Basic Genetic Algorithm for 4-Parameter Optimization

Genetic Algorithm (GA) is an optimization method that simulates natural evolution processes, commonly used for multi-parameter optimization problems. For PID controller parameter optimization, GA gradually approaches optimal solutions by simulating selection, crossover, and mutation operations.

### Basic Workflow Population Initialization Randomly generate a set of candidate solutions (individuals), where each individual represents a set of PID parameters (Kp, Ki, Kd, and possibly additional parameters). Population size is typically determined by problem complexity, commonly ranging from 50-200 individuals. In code implementation, this involves creating a population matrix with random values within specified parameter bounds.

Fitness Evaluation Each individual's fitness reflects its control performance, measured through error indicators (such as ISE, IAE, or ITAE). Higher fitness indicates better parameter combinations. The fitness function typically calculates performance metrics by simulating the control system with candidate parameters.

Selection Operation Implement roulette wheel or tournament selection methods to preferentially retain high-fitness individuals, ensuring excellent genes pass to the next generation. Code implementation involves probability-based selection where fitter individuals have higher selection probabilities.

Crossover and Mutation Crossover: Randomly select two parent individuals and exchange partial parameters (e.g., single-point crossover) to generate new offspring. In programming, this involves swapping parameter values between selected parents at random crossover points. Mutation: Randomly adjust certain parameters with low probability to enhance population diversity and prevent premature convergence. Code implementation typically adds small random perturbations to parameters with a predefined mutation rate.

Iterative Update Repeatedly execute evaluation, selection, crossover, and mutation until termination conditions are met (e.g., maximum iteration count or fitness threshold). The algorithm structure typically uses a while-loop or for-loop with convergence checking.

### Optimization Key Points Encoding Method: Real-number encoding is more intuitive for continuous parameters; binary encoding requires precision setting. Real encoding directly uses parameter values while binary encoding needs conversion functions. Constraint Handling: Limit parameter ranges (e.g., Kp>0) to avoid invalid solutions. Implement boundary checks or penalty functions in the fitness calculation. Premature Convergence Prevention: Dynamically adjust crossover/mutation probabilities or introduce elite preservation strategies. Elite preservation copies best individuals directly to the next generation.

### Application Scenarios This method is particularly suitable for nonlinear, multi-peak optimization problems like PID tuning, avoiding the inefficiency of traditional trial-and-error methods. By adjusting algorithm parameters (such as mutation rate), it can balance global search and local refinement capabilities. The algorithm can be implemented using optimization toolboxes or custom MATLAB/Python code with system simulation integration.