Hybrid Surrogate-Based Constrained Optimization With a New Constraint-Handling Method.

Area of Science:

• Computational Mathematics
• Optimization Theory
• Engineering Optimization

Background:

• Surrogate-based optimization is crucial for computationally expensive systems but faces challenges with constraint handling, especially equality constraints.
• Efficiently sampling points within the feasible region to improve surrogate model predictions is a key difficulty.

Purpose of the Study:

• To propose a novel hybrid surrogate-based constrained optimization method (HSBCO) for expensive black-box systems.
• To develop an innovative constraint-handling technique that transforms the feasible region into the Euclidean subspace origin.

Main Methods:

• HSBCO employs a new constraint-handling method mapping the feasible region to the origin, transforming all constraints into an equivalent equality constraint.
• Constraint violation is quantified by the distance to the origin, enabling Gaussian penalty function integration to create an unconstrained problem.
• A hybrid strategy combines Kriging-based efficient global optimization (EGO) for local search with Radial Basis Function (RBF)-model-based global and local search.

Main Results:

• The proposed method effectively handles both inequality and equality constraints in expensive black-box optimization.
• HSBCO demonstrated superior performance on 23 test problems, converging more closely and efficiently to the global optimum.
• The hybrid approach balances local and global search, ensuring convergence within a maximum number of function evaluations.

Conclusions:

• HSBCO offers a robust and efficient solution for surrogate-based constrained optimization of expensive systems.
• The novel constraint-handling and hybrid search strategies significantly advance the field.
• The method outperforms existing leading techniques in achieving global optima accurately and efficiently.