Audet, CharlesDennis, J.E. Jr.2018-06-182018-06-181999-05Audet, Charles and Dennis, J.E. Jr.. "Pattern Search Algorithms for Mixed Variable Programming." (1999) <a href="https://hdl.handle.net/1911/101908">https://hdl.handle.net/1911/101908</a>.https://hdl.handle.net/1911/101908Many engineering optimization problems involve a special kind of discrete variable that can be represented by a number, but this representation has no significance. Such variables arise when a decision involves some situation like a choice from an unordered list of categories. This has two implications: The standard approach of solving problems with continuous relaxations of discrete variables is not available, and the notion of local optimality must be defined through a user-specified set of neighboring points. We present a class of direct search algorithms to provide limit points that satisfy some appropriate necessary conditions for local optimality for such problems. We give a more expensive, version of the algorithm that guarantees additional necessary optimality conditions. A small example illustrates the differences between the two versions. A real thermal insulation system design problem illustrates the efficacy of the user controls for this class of algorithms.22 ppengTechnical reportTR99-02