NIMBUS method

Interactive methods, as the name implies, requires interaction with the DM during the solution of the MOO problem. After an iteration of these methods, s/he reviews the Pareto-optimal solution(s) obtained and articulates, for example, further change (either improvement, compromise or none) desired in each of the objectives. These preferences of the DM are then incorporated in formulating and solving the optimization problem in the next iteration. At the end of the iterations, the interactive methods provide one or several Pareto-optimal solutions. Examples of these methods are interactive surrogate worth trade-off method and the NIMBUS method, which have been apphed to several chemical engineering applications. 

Interactive Methods (e.g., interactive surrogate worth tradeoff and NIMBUS methods) Decision maker plays an active role during the solution by interactive methods, which are promising for problems with many objectives. Since they find one or a few optimal solutions meeting the preferences of the DM and not many other solutions, one may consider them as computationally efficient. Time and effort from the DM are continually required, which may not always be practicable. The full range of Pareto optimal solutions may not be available. 

Next, we briefly introduce the satisficing trade-off method and then describe the NIMBUS method in some more detail. We pay more attention to NIMBUS (and software implementing it) because we shall refer to it later when discussing applications. 

The NIMBUS method (Miettinen, 1999 Miettinen and Makela, 1995, 1999, 2000, 2006) is an interactive method based on classification of the objective functions into up to five classes. To be more specific, the DM is asked to specify how the current Pareto optimal solution f(x ) should be improved by classifying the objective functions into classes where the functions /j... 

In the initialization phase of the NIMBUS method, the ranges in the Pareto optimal set, that is, the ideal and the nadir objective vectors are computed to give the DM some information about the possibilities of the problem. The starting point of the solution process can be specified by the DM or it can be a neutral compromise solution located approximately in the middle of the Pareto optimal set. To get it, we set + z )/2 as a reference point and solve (6.4). 

Currently, the NIMBUS method has two implementations WWW-NIMBUS and IND-NIMBUS . The WWW-NIMBUS system (Miettinen and Makela, 2000, 2006) has been operating via the Internet at http //nimbus.it.jyu.fi since 1995 and can be used free of charge for teaching and academic purposes. Only a browser is required for using WWW-NIMBUS and, therefore, the user has always the latest version available. All the computation is performed in the server computer at the University of Jyvaskyla. 

In what follows, we describe and summarize research on multi-objective optimization in chemical engineering reported in Hakanen (2006) and Haka-nen et al. (2004, 2005, 2006, 2008, 2007). These studies have focused on offering chemical engineering an efficient and practical way of handling all the necessary aspects of the problem, that is, to be able to simultaneously consider several conflicting objective functions that affect the behaviour of the problem considered. Therefore, they have been solved using the interactive NIMBUS method. 

WWW-NIMBUS is an implementation of the interactive NIMBUS method operating on the Internet (http //nimbus.it.jyu. fi/). Study the tutorial of the WWW-NIMBUS system (http //nimbus.it.jyu.fi/N4/tutorial/index.html) and answer the following questions. 

This method is based on the affinity of the new chemical entity to a membrane, consisting of human serum albumin immobilized on Transil beads. The silica beads are coated with egg yolk phosphatidylcholine and are commercially available under the trademark Transil from Nimbus (Nimbus Leipzig Germany). 

Reinsel G., Tiao G.C., Lewis R. and Bobkoski M., Analysis of upper stratospheric ozone profile data from the ground-based umkehr method and the Nimbus-4 BUV satellite experiment. J. Geophys. Res. , 88, 5393-5402 (1983). 

In NIMBUS, the DM iteratively expresses his/her desires and learns about the feasible solutions available for the problem considered. Unlike some other methods based on classification, the success of the solution process does not depend entirely on how well the DM manages in specifying... 

Miettinen, K. and Makela, M. (1995). Interactive bundle-based method for non-differentiable multiobjective optimization NIMBUS, Optimization 34, pp. 231-246. 

Method Nondifferentiable interactive multiobjective bundle-based optimization Authors Kaisa Miettinen, University of Jyvaskyla, Finland Contact http //nimbus.mit.jyu.fl/... 

This paper describes the method used to insulate a 105,000-gal liquid-hydrogen tank for Aerojet General at Nimbus Station, California. Extension of this technique to large barges and space simulator cryopanels is also described. 

I think it unnecessary to stress that only the first system, HDRSS, is of interest to us. For Nimbus 1 and 2 a single taperecorder was used (HRIR). Nimbus 3 inaugurated the method of doubling up recorders. Nimbus 1 ended its brief career with a malfunction of its solar panels. For Nimbus 2 through 5 the difficulties centered on taperecorder malfunctions. It is curious to note that the chief weak point in satellites occurs in the utilization of magnetic tape. The future - a close one we hope - will short-circuit onboard recording and operate directly and continuously via relay satellites. 

I will set aside the case of Nimbus 5 and F their methods of operation are the same as for the earlier Nimbus (see Chapter IV and Appendix D). For ERTS, the situation is different. 

The retrieval method has been used extensively for temperature profile retrieval in both the terrestrial and other planetary atmospheres. Examples of profiles obtained by this technique for Earth, Mars, Jupiter, Saturn, Uranus, and Neptune are shown in Fig. 8.2.2. Also included is a Titan profile obtained from radio occultation data. The profiles for Earth and Mars were derived from measurements obtained with the Fourier transform spectrometers carried on Nimbus 3, 4, and Mariner 9, respectively. In both cases data from the 15 ptm. CO2 absorption band were used. The profiles for the outer planets were obtained by inversion of measurements from the Voyager Fourier transform spectrometers. For Jupiter and Saturn, data from the S(0) and S(l) collision-induced H2 lines between 200 and 600 cm were used, along with measurements from the CH4 V4-band centered near 1300 cm . Because of the extremely low temperatures encountered on Uranus and Neptune, adequate signal-to-noise ratio for the retrieval of vertical thermal stmctures was obtained... 

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