Multi-objective differential

Multi-objective differential evolution (MODE) The work Babu et al. (2005) is very similar to that of Yee etal. (2003) except for different values for some model parameters (which affect the results). Babu et al. (2005)... 

I-MODE Improved Multi-objective Differential Evolution... 

Sharma, S. and Rangaiah, G.R (2013b) An improved multi-objective differential evolution with a termination criterion for optimizing chemical processes. Computers Chemical Engineering, 56, 155-173. 

Multi-Objective Differential Evolution (MODE). This is a custom multiobjective variant (with elitism) of Differential Evolution (DE) [24], that simply combines with the classic DE mutation/crossover operators the non-dominated sorting and crowding distance mechanisms used in NSGA2 (see below). We set crossover rate Cr = 0.3 and scale factor F = 0.5. 

Babu, B. and Jeban, M. M. L. (2003). Differential evolution for multi-objective optimization, in Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Vol.4 (IEEE Press, Canberra, Australia), pp. 2696-2703. 

The SMB model consists of partial differential equations (PDFs) for the concentrations of chemical components, restrictions for the connections between different columns and cyclic steady-state constraints (Kawajiri and Biegler, 2006b). Previously, the SMB processes have been usually optimized with respect to one objective only. Recently, multi-objective optimization has been applied in periodic separation processes (Ko and Moon, 2002), in gas separation and in SMB processes (Subramani et al., 2003). Ko and Moon used a modified sum of weighted objective functions to obtain a representation of the Pareto optimal set. Their approach is valid for two objective functions only. On the other hand, Subramani et al. applied EMO to a problem where they had two or three objective functions. 

In this chapter, the integrated design and control of bioprocesses was considered as a multi-objective optimization problem subject to non-linear differential-algebraic constraints. This formulation has a number of advantages over the traditional sequential approach, not only because it takes into account the process dynamics associated to a particular design, but also it provides a set of possible solutions from which the engineer can choose the most appropriate to his/her requirements. However, these problems are usually challenging to solve due to their non-convexity, which causes the failure of procedures based on local (e.g. SQP) NLP solvers. 

Spectroscopy has become a powerful tool for the determination of polymer structures. The major part of the book is devoted to techniques that are the most frequently used for analysis of rubbery materials, i.e., various methods of nuclear magnetic resonance (NMR) and optical spectroscopy. One chapter is devoted to (multi) hyphenated thermograviometric analysis (TGA) techniques, i.e., TGA combined with Fourier transform infrared spectroscopy (FT-IR), mass spectroscopy, gas chromatography, differential scanning calorimetry and differential thermal analysis. There are already many excellent textbooks on the basic principles of these methods. Therefore, the main objective of the present book is to discuss a wide range of applications of the spectroscopic techniques for the analysis of rubbery materials. The contents of this book are of interest to chemists, physicists, material scientists and technologists who seek a better understanding of rubbery materials. 

Differential equations of the mentioned multi-state object can be written in matrix shape ... 

Object-oriented modelling based on differential algebraic equations offers large expressive power for establishing multi-disciplinary engineering tools. In addition, the structure of an Object-Oriented Model (OOM) resembles the functional paths that cause a technical system to operate. This property is exploited by the minimal path sets detection method. 

---