Sequential simplex optimization (by S.N. Deming and S.L. Morgan)

188

trendsin analyticalchemistry, vol. 8, no,5,1989

25 P. Divry, C. Vianey-Liaud and J. Cottee, Biomed. Environ. Mass Spectrom., 14 (1987) 663. 26 M. J. Bennett, E. Worthy and R. J. Pollitt, Anal. Proc., 24 (1987) 322. 27 C. L. Hoppel, E. P. Brass, A. P. Gibbons and J. S. Turkaly, Anal. Biochem., 156 (1986) 111. 28 K. Kidouchi, N. Sugiyama, H. Morishita, Y. Wada, S. Nagai and J. Sakakibara, J. Chromatogr., 423 (1987) 297. 29 K. Kidouchi, N. Sugiyama, H. Morishita, M. Kabayashi, Y. Wada and D. Nohara, Clin. Chim. Acta., 164 (1987) 297. 30 K. Kidouchi, T. Niwa, D. Nohara, K. Asai, N. Sugiyama, H. Morishita, M. Kabayashi and Y. Wada, Clin. Chim. Acta., 173 (1988) 263.

31 A. K. M. J. Bhuiyan and K. Bartlett, Biochem. Sot. Trans., 16 (1987) 796. 32 G. P. Weavind, G. A. Mills and V. Walker, Ann. Clin. Biothem., 25 (1988) 233s. 33 P. E. Minkler, S. T. Ingalls, L. S. Kormos, D. E. Weir and C. L. Hoppel, J. Chromatogr., 336 (1984) 271. 34 B. M. Tracey, R. A. Chalmers, J. R. Rosankiewicz, C. De Sousa and T. E. Stacey, Biochem. Sot. Trans., 14 (1986) 700.

35 P. E. Minkler, S. T. Ingalls, L. S. Kormos, D. E. Weir and C. L. Hoppel, J. Chromatogr., 420 (1987) 385. 36 A. L. Yergey, D. J. Liberato and D. S. Millington, Anal. Biochem., 139 (1984) 278. 37 D. S. Millington, C. R. Roe and D. A. Maltby, Biomed. Environ. Mass Spectrom., 14 (1987) 711. 38 M. Duran, D. Ketting, T. E. Beckeringh, D. Leupold and S. K. Wadman, J. Inher. Metab. Dis., 9 (1986) 202. 39 A. K. M. J. Bhuiyan, N. J. Watmough, D. M. Turnbull, A. Aynsley-Green, J. V. Leonard and K. Bartlett, Clin. Chim. Acta, 165 (1987) 39. 40 S. Yamamoto, H. Kakinuma, T. Nishimuta and K. Mori, Zyo Masu Kenkyukai Koenshu, ll(l986) 151.

41 R. A. Iles, A. J. Hind and R. A. Chalmers, Clin. Chem., 31 (1986) 1795. 42 R. A. Iles, J. R. Jago, S. R. Williams, T. E. Stacey, C. De Sousa and R. A. Chalmers, Biochem. Sot. Trans., 14 (1986) 702.

43 G. Hvistendahl,

K. Undheim

and J. Bremer,

Org. Mass

Spectrom., 3 (1970) 1433.

44 M. Barber, R. S. Bordoli, R. D. Sedgwick and A. N. Tyler, J. Chem. Sot., Chem. Commun., (1981) 325. 45 M. L. Vestal, in A. L. Burlingame and N. Castagnoli, Jr. (Editors), Mass Spectrometry in the Health and Life Sciences (Proceedings of an Int. Symp., San Francisco, CA, September 9-13,1984), Elsevier, Amsterdam, 1985, p. 99. 46 F. W. McLafferty (Editor), Tandem Mass Spectrometry, Wi-

ley, New York, 1983. 47 D. S. Millington, T. P. Bohan, C. R. Roe, A. L. Yergey and D. J. Liberato, Clin. Chim. Acta, 145 (1985) 69. 48 D. S. Millington, C. R. Roe and D. A. Maltby, Biomed. Mass Spectrom., ll(l984) 236. 49 C. R. Roe, D. S. Millington, D. A. Maltby and P. Kinnebrew, J. Pediatr., 108 (1986) 13. 50 R. A. Chalmers, B. M. Tracey, T. E. Stacey, K. N. Cheng, M. J. Madigan and A. M. Lawson, Biochem. Sot. Trans., 14 (1986) 967.

51 C. R. Roe, D. S. Millington and D. A. Maltby, J. Clin. Znvest., 77 (1986) 1391. 52 S. J. Gaskell, C. Guenat, D. S. Millington, D. A. Maltby and C. R. Roe, Anal. Chem., 58 (1986) 2801. 53 B. M. Tracey, K. N. Cheng, J. R. Rosankiewicz, T. E. Stacey and R. A. Chalmers, Clin. Chim. Acta., 175 (1988) 79. 54 M. Duran, D. Ketting, L. Dorland and S. K. Wadman, J. Znher. Metab. Dis., 8 Suppl. 2 (1985) 143. Malcolm E. Rose and Stephen Lowes are at the Department of Chemistry, The Open University, Walton Hall, Milton Keynes, MK7 6AA, V. K.

