Yes-No Constraints - An Open Problem

Abstract

Scientific and engineering simulations are typically designed to closely approximate systems in regions that are physically realistic. Outside these regions the simulations, often purposefully, return no results. These problems have "yes/no" constraints in the sense that the only constraint information available is whether or not a simulation is feasible at a specified point. No information is typically available about how close or how far away the constraint boundaries are from any given point.

These cases are something of an embarrassment for the optimization community due to their ubiquitous nature, apparent simplicity, and actual intractability. Although direct search methods are at least well defined on these problems, most commonly known methods are only sporadically effective.

We present a set of sample testbench problems based on a number of properties that can make such cases difficult to solve. Each testbench problem is intended to illustrate one difficulty, and is otherwise as benign as possible.

Brief description of testbench problems.

Fortran sourcecode for the testbench problems. Version 0.8, May 1 1999.

Matlab visualization macros (including precomputed maps of objective and constraints) for the testbench problems. About 660K, unpacks to about 18 meg.

Brief description of Matlab visualization tool.

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