Multiple objectives

The following points are worthy of note in terms of the placement of data. In the case of studies with multiple objectives, reports should be placed in the section corresponding to their primary purpose. Reports of laboratory studies conducted with human materials to investigate pharmacokinetic effects should be placed in Section 5.3.2 of the clinical module, as opposed to the non-clinical module. A US submission requires that the individual case report forms of all trial subjects that died or were dropped from a study due to adverse events are included in Section 5.3.7. 

Abstract The basic principles of astronomical spectroscopy are introduced and the main types of dispersing element surveyed. The principles behind two modem spectroscopic techniques, multiple object and integral held spectroscopy, are also discussed. 

Figure 4. The efficiency of gratings used in the Gemini Multiple Object Spectrograph (CMOS) from measurements by the vendor in Littrow configuration.

Developing new chemical engineering design tools to deal with the multiple objectives of minimum cost process resilience to changes in inputs minimization of toxic intermediates and products and safe response to upset conditions, start-up, and shutdown. 

Gillet VJ. Designing combinatorial libraries optimized on multiple objectives. Methods Mol Biol 2004 275 335-54. 

In this section we describe extensions of the basic learning methodologies introduced in Sections IV and V that, while preserving the same premises and paradigms, enlarge considerably their scope by adding the capability to consider simultaneously multiple objectives. As before, and without loss of generality, we will focus our attention on the coexistence of several quality-related objectives. 

To conclude this section on systems with multiple objectives, we will consider a specific plasma etching unit case study. This unit will be analyzed considering both categorical and continuous performance measurement variables. Provided that similar preference structures are expressed in both instances, we will see that the two approaches lead to similar final answers. Additional applications of the learning methodologies to multiobjective systems can be found in Saraiva and Stephanopoulos (1992b, c). 

We presented extensions and variations of the basic learning methodologies aimed at enlarging their flexibility and cover a number of different situations, including systems where performance is evaluated by categorical or continuous variables, with single or multiple objectives, simple or complex plants containing some type of internal structure and composed of a number of interconnected subsystems. 

Objectives of the Study. A clear statement of the objectives of the study Is required If statistical methods are to be used effectively In study planning. Many studies have multiple objectives which compete for study resources. An understanding of these objectives by all Involved parties at the outset usually leads to better studies. 

Cavalieri, S. and Gaiardelli, P. (1998) Hybrid genetic algorithms for a multiple-objective scheduling problem. 

Rusnak, I. A. Guez and I. Bar-Kana. Multiple Objective Approach to Adaptive Control of Linear Systems. In Proceedings of the American Control Conference. San Francisco, pp. 1101-1105 (1993). 

Rustem, B. Algorithms for Nonlinear Programming and Multiple Objective Functions. Wiley, New York (1998). 

The second kind of action is a joint action To describe behavior and interactions of a group of objects, we focus on the net effect of interactions between multiple objects, and we specify that effect as a higher-level action with all objects involved. A joint action is written... 

Components are often larger-grained than traditional objects and can be implemented as multiple objects of different classes. They often have complex actions at their interfaces, rather than single messages. 

Keeney, R. L. and Raiffa, R. (1976). Decisions with Multiple Objectives Preferences and Value Tradeoffs. New York John Wiley Sons. 

Designing Combinatorial Libraries Optimized on Multiple Objectives... 

In this chapter, we will give a brief introduction to the basic concepts of chemoinformatics and their relevance to chemical library design. In Section 2, we will describe chemical representation, molecular data, and molecular data mining in computer we will introduce some of the chemoinformatics concepts such as molecular descriptors, chemical space, dimension reduction, similarity and diversity and we will review the most useful methods and applications of chemoinformatics, the quantitative structure-activity relationship (QSAR), the quantitative structure-property relationship (QSPR), multiobjective optimization, and virtual screening. In Section 3, we will outline some of the elements of library design and connect chemoinformatics tools, such as molecular similarity, molecular diversity, and multiple objective optimizations, with designing optimal libraries. Finally, we will put library design into perspective in Section 4. 

When optimizing multiple objectives, usually there is no best solution that has optimal values for all, and oftentimes competing, objectives. Instead, some compromises need to be made among various objectives. If a solution A is better than another solution B for every objective, then solution UB is dominated by A. If a solution is not dominated by any other solution, then it is a nondominated solution. These nondominated solutions are called Pareto-optimal solutions, and very good compromises for a multiobjective optimization problem can be chosen among this set of solutions. Many methods have been developed and continue to be developed to find Pareto-optimal solutions and/or their approximations (see, for example, references (50-52)). Notice that solutions in the Pareto-optimal set cannot be improved on one objective without compromising another objective. 

Searching for Pareto-optimal solutions can be computationally very expensive, especially when too many objectives are to be optimized. Therefore, it is very appealing to convert a multiobjective optimization problem into a much simpler single-objective optimization problem by combining the multiple objectives into a single objective function as follows (53-55) ... 

Problems that require the accommodation of multiple objectives, such as molecular library design, are widely known as multiobjective problems (MOP) or vector optimization problems... 

Gillet, V. J. (2004) Designing combinatorial libraries optimized on multiple objectives in methods in molecular biology, in (Bajorath, J., ed.) Chemoinformatics Concepts, Methods, and Tools for Drug Discovery. Humana Press, Totowa, NJ, 275, pp. 335-354. 

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