Basic Differential Evolution Algorithm in MATLAB

Differential Evolution (DE) is a population-based global optimization algorithm primarily used for solving optimization problems in continuous spaces. Its core concept involves evolving populations through differential mutation, crossover, and selection operations to ultimately find optimal solutions.

Implementing Differential Evolution in MATLAB typically involves these key steps:

Population Initialization: Randomly generate a set of initial solutions (individuals), where each individual represents a potential solution to the problem. In MATLAB, this can be implemented using rand() or randn() functions with appropriate dimension scaling.

Mutation Operation: Select distinct individuals from the current population and generate mutant individuals through differential calculations. Common mutation strategies include DE/rand/1 (random base vector) and DE/best/1 (best solution as base vector), implemented using indexing and vector operations.

Crossover Operation: Perform crossover between mutant individuals and target individuals to generate trial individuals, typically using binomial crossover or exponential crossover methods. This involves element-wise comparison with crossover probability (CR) parameters.

Selection Operation: Compare fitness values between trial individuals and target individuals, retaining superior solutions for the next generation population. This greedy selection process ensures monotonic improvement in solution quality.

Termination Condition: The algorithm terminates when reaching maximum iterations or fitness convergence, outputting the optimal solution. Convergence can be monitored through fitness value stabilization or generation count thresholds.

DE's advantages include low dependency on objective function characteristics, requiring no gradient information, making it suitable for complex nonlinear optimization problems. In MATLAB implementation, parameters like mutation factor (F) and crossover probability (CR) can be flexibly adjusted to improve convergence speed and optimization performance.

For first-time DE users, experimenting with different mutation strategies and parameter combinations is recommended to find optimal configurations for specific problems. Parameter tuning can be systematically approached through sensitivity analysis or grid search techniques.