robust optimization

Robust Optimization is a mathematical optimization framework that seeks solutions performing well under worst-case parameter uncertainty — ensuring the solution remains feasible and near-optimal for all realizations within a defined uncertainty set, even when the worst case occurs.

How Robust Optimization Works

• Uncertainty Set: Define the range of uncertain parameters (e.g., CD variation ±2 nm, temperature ±3°C).
• Worst Case: Optimize the objective for the worst-case parameter realization within the uncertainty set.
• Deterministic Reformulation: Convert the uncertain problem into a deterministic (tractable) optimization problem.
• Trade-Off: Robustness vs. optimality — more robustness typically means slightly worse average performance.

Why It Matters

• Guaranteed Performance: Unlike stochastic optimization, robust solutions guarantee performance for all scenarios in the uncertainty set.
• Process Windows: Finds the center of the process window — maximizing the margin to specification limits.
• Risk-Averse: Appropriate for high-consequence decisions where worst-case performance matters (yield loss, scrapped wafers).

Robust Optimization is designing for the worst day — finding solutions that maintain performance even under the most adverse parameter combinations.