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.