Sequential Optimization Methods

Comprehensive Chemometrics

Volumn 1, Issue , 2009, Pages 547-575

  Dejaegher, B ^a   Heyden, Y V ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Doehlert designs; Evolutionary operation; Fibonacci numbers; Full factorial designs; Mixed sequential simultaneous optimization methods approaches; Modified simplex method; One variable at a time approach; Sequential optimization method; Simplex method; Steepest ascent method; Univariate optimization

Indexed keywords

EID: 67650359427     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452701-1.00036-3     Document Type: Chapter

References (49)

1. Massart D.L., Vandeginste B.G.M., Buydens L.M.C., De Jong S., Lewi P.J., Smeyers-Verbeke J. Handbook of Chemometrics and Qualimetrics: Part A 1997, Elsevier, Amsterdam.
2. Massart D.L., Dijkstra A., Kaufman L. Evaluation and Optimization of Laboratory Methods and Analytical Procedures, a Survey of Statistical and Mathematical Techniques 1978, Elsevier, Amsterdam.
3. Walters F.H., Parker L.R., Morgan S.L., Deming S.N. Sequential Simplex Optimization, a Technique for Improving Quality and Productivity in Research, Development, and Manufacturing 1991, CRC Press, Boca Raton, FL.
4. Vander Heyden Y., Perrin C., Massart D.L. Optimization Strategies for HPLC and CZE. Handbook of Analytical Separations, 1, Separation Methods in Drug Synthesis and Purification 2000, Elsevier, Amsterdam, pp 163-212.
5. Xiaoning W., Smeyers-Verbeke J., Massart D.L. Linearization of Atomic Absorption Calibration Curves. Analusis 1992, 20:209-215.
6. Spendley W., Hext G.R., Himsworth F.R. Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation. Technometrics 1962, 4:441-461.
7. Burton K.W.C., Nickless G. Optimisation via Simplex, Part I. Background, Definitions and a Simple Application. Chemom. Intell. Lab. Syst. 1987, 1:135-149.
8. Nelder J.A., Mead R. A Simplex Method for Function Minimization. Comput. J. 1965, 7:308-313.
9. Morgan E., Burton K.W., Nickless G. Optimization Using the Modified Simplex Method. Chemom. Intell. Lab. Syst. 1990, 7:209-222.
10. Long D.E. Simplex Optimization of the Response from Chemical Systems. Anal. Chim. Acta 1969, 46:193-206.
11. Morgan S.L., Deming S.N. Simplex Optimization of Analytical Chemical Methods. Anal. Chem. 1974, 46:1170-1181.
12. Berridge J.C. Simplex Optimization of High-Performance Liquid Chromatographic Separations. J. Chromatogr. 1989, 485:3-14.
13. Aberg E.R., Gustavsson A.G.T. Design and Evaluation of Modified Simplex Methods. Anal. Chim. Acta 1982, 144:39-53.
14. Yarbro L.A., Deming S.N. Selection and Preprocessing of Factors for Simplex Optimization. Anal. Chim. Acta 1974, 73:391-398.
15. Öberg T. Importance of the First Design Matrix in Experimental Simplex Optimization. Chemom. Intell. Lab. Syst. 1998, 44:147-151.
16. Derringer G., Suich R. Simultaneous Optimization of Several Response Variables. J. Qual. Technol. 1980, 12:214-219.
17. Smilde A.K., Knevelman A., Coenegracht P.M.J. Introduction of Multi-Criteria Decision Making in Optimization Procedures for High-Performance Liquid Chromatographic Separations. J. Chromatogr. 1986, 369:1-10.
18. Routh M.W., Swartz P.A., Denton M.B. Performance of the Super-Modified Simplex. Anal. Chem. 1977, 49:1422-1428.
19. Morgan E., Burton K.W., Nickless G. Optimization Using the Super Modified Simplex Method. Chemom. Intell. Lab. Syst. 1990, 8:97-107.
20. Ryan P.B., Barr R.L., Todd H.D. Simplex Techniques for Nonlinear Optimization. Anal. Chem. 1980, 52:1460-1467.
21. van der Wiel P.F.A. Improvement of the Super-Modified Simplex Optimization Procedure. Anal. Chim. Acta 1980, 122:421-433.
22. van der Wiel P.F.A., Maassen R., Kateman G. The Symmetry-Controlled Simplex Optimization Procedure. Anal. Chim. Acta 1983, 153:83-92.
23. Subrahmanyam M.B. An Extension of the Simplex Method to Constrained Nonlinear Optimization. J. Optim. Theory Appl. 1989, 62:311-319.
24. Shao M.H. Techniques and Performance of the Advanced Regular Simplex Method. Anal. Chim. Acta 1991, 248:31-39.
25. Hedlund P., Gustavsson A. Design and Evaluation of Modified Simplex Methods Having Enhanced Convergence Ability. Anal. Chim. Acta 1992, 259:243-256.
26. Hedlund P., Gustavsson A. Design and Evaluation of an Improved Simplex Method. Anal. Chim. Acta 1998, 371:9-21.
27. Hedlund P., Gustavsson A. Design and Evaluation of an Effective Modified Simplex Method. Anal. Chim. Acta 1999, 391:257-267.
28. Santos-Delgado M.J., Crespo-Corral E., Polo-Díez L.M. Determination of Herbicides in Soil Samples by Gas Chromatography: Optimization by the Simplex Method. Talanta 2000, 53:367-377.
