Multicriteria optimization

Multiobjective/multicriteria optimization and decision support in drug discovery, in Comprehensive Medicinal Chemistry II, Volume 4 (eds-in-chief J.B. Taylor and D.J. Triggle) (ed J.S. Mason), Elsevier, Oxford, Chapter 30, pp 767-72. 

For readers with no prior knowledge of optimization methods In the textbook of Box et.al. [14] the basic principles of optimization are also explained. The sequential simplex method is presented in Walters et.al. [20]. Multi-criteria optimization is presented in Chapter 4 on an introductory level. For those readers who want to know more about multicriteria optimization, see the references given in Section 1.3.4 and Chapter 4. 

For readers with some knowledge of optimization methods Start reading Chapter 2 and 4, that gives the background material which should be understandable. If a more detailed understanding of, e.g., multicriteria optimization is wanted, then the references in Chapter 4 will suffice. 

Das, I., Dennis, J. E. (1998) Normalboundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8, 631-657. 

In this section, the important aspects of the mathematical basis for optimization methods are described. This will provide the necessary background to understand the most widely used method, LP. Then descriptions of two more effective NLP methods are outlined the generalized reduced gradient method and the successive LP method. Then methods for mixed-integer and multicriteria optimization problems are summarized. 

Halsall-Whitney, H., Taylor, D. and Thibault, J. (2003). Multicriteria optimization of gluconic acid production using net flow. Bioprocess Biosyst. Eng., 25, pp. 299-307. 

Mokeddem, D. and Khellaf, A. (2007). Pareto-optimal solntions for multicriteria optimization of a chemical engineering process nsing a diploid genetic algorithm, Comput. Chem. wg., in press, doi 10.1016/j.compchemeng.2006.12.006. 

Das, I. and Dennis, J. E. (1997). A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems, Structural Optimization 14, 1, pp. 63-69. 

Klamroth, K. and Miettinen, K. (2007). Integrating approximation and interactive decision making in multicriteria optimization. Operations Research To appear (D01 10.1287/opre.l070.0425). 

Klamroth, K., Tind, J. and Wiecek, M. M. (2002). Unbiased approximation in multicriteria optimization, Mathematical Methods of Operations Research 56, pp. 413-437. 

Muniglia, L., Kiss, L.N., Fonteix, C., and Marc, I. (2004). Multicriteria optimization of a single-cell oil production, European J. Oper. Research, 153, 2, 360-369. 

Thibault, J., Taylor, D., and Eonteix, C. (2001). Multicriteria optimization for the production of gluconic acid. 8 International Conference on Computer Applications in Biotechnology Modeling and Control of Biological Processes, Quebec City, Canada, 24-27. 

Vera, J., de Atauri, P., Cascante, M. and Torres, N. V. (2003). Multicriteria optimization of biochemical systems by linear programming application to production of ethanol by Saccharomyces cerevisiae. Biotechnology and Bioengineering, 83(3), 335-343. 

A search of parameters of the model Xopt, which provide the optimal, in a definite sense, approximation to the set of simultaneously unachieved properties, leads to the multicriteria optimization problem. It is formulated as follows To find... 

Besides interesting simulations, optimization tasks can also be performed, if, for instance there is a need to achieve an optimal result with minimal negative factors - harmful side products, costs, etc. The various goals are often contradictory and lead to a multitarget optimization task. Typically, the objective function has to be specified by the user, which means that while the objective functions for parameter estimation and optimal design are usually built-in routines in software like ModEst 6.1, the optimization task requires a user written subroutine. The desirability function technique is especially easy to implement and in many cases sufficient for multicriteria optimization. 

P. Franquart, Multicriteria optimization and methodology of experimental research, Thesis, University of Aix-Marseilles, 1992. 

For multicriteria optimization, the individual criteria are described by means of fuzzy sets and are aggregated then to an appropriate objective function. To define the membership functions of those objective functions, heuristic knowledge can be included. 

Multicriteria optimization Fuzzy sets Enzymatic determination... 

Multicriteria optimization Optimization Atomic emission spectrometry... 

In this chapter, we will report on six basic concepts of multicriteria optimization. Just as the three primary colors (red, yeUow, and blue) can produce an infinite number of pictures and the seven basic notes of the musical scale (do, re, mi, etc.) can produce an infinite number of songs, the six basic concepts we will describe should allow the reader to generate an infinite number of models to solve the complex multiple-criteria decision problems. The six basic concepts are ... 

Z Value functions, in which preferences are represented by powerful numerical ordering and multicriteria optimization problems are reduce to single-criterion optimization (Section 3). 

In Section 8, we offer further comments on multicriteria optimization. 

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