MATLAB Implementation of SPEA2 Multi-Objective Evolutionary Algorithm

SPEA2 (Strength Pareto Evolutionary Algorithm 2) is an efficient evolutionary algorithm in the field of multi-objective optimization, particularly suitable for solving optimization problems with multiple conflicting objectives. Compared to the first-generation SPEA, SPEA2 significantly improves algorithm performance through enhanced fitness assignment mechanisms and the introduction of environmental selection strategies. Core Implementation Approach Population Initialization: Randomly generate initial population containing a set of potential solutions using MATLAB's rand() or randn() functions with proper boundary constraints. Fitness Calculation: - Strength Value: Count the number of solutions dominated by each individual using matrix-based domination comparisons - Raw Fitness: Calculate based on domination relationships - individuals with fewer domination occurrences receive higher fitness scores through efficient sorting algorithms - Density Estimation: Evaluate solution distribution density using k-nearest neighbor method to prevent clustering, implemented with Euclidean distance calculations and sorting operations Environmental Selection: Combine fitness and density information to preserve non-dominated solutions while eliminating redundant individuals, maintaining a fixed-size archive set through advanced sorting and selection mechanisms. Genetic Operations: Generate next-generation population through crossover and mutation operations, gradually approaching the Pareto front using simulated binary crossover and polynomial mutation. MATLAB Implementation Key Features - Utilize matrix operations for efficient population evaluation and domination relationship judgments, leveraging MATLAB's vectorization capabilities - Custom archive update logic ensures solution set diversity and convergence through sophisticated ranking and crowding distance calculations - Visualization module can plot Pareto front using plot() and scatter() functions, providing intuitive display of optimization results Extension Applications SPEA2 is suitable for complex scenarios like engineering design and resource scheduling. Potential improvements include introducing adaptive parameter adjustment mechanisms or combining local search strategies to enhance convergence speed. The implementation can be extended with parallel computing using MATLAB's Parallel Computing Toolbox for large-scale problems.