29. Pasamontes A., Callao P. Fractional Factorial Design and Simplex Algorithm for Optimizing Sequential Injection Analysis (SIA) and Second Order Calibration. Chemom. Intell. Lab. Syst. 2006, 83:127-132.
30. Kolossváry G.J. Optimization of Lipase Activity from Rhizopus sp. in Triglyceride Hydrolysis Using a Modified Simplex Method. Process Biochem. 1996, 31:595-600.
31. Snijders H., Janssen H.G., Cramers C. Optimization of Temperature-Programmed Gas Chromatographic Separations, II. Off-Line Simplex Optimization and Column Selection. J. Chromatogr. A 1996, 756:175-183.
32. Vereda E., Rios A., Valvárcel M. Quality Compromises Incorporated in Simplex Optimization of a Flow Injection System. Anal. Chim. Acta 1997, 348:129-134.
33. Zuloaga O., Etxebarria N., Fernández L.A., Madariaga J.M. MultiSimplex Optimisation of Purge-and-Trap Extraction of Phenols in Soil Samples. J. Chromatogr. A 1999, 849:225-234.
34. Zuloaga O., Etxebarria N., Fernández L.A., Madariaga J.M. MultiSimplex Optimisation and Comparison of Different Purge-and-Trap Extractions of Volatile Organic Compounds in Soil Samples. Anal. Chim. Acta 2000, 416:43-53.
35. Vannecke C., Nguyen Minh Nguyet A., Bloomfield M.S., Staple A.J., Vander Heyden Y., Massart D.L. Development and Optimisation of a Flow Injection Assay for Fluticasone Propionate Using an Asymmetrical Design and the Variable-Size Simplex Algorithm. J. Pharm. Biomed. Anal. 2000, 23:291-306.
36. Srijaranai S., Burakham R., Deming R.L., Khammeng T. Simplex Optimization of Ion-Pair Reversed-Phase High Performance Liquid Chromatographic Analysis of Some Heavy Metals. Talanta 2002, 56:655-661.
37. Murillo Pulgarín J.A., Alañón Molina A., Alañón Pardo M.T. The Use of Modified Simplex Method to Optimize the Room Temperature Phosphorescence Variables in the Determination of an Antihypertensive Drug. Talanta 2002, 57:795-805.
38. Murillo Pulgarín J.A., Alañón Molina A., Alañón Pardo M.T. Determination of 4-Methylpropranolol in Cerebrospinal Fluid, Serum, and Urine by Nonprotected Fluid Room-Temperature Phosphorescence Using Simplex Optimization. Anal. Biochem. 2002, 306:270-277.
39. Cortazar E., Zuloaga O., Sanz J., Raposo J.C., Etxebarria N., Fernández L.A. MultiSimplex Optimisation of the Solid-Phase Microextraction-Gas Chromatographic-Mass Spectrometric Determination of Polycylic Aromatic Hydrocarbons, Polychlorinated Biphenyls and Phthalates from Water Samples. J. Chromatogr. A 2002, 978:165-175.
40. Kuppithayanant N., Rayanakorn M., Wongpornchai S., Prapamontol T., Deming R.L. Enhanced Sensitivity and Selectivity in the Detection of Polycyclic Aromatic Hydrocarbons Using Sequential Simplex Optimization, the Addition of an Organic Modifier and Wavelength Programming. Talanta 2003, 61:879-888.
41. Murillo Pulgarín J.A., Alañón Molina A., Alañón Pardo M.T. Simplex Optimization and Kinetic Determination of Nabumetone in Pharmaceutical Preparations by Micellar-Stabilized Room Temperature Phosphorescence. Anal. Chim. Acta 2005, 528:77-82.
42. Murillo Pulgarín J.A., Alañón Molina A., Alañón Pardo M.T. Simplex Optimization of the Variables Affecting the Micelle-Stabilized Room Temperature Phosphorescence of 6-Methoxy-2-Naphtylacetic Acid and Its Kinetic Determination in Urine. Anal. Biochem. 2005, 339:157-164.
43. Tinoi J., Rakariyatham N., Deming R.L. Simplex Optimization of Carotenoid Production by Rhodotorula glutinis Using Hydrolyzed Mung Bean Waste Flour as Substrate. Process Biochem. 2005, 40:2551-2557.
44. Dahlén J., von Eckardstein S. Development of a Capillary Zone Electrophoresis Method Including a Factorial Design and Simplex Optimization for Analysis of Amphetamine, Amphetamine Analogues, Cocaine, and Heroin. Forensic Sci. Int. 2006, 157:93-105.
45. Sultan S.M., El-Mubarak A.H. High Performance Liquid Chromatographic Method for the Separation and Quantification of Some Psychotherapeutic Benzodiazepines Optimized by the Modified Simplex Procedure. Talanta 1996, 43:569-576.
46. Dol I., Knochen M. Flow-Injection Spectrophotometric Determination of Salbutamol with 4-Aminoantipyrine. Talanta 2004, 64:1233-1236.
47. Brooks S.H. A Comparison of Maximum-Seeking Methods. Oper. Res. 1959, 7:430-457.
48. Box G.E.P. Evolutionary Operation, a Method for Increasing Industrial Productivity. Appl. Stat. 1957, 6:81-91.
49. García Campaña A.M., Cuadros Rodríguez L., Lupiañez González A., Alés Barrero F., Román Ceba M. Sequential Response Surface Methodology for Multioptimization in Analytical Chemistry with Three-Variable Doehlert Designs. Anal. Chim. Acta 1997, 348:237-246.