Multi-objective optimization and decision visualization of batch stirred tank reactor based on spherical catalyst particles

Abstract

This paper presents a Bayesian approach rooted algorithm oriented to the properties of multi-objective optimization problems. The performance of the developed algorithm is compared with several other multi-objective optimization algorithms. The approach is applied to the multiobjective optimization of a batch stirred tank reactor based on spherical catalyst microreactors. The microbioreactors are computationally modeled by a two-compartment model based on reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten enzyme kinetics. A two-stage visualization procedure based on the multi-dimensional scaling is proposed and applied for the visualization of trade-off solutions and for the selection of favorable configurations of the bioreactor.

On the unique weak solvability of second-order unconditionally stable difference scheme for the system of sine-Gordon equations

“…and by (32) sin δw km → sin δ wk strongly in L 2 (0, T ; H), which proves the existence of wk a.e. in H and w0 = w 0 .…”

“…The weak and global solutions, nonlinear dynamics of PDEs, finite-difference and finite-element methods are extensively studied by many scientists (see [1,6,[13][14][15][16][17][18][19][20][21][22][23]28,32] and the references given therein).…”