Surrogate-Assisted Optimization
When each objective evaluation is expensive, a surrogate guides the search, spending real evaluations only where they most improve the design.
Optimizing expensive functions
Design optimization often means minimizing an objective that requires a costly simulation for each candidate. Gradient descent or evolutionary search would need thousands of evaluations - infeasible. Surrogate-assisted optimization builds a cheap model of the objective, optimizes on it, and validates promising points with the true expensive function, iterating toward the optimum with far fewer real evaluations.
The loop
- Evaluate an initial design of experiments with the expensive function
- Fit a surrogate to the results
- Use the surrogate to propose the next promising candidate
- Evaluate that candidate with the expensive function and add it to the data
- Refit and repeat until convergence or budget exhaustion
Exploration versus exploitation
The proposal step must balance refining near the current best (exploitation) against probing uncertain, unexplored regions that might hide a better optimum (exploration). Pure exploitation gets stuck in local optima; pure exploration wastes the budget. Acquisition functions that use the surrogate's uncertainty - most famously expected improvement - blend the two automatically, which is why Gaussian-process surrogates are favored here.
Constraints and multiple objectives
Real designs carry constraints and competing objectives. Surrogates can model each constraint and objective, and the acquisition function is extended to respect feasibility (constrained expected improvement) or to advance a Pareto front (expected hypervolume improvement) when trading off objectives.
Local surrogate methods
An alternative to global Bayesian optimization builds trust-region local surrogates that are refit and re-centered as the search moves, which scales better to moderate dimensions and to noisy objectives. Evolutionary algorithms also use surrogates to pre-screen candidates before spending real evaluations on the best.
In fusion design
Kronos design optimization uses surrogates of the machines to search operating and geometric parameters efficiently, with expensive full-fidelity runs reserved for validating candidate optima. This makes it possible to explore trade-offs across a design space that would be unreachable by direct optimization on the full simulations.