.) update a, A, and C 10.) Calculate the fitness of all search agents. 11.) update 𝑿_𝜶, 𝑿_𝜷, 𝑿_𝜹 12.) t = t+1 end while 13.) return 𝑿_𝜶 Grey Wolf Optimization Algorithm Numerical Example STEP 1.  Initialize the Grey wolf Population [Initial Position for each Search Agent] 𝒙_(𝒊  )  (i = 1,2,3,…n)     n = 6 // Number of Search Agents  [ -100, 100] // Range Initial Wolf Position      3.2228     4.1553    -3.8197     4.2330  ...

 Grey Wolf Optimization Algorithm  (GWO) Grey Wolf Optimization Grey Wolf Optimization Algorithm is a metaheuristic proposed by Mirjaliali Mohammad and Lewis, 2014. Grey Wolf Optimizer is inspired by the social hierarchy and the hunting technique of Grey Wolves. What is Metaheuristic? Metaheuristic means a High-level problem-independent algorithmic framework (develop optimization algorithms). Metaheuristic algorithms find the best solution out of all possible solutions of optimization. Who are the Grey Wolves? Wolf (Animal): Wolf Lived in a highly organized pack. Also known as Gray wolf or Grey Wolf, is a large canine. Wolf Speed is 50-60 km/h. Their Lifespan is 6-8 years (in the wild). Scientific Name: Canis Lupus. Family: Canidae (Biological family of dog-like carnivorans). Grey Wolves lived in a highly organized pack. The average pack size ranges from 5-12.  4 different ranks of wolves in a pack: Alpha Wolf, Beta Wolf, Delta Wolf, and Omega Wolf. How Grey Wolf Optimiza...

Invasive Weed Optimization (IWO) Algorithm with Example Invasive Weed Optimization The invasive weed optimization algorithm (IWO) is a population-based metaheuristic optimization method inspired by the behavior of weed colonies. Weeds are u nwanted plants (plant in the wrong place). Weeds can change their behavior according to the environment and gets fitter. Weeds plant can be easily found in: Parks, Fields, Garden, and Lawns Invasive Weed Optimization Algorithm Steps. 1.) Initialization Phase Initialize all important parameters. 2.) Initialize Population. The initial population is created by spreading the finite number of seeds randomly in the search space. 3.) Compute Fitness Values.  Every seed will grow into a flowering plant and produce seeds. [Reproduction].  Seed production is based on fitness values so compute: Individual Fitness Value Best Fitness Value Worst Fitness Value 4.) Random distribution of germinated seeds. Determine new positions of seeds in the search sp...

 PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. - PART 2 [Example 2] 1.) Initialize Population [Current Iteration (t) = 0] Population Size = 4; 𝑥𝑖 : (i = 1,2,3,4) and (t = 0) 𝑥1 =1.3; 𝑥2=4.3; 𝑥3=0.4; 𝑥4=−1.2 2.) Fitness Function u...

Firefly algorithm is a swarm-based metaheuristic algorithm that was introduced by Yang. Firefly Algorithm is inspired by the FLASHING Behavior of Fireflies.  Assumptions Fireflies are attracted to each other. Attractiveness is proportional to BRIGHTNESS.  Less Brighter Firefly is attracted to the Brighter Firefly. Attractiveness decrease as the distance between 2 fireflies increase. If brightness for both is the same, fireflies move randomly. New Solutions are generated by Random walks & the Attraction of fireflies. Video Link:  https://youtu.be/QvpEMR-Jp0U Firefly Optimization Algorithm Steps Initialize Parameters. Generate Population of n Fireflies. Calculate Fitness Value for Each Firefly. Check stopping criteria if (CurrentIteration := 1 to MaximumIteration ).  Update Position and Light Intensity for Each Firefly. Report the Best Solution. Initialize Parameters, Population of Fire Fly Swarm. Population Size (n) = 20; Maximum Iteration (Maxt) = 50; Dimension ...

Manta Ray Foraging Optimization (MRFO) Manta ray foraging optimization (MRFO) is a new optimization approach for global optimization problems. The Manta ray optimization algorithm is developed by Zhao et al. (2020). Manta ray optimization algorithm is a bio-inspired optimization technique. Manta ray optimization algorithm is inspired by foraging strategies of manta rays. Manta ray optimization algorithm is used to solve optimization problems. Manta Ray basic structure Manta Ray foraging is often found in groups. Three main manta Rays Foraging Strategies:  Chain Foraging Cyclone Foraging Somersault Foraging Chain Foraging: More than 50 Manta Rays line up. One behind another. (the line is formed by Manta Rays). Manta Rays observe plankton’s position and swim towards it. Manta Rays form a foraging chain by line-up from head to tail. Assumed that BEST Solution is plankton with high concentration manta rays want to approach. In every generation, all individuals will update their positi...

Particle Swarm Optimization (PSO) Algorithm Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. 🌞 Particle Swarm Optimization (PSO) Algorithm Matlab code. Particle Swarm Optimization Main File: main.m pso; Particle Swarm Optimization Function File: Sphere(x) function F1 = Sphere(x) F1 = sum(x.^2); end Particle Swarm Optimization File Name Save as: pso.m clear; close all; %% Fitness Function Calling FitnessFunction=@(x) Sphere(x); % Fitness Function Calling % Total Number of Decision Variables Used nVar=10; % Size of Decision Variables Matrix VarSize=[1 nVar]; % Lower Bound LowerBound =-10; % Upper Bound UpperBound = 10; %% Parameters Initialization Phase % Maximum Number of Iterations used. MaxT=100; % Total Number of Search Agents used. PopulationSize = 10; % Initialize PS...

  Software Engineering   Software Engineering: Software Engineering (S.E.) is a profession dedicated to the designs, implementation, and modification of software.  Applications of Software Engineering are:  Re-engineering of software Software Testing Software Maintainance  Software Analysis Software Design Software Implementation The objective of software engineering is to produce good quality software, on time and within budget. To obtain this objective it is very important to focus on Software Quality and Software Development Process. Software Characteristics are:  Reusability of the components. Softwares are not manufactured as hardware.  In the Software development process, there is no wear-out phase. Software is fixable. Software Life Cycle Models: Software life cycle means the time period when a software product is conceived and when the software product is no longer available for use. The software Life cycle includes different phases: Requiremen...

Chemical Reaction Optimization Algorithm Chemical Reaction Optimization algorithm is a population-based metaheuristic algorithm. Chemical Reaction Optimization algorithm is inspired by Chemical reactions. Chemical Reaction Optimization algorithm is developed by Albert Y.S. Lam and Victor O.K. Li. In this algorithm, Molecular structure (sum all characteristics) is used to compute the solution. Chemical Reaction Optimization algorithm is used to solve optimization problems. Chemistry Basic Fundamentals:  Atom / Molecule / Chemical Bonding / Molecular Structure / Molecule Energy / Chemical Reations/ Elementary Reactions  Atom:   According to Dalton (in 1808), an atom is the smallest part of an element that exists as the smallest entity. 3 important fundamental particles of an atom are Proton, Electron, and Neutron. For Example Oxygen (O), Nitrogen (N), Hydrogen (H), etc. Molecule: A molecule  is composed of 2 or more atoms held together by chemical bonds. The molec...