A New Method For Numerical Constrained Optimization
Numerical constrained optimization is an important tool with extensive applications in many diverse fields. An ideal problem for constrained optimization is one that has a single measure defining the quality of a solution (the objective function) plus some requirements upon that solution that must not be violated (the constraints). A constrained optimization solver maximizes (or minimizes) the objective function while satisfying the constraints. We have developed a new method for constraint handling that can be applied to established optimization algorithms and which significantly improves their ability to traverse through constrained space.
Background & Objective: The applicability of optimization methods is widespread, reaching into almost every activity in which numerical information is processed (e.g., science, engineering, mathematics, economics, and commerce). We have focused on solving difficult constrained optimization problems with characteristics common in many engineering applications such as process control (e.g., nonlinear, nondifferentiable, and noisy objective functions and constraints).
Technical Discussion: Many constrained problems have optima that lie near constraint boundaries. Consequently, avoidance of constraints can hinder an algorithm's path to the answer. By allowing (and even encouraging) an optimization algorithm to move its vertices into constrained space, a more efficient and robust algorithm emerges. In the new method, constraints are partitioned into multiple levels. A constrained performance, independent of the objective function, is defined for each level. A set of rules, based on these partitioned performances, specify the ordering and movement of vertices as they straddle constraint boundaries; these rules (employing the insight stated above) have been shown to significantly aid motion along constraints toward an optimum. Note that the new approach uses no penalty function and thus does not warp the performance surface, thereby avoiding the possible ill-conditioning of the objective function typical in penalty methods.
Contact: Ron Perry
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| A New Method For Numerical Constrained Optimization | |
Technology Area: Artificial Intelligence
Modification Date: July 6, 2001
