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Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
 SIAM Journal on Optimization
, 2004
"... A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for gene ..."
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A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictate what can be proved about certain limit points generated by the algorithm. To demonstrate the usefulness of the algorithm, the algorithm is applied to the design of a loadbearing thermal insulation system. We believe this is the first algorithm with provable convergence results to directly target this class of problems.
Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System
, 2000
"... : In the literature, thermal insulation systems with a xed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization ..."
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Cited by 25 (6 self)
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: In the literature, thermal insulation systems with a xed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization variables are categorical if the objective function or the constraints can not be evaluated unless the variables take one of a prescribed enumerable set of values. The key issue is that categorical variables can not be treated as ordinary discrete variables are treated by relaxing them to continuous variables with a side constraint that they be discrete at the solution. A new mixed variable programming (MVP) algorithm makes it possible to optimize directly with respect to mixtures of discrete, continuous, and categorical decision variables. The result of applying MVP is shown here to give a 65% reduction in the ...
Mixed variable optimization of a loadbearing thermal insulation system
, 2002
"... categorical variables, mixed variable programming, pattern search algorithm, filter algorithm, nonlinear constraints Abstract: This paper describes the optimization of a loadbearing thermal insulation system characterized by hot and cold surfaces with a series of heat intercepts and insulators betw ..."
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categorical variables, mixed variable programming, pattern search algorithm, filter algorithm, nonlinear constraints Abstract: This paper describes the optimization of a loadbearing thermal insulation system characterized by hot and cold surfaces with a series of heat intercepts and insulators between them. The optimization problem is represented as a mixed variable programming (MVP) problem with nonlinear constraints, in which the objective is to minimize the power required to maintain the heat intercepts at fixed temperatures so that one surface is kept sufficiently cold. MVP problems are more general than mixed integer nonlinear programming (MINLP) problems in that the discrete variables are categorical; i.e., they must always take on values from a predefined enumerable set or list. Thus, traditional approaches that use branch and bound techniques cannot be applied. In a previous paper, a linearly constrained version of this problem was solved numerically using the AudetDennis generalized pattern search (GPS) method for MVP problems. However, this algorithm may not work for problems with general nonlinear constraints. A new algorithm that extends that of Audet and Dennis by incorporating a filter to handle nonlinear constraints makes it possible to solve the more general problem. Additional nonlinear constraints on stress, May 5, 2003 2 mass, and thermal contraction are added to that of the previous work in an effort to find a more realistic feasible design. Several computational experiments show a substantial improvement in power required to maintain the system, as compared to the previous literature. The addition of the new constraints leads to a very different design without significantly changing the power required. The results demonstrate that the new algorithm can be applied to a very broad class of optimization problems, for which no previous algorithm with provable convergence results could be applied. 1
Optimization using Surrogates for Engineering Design
, 2002
"... The goal of these lectures is to acquaint the audience with some approaches to a class of nasty optimization problems involving nonconvex nonlinear extendedvalued functions. Such functions arise often in multidisciplinary optimization (MDO). The first three lectures are meant to set the context for ..."
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Cited by 2 (0 self)
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The goal of these lectures is to acquaint the audience with some approaches to a class of nasty optimization problems involving nonconvex nonlinear extendedvalued functions. Such functions arise often in multidisciplinary optimization (MDO). The first three lectures are meant to set the context for applying our algorithms. The context determines the form of the algorithms, and to present this context requires a bit more than just a short list of assumptions. Briefly though, the objective function and constraints depend not only on the optimization variables, but also on some ancillary variables such as the solutions of some coupled systems by standalone solvers for partial differential equations, table lookups, and other nonsmooth simulation codes. This has important algorithmic implications. First, the function and constraint values may be very expensive. Second, the functions may be nondifferentiable and discontinuous. In fact, they are often treated as extended valued since a function call may not return a value even if all the specified constraints are satisfied. The approach we treat in these lectures has been successful for some real problems in engineering design. We hope to convince engineers and mathematicians alike that not only are the algorithms given here useful, but the mathematics involved is interesting and relevant. We hope to convince mathematicians that good applied problems produce good mathematics, and that contrary to what they may have heard, they will suffer no loss of virtue as a direct result of considering them.
Pattern Search Algorithms for Mixed Variable General Constrained Optimization Problems
 Rice University, Department of
, 2002
"... Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, Catherinei and maintaining the data needed, and completing and reviewing the collection of information. Send comment ..."
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Cited by 1 (0 self)
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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, Catherinei and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this