Function Optimization Using Genetic Algorithm

This project implements function optimization using genetic algorithms to find the convergence value for the function f(x) = Σ(i=1 to n) x_i * sin(√|x_i|). The optimization process is visualized through 3D surface plots and fitness evolution curves showing both best and average fitness values. Genetic algorithm is an evolutionary optimization method that mimics biological evolution principles. The implementation involves simulating natural selection, crossover, and mutation operations to progressively search the solution space. In code implementation, this typically requires defining a fitness function, initializing a population, and iterating through selection, crossover, and mutation operations. The process begins by defining a fitness function that evaluates individual solutions. For function f(x), the output value directly serves as the fitness metric. The algorithm initializes a population of randomly generated individuals, where each individual represents a potential solution vector. The selection operation uses fitness-proportional methods like roulette wheel selection or tournament selection to choose parents for reproduction. Crossover operations combine genetic information from two selected parents to create offspring. Common implementations include single-point or multi-point crossover where gene segments are exchanged between parent chromosomes. Mutation operations introduce diversity by randomly altering gene values with a small probability, preventing premature convergence to local optima. Through iterative generations of selection, crossover, and mutation, the population evolves toward optimal solutions. The convergence can be monitored by tracking the best fitness value in each generation. The algorithm typically terminates when reaching maximum generations or when fitness improvement plateaus. Visualization plays a crucial role in understanding the optimization progress. A 3D plot is generated with x-axis representing the input variable range, y-axis showing function values, and z-axis displaying fitness values. Additionally, fitness evolution curves plot both the best fitness and average fitness across generations, providing insights into convergence speed and population diversity. This genetic algorithm implementation demonstrates effective function optimization while providing valuable insights into evolutionary computation methods. The approach can be extended to solve various optimization problems by adapting the fitness function and parameter settings accordingly.