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Response Surface Aberrations

## Excerpt

The term surface aberrations refers to features of the OF response to DVs, features of the topology, that make it difficult for optimization algorithms. Finding the optimum of an unconstrained quadratic surface is a trivial exercise. However, for many applications several types of OF features cause difficulty for the algorithm. These are easily visualized in the three dimension of a 2-D application (OF response to DV1 and DV2) but translate to 1-D and N-D applications. The following illustrations show the 3-D net and/or 2-D contour map patterns.

The term surface aberrations refers to features of the OF response to DVs, features of the topology, that make it difficult for optimization algorithms. Finding the optimum of an unconstrained quadratic surface is a trivial exercise. However, for many applications several types of OF features cause difficulty for the algorithm. These are easily visualized in the three dimension of a 2-D application (OF response to DV1 and DV2) but translate to 1-D and N-D applications. The following illustrations show the 3-D net and/or 2-D contour map patterns.

31.1Introduction
31.2Cliffs (Vertical Walls)
31.3Sharp Valleys (or Ridges)
31.4Striations
31.5Level Spots (Functions 1, 27, 73, 84)
31.6Hard-to-Find Optimum
31.7Infeasible Calculations
31.8Uniform Minimum
31.9Noise: Stochastic Response
31.10Multiple Optima
31.11Takeaway
31.12Exercises
31.1Introduction
31.2Cliffs (Vertical Walls)
31.3Sharp Valleys (or Ridges)
31.4Striations
31.5Level Spots (Functions 1, 27, 73, 84)
31.6Hard-to-Find Optimum
31.7Infeasible Calculations
31.8Uniform Minimum
31.9Noise: Stochastic Response
31.10Multiple Optima
31.11Takeaway
31.12Exercises
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