MATLAB Differential Evolution Algorithm Implementation Example with Code Techniques

As an efficient global optimization method, the differential evolution algorithm implementation in MATLAB primarily consists of four core steps: population initialization, mutation, crossover, and selection. The Differential Evolution (DE) algorithm serves as a typical example, where the basic workflow begins with randomly generating an initial population, with each individual representing a candidate solution in the solution space. During the mutation phase, the algorithm selects three distinct individuals from the current population and generates mutation vectors through weighted differential operations. Common mutation strategies like "DE/rand/1" utilize randomly selected individuals for perturbation, enhancing the algorithm's exploration capability. In MATLAB implementation, this can be coded using vectorized operations: mutation_vector = population(r1,:) + F * (population(r2,:) - population(r3,:)), where F represents the scaling factor and r1, r2, r3 are distinct random indices. The crossover operation is controlled by the crossover probability parameter (CR), which blends the mutation vector with the target individual to produce trial vectors. This can be implemented using logical indexing: trial_vector = target_vector; crossover_mask = rand(1,dim) < CR; trial_vector(crossover_mask) = mutation_vector(crossover_mask); where dim indicates the problem dimensionality. The selection operation employs a "survival of the fittest" mechanism, comparing the fitness of trial vectors against target vectors and retaining superior solutions for the next generation. This greedy selection strategy ensures monotonic non-degradation of population quality. In code implementation, this translates to: new_population(i,:) = trial_vector if f(trial_vector) < f(target_vector) else target_vector; where f() represents the objective function. Key parameters like scaling factor (F) and crossover rate (CR) require careful tuning in MATLAB implementations as they directly influence convergence speed and solution accuracy. Typical applications include engineering optimization and neural network training for continuous optimization problems. The algorithm can leverage MATLAB's matrix operations for computational efficiency, with convergence curves visualized using plot() or semilogy() functions. Compared to traditional optimization algorithms, differential evolution demonstrates lower sensitivity to initial values and superior robustness. MATLAB implementations benefit from built-in functions like rand(), randperm() for population initialization, and vectorized operations for efficient computation across population members.