A multi-objective Gaussian mixture-based estimation of distribution algorithm for structural design optimization

Structural design optimization in the Architecture-Engineering-Construction (AEC) domain often involves complex, constrained and computationally intensive tasks. These problems are typically formulated as constrained multi-objective optimization tasks, where conflicting objectives, such as cost, sustainability, and constructability, must be balanced subject to structural performance requirements. In this context, population-based metaheuristics are effective for navigating black-box and non-convex design spaces. Among these, Estimation of Distribution Algorithms (EDAs) are well suited for this purpose, as they guide search through learned probability distributions over high-performing regions. This study introduces MOEDA-GMM, a multi-objective EDA that models the selected population using a Gaussian Mixture Model fitted via Expectation-Maximization. A power-law covariance decay schedule governs the transition from exploration to exploitation. The algorithm is evaluated on four constrained structural benchmarks and three analytical test functions, and compared against NSGA-II, SMS-EMOA, and RVEA under equal evaluation budgets. A factorial sensitivity analysis of the three hyperparameters and non-parametric statistical tests support the comparison. MOEDA-GMM shows rapid early-stage convergence and significantly outperforms NSGA-II on two structural problems, while established algorithms retain a final-convergence advantage on the analytical suite. The sensitivity analysis identifies a compact region of robust settings across problems, confirming the viability of mixture-model EDAs for constrained structural optimization under limited evaluation budgets.