Model Improvement Points

At each search step, SEQOPT will select up to nglobal model improvement points. SEQOPT will execute your analysis code at these points, and the surrogate models will be updated with the resulting data.

The model improvement points are selected not because SEQOPT believes that the best design is located there, but because these points are far from existing known designs and because the surrogate models indicate that they may be "promising". Points are considered "promising" if the combination of model-predicted values and estimated surrogate model errors indicate a "reasonable" chance for feasibility and good objective values. Since the method tends to select points far from existing data points, it truly emphasizes the global aspect of the search. The algorithm attempts to balance the considerations of local and global search of the design space.

For best utility, the model improvement algorithm (CBLGS) must run quickly. Thus, it is undesirable to have to solve a difficult optimization problem to find model-improvement points. Instead, CBLGS relies on model evaluations and error bound estimates over a large set (dense cloud) of points, numbering say 10,000 to 100,000, that are well-spread-out in design space. In doing this, CBLGS takes advantage of the fact that large sets of well-spread-out points can be obtained quickly, and model evaluations and model error estimates can be computed very cheaply. The dense clouds of points used in CBLGS are orthogonal array-based Latin hypercubes [1]. For "reasonably" shaped feasible regions, the feasible subset of the dense cloud will retain the property of being well-spread out in design space.

Starting with the initial point cloud, CBLGS uses the surrogate models to compute the expected feasibility and expected improvement of each design point in the cloud [2]. The expected feasibility and expected improvement calculations take into account both the surrogate model predictions and the estimated accuracy of the surrogate model at a given point. The point cloud is filtered to exclude those points with a low expected feasibility, and the remaining points are then ranked according to their expected improvement. The top nglobal design points from this list are selected as model improvement points.

The size of the initial point cloud used by CBLGS can be specified by the parameter ncloud in the SEQOPT advanced options dialog.

Additional information about the CBLGS process can be found in [2].

[1] Owen, A.B., "Orthogonal Arrays for Computer Experiments, Integration and Visualization", Statistica Sinica, 2:439-452, 1992.

[2] Audet, C., Dennis, J.E., Moore, D.W., Booker, A.J., and Frank P.D., "A Surrogate-Model-Based Method for Constrained Optimization," 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Long Beach, CA, (September 8, 2000) AIAA-2000-4891.