Optimization Using Genetic Algorithm in MATLAB

Explore optimization concepts, including constrained and unconstrained problems, objective functions, and decision variables, via a cantilever beam design and feasibility in multimodal landscapes.

Constraints shape the optimal solution: the unconstrained minimum is -2.25 at x=2.5, but enforcing f(x) >= 0 yields minima at x=1 and x=4, and adding x >= 2.5 selects x=4.

Explore key terminologies in nature-inspired optimization, such as random solution, population, fitness function, and generation. Learn the basic pseudo-code steps and how evolutionary and swarm intelligence algorithms use them.

Explore the inspiration behind genetic algorithms, tracing John Holland's 1970s work to natural selection. Learn the four stages—selection, crossover, mutation, evaluation—and how fitness guides optimization in MATLAB.

Use roulette wheel selection with fitness-based probabilities and cumulative probabilities from f(x1,x2)=x1^2+x2^2 within -5 to 5 to pick two parents for crossover.

Learn crossover between two parents to produce two offspring using alpha, clip any out-of-bounds values to -5 or 5, then mutate a single gene with sigma perturbation and recheck bounds.

Evaluate the fitness of nine genetic algorithm solutions, retain the six best, discard the rest, and perform hundreds of iterations toward the best solution, before learning MATLAB implementation.

Learn how to implement a genetic algorithm in MATLAB to solve the unconstrained Matyas function, with a global minimum at zero in the -10 to 10 domain.

Formulate the Matyas function problem in MATLAB by setting bounds for two decision variables, determining their count, and defining the x limit matrix.

Initialize a random population matrix X, scale to xmin and xmax for P by D, compute Z with the Matyas function, and store the best cost and parameters.

In MATLAB, this lecture builds the genetic algorithm's main loop: compute fitness, derive selection probabilities via roulette wheel, and perform uniform crossover for Matyas function solutions.

Describe mutation in the Matyas function: randomly pick a parent, mutate one variable using a normally distributed perturbation, via a dedicated mutate function.

Learn to merge crossover and mutation results into a population, apply truncation and natural selection, track the best objective function, and plot convergence over iterations in MATLAB.

Run the MATLAB genetic algorithm to optimize the Matyas function. Observe convergence to a near-zero objective value after about 600 iterations, with x1 and x2 approaching zero.

Explore solving the Rosenbrock function as a constrained optimization using a disk-restricted roadblock. Learn how x^2 + y^2 <= 2 and bounds -1.5 to 1.5 guide the genetic algorithm.

Learn to solve a constraint optimization of the Rosenberg function with a genetic algorithm by adding a constraint function and lambda penalties, and adjusting limits to -1.5 to 1.5.

Apply a genetic algorithm to minimize porosity in aluminium alloy die casting, using the porosity equation and parameter bounds, and reproduce the cited study's 0.25 minimum in MATLAB.

Code a genetic algorithm in MATLAB to optimize porosity in a capstone project, adjust lower and upper bounds for decision variables, and implement the porosity function.