Optimization of dual response systems: A comprehensive procedure for degenerate and nondegenerate problems |
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| Institution: | 1. School of Social Work, College for Public Health and Social Justice, Saint Louis University, Tegeler Hall, 3550 Lindell Blvd., St. Louis, MO 63103, United States;2. Department of Epidemiology, College for Public Health and Social Justice, Saint Louis University, 3545 Lafayette Avenue, St. Louis, MO 63104, United States;3. School of Social Work, The University of Texas at Austin, 1925 San Jacinto Blvd D3500, Austin, TX 78712-0358, United States;4. Criminal Justice Studies, Iowa State University, 203A East Hall, Ames, IA 50011-1070, United States;1. Institute of Advanced Manufacturing and Intelligent Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China;2. Key Laboratory of CNC Equipment Reliability, Ministry of Education, School of Mechanical and Aerospace Engineering, Jilin University, Jilin 130012, China;3. Mechanical Industry Key Laboratory of Heavy Machine Tool Digital Design and Testing Technology, Beijing University of Technology, Beijing 100124, China |
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| Abstract: | Most dual response systems (DRSs) arising in response surface modeling can be approximated using a nonlinear (and typically nonconvex) mathematical program involving two quadratic functions. One of the quadratic functions is used as the objective function, the other for imposing a target constraint. This paper describes an effective heuristic for computing global (or near-global) optimal solutions for this type of problem. The first part of the paper addresses the special case of degeneracy, a condition that makes the system more difficult to solve. Included are means for detecting degeneracy as well as issues relating to its likelihood in practice. The subsequent part of the paper describes our new procedure, AXIS, which rotates a degenerate problem and then decomposes it into a finite sequence of nondegenerate subproblems of lower dimension. The nondegenerate subproblems are solved using the algorithm DRSALG developed earlier. In the final parts of the paper, the AXIS and DRSALG algorithms are integrated into a single dual response solver termed DR2. DR2 is tested against two nonlinear optimization procedures that have been used frequently in dual response applications. The new solver proves to be extremely effective at locating best-practice operating conditions. |
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