General Optimization Overview

Statistica General Optimization is used for optimizing an arbitrary mathematical function using the simplex, grid search, and genetic algorithms.

Given an arbitrary function f(X) with a number of input parameters, denoted by X, the function f(X) returns a single real value.

Using this module, you can find the value of the parameters X that yield a minimum value returned by the function f(X). For functions with multiple minima, the analysis returns the first solution encountered. This could be a local or a global minimum.

Throughout Statistica's consulting practice, numerous applications have presented themselves that called for optimization of complex functions, typically in the form of predictive models for multiple outcomes. Following are some examples:

• When optimizing coal furnaces simultaneously for low CO and NOx emissions, the task typically is to optimize two predictive models and specialized loss functions (e.g., to optimize for robust system performance).
• For marketing campaign optimization, the typical task is to optimize multiple predictive models and functions subject to business constraints; for example, direct mail marketing campaigns need to optimize expected target responses for the least cost.
• In engineering design of complex systems, a typical use case is to optimize the expected response of the system, where each subsystem or component itself is a designed (often via CFD) component; in those applications, it is not possible to optimize explicitly all (such as CFD) models for all subsystems simultaneously because of the inherent complexity (high dimensionality) of the system, and because often those subsystems are designed using incompatible parameterization and approaches. However, random data generated from those explicit models can themselves serve as inputs into empirical optimization, using general approximators such as neural networks as proxi-models to represent the complex process.
• In general, practically all data mining projects eventually aim to either predict some process or optimize a process, marketing campaign, investment portfolio, etc.