Function Optimizations

Abstract

Optimization is the process of improving a particular task or progress in order to find the “best” way for performing the requirement. Let us first consider a simple example of the following task (from real life, and quite a common occurrence at that): filling a tub with hot water. The person performing this task has at his/her disposal two faucets: hot and cold. If we assume that hot water is a valuable resource that cannot be wasted; the optimization problem simply stated is that of finding the proper opening gauge for the hot and cold water to achieve the task with minimal hot water expenditure. As you can imagine, the problem becomes more interesting when the person has a time constraint for filling the tub, or possibly an externally imposed schedule on the opening and closing of the faucets. Of course, we argue that the best way to handle this is by using an intelligent controller to solve this constrained optimization problem. Note that we assume throughout this work that the environment imposes a known (finite) set of constraints over the lifetime of the controller and a static analysis can be done once before the function and architecture are fixed. This may not be the case in general for a constantly changing environment. In this latter case techniques such as introspection [65], where the controller needs to reconfigure itself based on the environmental demands through machine learning [90], need to be applied.