Inverse Graphical Method for Global Optimization and Application to Design Centering Problem

TL;DR

This paper introduces an inverse graphical method for global optimization, which estimates feasible points by bounding the objective value, offering efficiency advantages over traditional methods especially in design centering problems.

Contribution

It presents a novel inverse optimization algorithm based on bisection of the objective range, improving efficiency for global optimization tasks with certain problem structures.

Findings

Inverse method reduces computational effort in global optimization.

The approach is particularly effective for design centering problems.

Compared to conventional methods, the inverse scheme is more efficient in specific cases.

Abstract

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for solving such a problem are based on user-supplied routines computing the objective value at some points. We study another approach called inverse relying on some procedure to estimate the set of points instead having objective values bounded by a specified constant. In particular, we present an inverse optimization algorithm derived from the bisection of the objective range. In case of seeking a proven global optimal solution inherently requiring many computations, and a problem with some kind of coherency utilized in estimation procedure, the inverse scheme is much more efficient than conventional ones. An example of such a problem, namely the design centering, is studied to compare the approaches.