Efficient Global Optimization Strategy Considering Expensive Constraints

Abstract

This paper proposes a novel augmented Lagrange multiplier based efficient global optimization strategy (denoted as L-EGO) to solve black-box design optimization problems involving computationally expensive constraints. The original objective function, constraint functions, multipliers and exterior penalty function are integrated to construct an augmented objective function. By optimizing the expected improvement of the augmented objective function, the sample points are sequentially generated to refine the Kriging metamodel, and the Lagrange multiplier and penalty factor are updated during the iteration, which leads the optimization process converging to the feasible optimum efficiently. Two benchmark problems are used to test the proposed method via comparing with another metamodel-based optimization algorithm (i.e., CiMPS). The comparison results show that L-EGO outperforms CiMPS in terms of global convergence, efficiency, and robustness. Finally, L-EGO is applied to solve a practical all-electric GEO satellite multidisciplinary design optimization (MDO) problem, which involves seven expensive constraints. Compared with the initial design, the optimized solution reduces the total mass of the satellite by 7.1% and satisfies all the constraints, which demonstrates the effectiveness and practicality of the proposed L-EGO method.