The simplex approach to optimization

Sequential Simplex Optimization, an ACS Audio Course (5 audiocassettes, 4.6 h playing time, 200-page manual, IBM PC diskette), by S. N. Deming and S. L. Morgan, American

Chemical Society, US$465.00 (U.S.A. + Canada)llJS$558.00 (rest of the world), additional manuals: US$35.00/ US$42.00, additional diskettes: US$28.OOlUS$34.00

This course consists of five tapes, each approximately 1 h, complemented by a manual and an IBM PC compatible floppy disk containing various exercises. The manual consists largely of diagrams, with occasional notes and exercises, roughly

corresponding to transparencies or slides that might accompany a series of seminars corresponding to the tapes. The audiotapes consist largely of descriptive lectures although there are three computer-based exercises. The course is intended to appeal to analytical chemists. The introductory sections attempt to justify why thinking about optimization is necessary, especially in analytical process control. The lecturers are careful to define how their approach to optimization differs from classical approaches and mention some limitations of the simplex approach. Chemometricians will probably be a little irritated by these sections: most statisticians feel that simultaneous

factorial designs are more efficient approaches to optimization unless there is difficulty in performing several experiments simultaneously or it is known with a high degree of certainty that only a limited number of factors are significant and that these factors are roughly equal in significance. Also, there is very little discussion of Taguchi methods, which are a very important and topical alternative approach to systems optimization. Chemists often like precise rules and methods and I think that the first lesson they should learn is that there is no automatic solution to their problems: unfortunately, although the introduction does indeed explain why they should be optimiz-

189

trendsinpnalyticalchemistry, vol. 8, no. 5,1989

ing their systems it does not sufficiently emphasize the pitfalls as well as the advantages of the simplex approach and the importance of method choice. I believe that chemists like simplex methods: chemists feel more secure when they are presented with rules; they might also feel that simplex approaches have the possibility of reaching an optimum faster than simultaneous factorial approaches, since, for the latter type of experimental design the chemist is faced with a minimum number of experiments (typically 20 or more) before the system can be adequately modelled and so optimised. So there is an important gap between the need to convince chemists that statistical experimental design really can help them, often best introduced via simplex approaches, and the need to educate chemometricians as to the best choice of design. The lecturers probably address the first problem well, but the students may end up with an oversimplistic and, on some occasions, possibly dangerously incorrect view of the use of experimental design in optimisation. The bulk of the tapes are a systematic description of the simplex approach. This is introduced via systems theory in which the input(s) and desired output(s) of a system are analyzed. The listener is then introduced to response surface methodology. A computer exercise in which the student is asked to optimize the profit of a chemical process dependent on three factors, without being provided with any rules, is then presented. This is analyzed in detail with reference to the shape of response surfaces. There is a very brief section on alternative optimization strategies. It is only roughly half way through the course that a simplex is defined and formally introduced, which I think is rather late into the course. A simplex is geometrically defined and simplex designs are contrasted to grid designs. Simplex rules are introduced, and a worksheet for calculation of simplexes is introduced: the student is then asked to perform an optimization using the IBM PC disk. This optimization is analysed in detail, and the student is introduced to the problems of choice

of stepsize: the advantages of a variable sized simplex are outlined. The next section outlines the rules for the variable sized simplex. Worksheets are introduced and a third computer based exercise, on the variable sized simplex, is introduced. The problems of choosing the initial simplex are then outlined, together with a number of algorithms. Next a strategy for choosing a sequential simplex is outlined. How to choose factors and recognise if significant factors have been omitted from the design are briefly discussed. The final section takes the form of a dialogue with a student who raises a number of problems with simplex methods, such as multioptima response surfaces, simplexes blowing up, stopping criteria, actual experimental measurement errors, replicates, sensitivity of responses and so on. The course strenuously avoidssophisticated mathematics and computer programming and has only limited reference to statistics. It is well co-ordinated, with diagrams, tables, worksheets, computer instructions and exercises closely correlated to the audio material. There are some stylistic differences in the course: the introductory sections are illustrated, in the manual, with brief synopses and summaries of key points as well as diagrams and tables, whereas these synopses are virtually absent in later sections. There are some irritating omissions. It would be useful if the manual indicated which sections correspond to which tape; for example, section J is at the beginning of side 5 (top side of tape 3). Indexes and cross referencing might also make the manual more useful. Although the authors are well known as excellent oral communicators and the course consists of well planned educational material, I do not believe it quite reaches its intended audience. The type of people interested in analytical chemometrics would normally have highly analytical minds and, in my experience, require rather atypical educational material, often preferring written to oral communication. They like to store methods in mental pigeon holes rather than linearly build up their knowledge bases, and to

search through files, texts and manuals in their own way. Students of many other disciplines prefer a linear approach to learning, building up concepts in a systematic way via a sequential series of face to face lectures and get bored working on their own: they are intimidated by large quantities of documentation and prefer listening and talking to writing and reading. Unfortunately, I believe that the course is aimed at this latter type of person, who is not very likely to opt to study highly analytical subjects. I do feel that the approach adopted is valuable but it would possibly be more appreciated by people with less analytical minds: therefore I think that the lecturers should have made strenuous efforts to choose in depth examples from outside analytical chemistry, such as in organic synthesis planning and spectroscopy, and so capture the imagination of mainstream chemists who might well better appreciate the material than more analytically oriented chemists. Overall this is technically well produced course material, presented by two well established and excellent lecturers. It would, however, probably not succeed in specialised analytical chemometrics courses, since the material is too rule based and slightly misleading. The audiotapes are nevertheless good value for money; I think that they could be used by mainstream chemistry students, and industrial scientists who are interested in finding out about simplex methods as a means of understanding the jargon spoken by their more analytical colleagues, rather than by students who wish to understand enough about experimental design to use these methods themselves. There is an important role for this type of educational material. For example, far more people know how to’ interpret a Fourier transform NMR spectrum than actually use a complex NMR spectrometer hands-on themselves. RICHARD G. BRERETON

Richard G. Brereton is at the School of Chemistry, CantockS Close, Bristol BS8 1 TS, U.K.