Optimal Non-isothermal Reactor Network for Van de Vusse Reaction

2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Ravindra S Waghmare ◽  
Arun S Moharir
Keyword(s):  
Reaction Scheme ◽  
Global Optimum ◽  
Phase Plane Analysis ◽  
Local Optima ◽  
True Solution ◽  
Attainable Set ◽  
Plane Analysis ◽  
Reactor Networks ◽  
Reaction Constants ◽  
Reactor Network

For complex reactions the optimal reactor networks can involve several reactors operating at various temperature profiles. The often-reported strategy of optimizing parameters of a heuristically predetermined reactor system (Super-structure Approach) falls short of obtaining true solution due to the presence of multiple local optima. Attainable set method gives Global optimum but requires study of each reaction scheme in depth. Here one such study using phase-plane analysis (instead of convexity based analysis) is reported for finding globally optimal non-isothermal reactor network for van de Vusse reaction (A -> B -> C, 2A -> D, objective is to maximize yield of B). Compared to two-reactor networks proposed earlier, it is found that up to 5 reactors (CSTR with/without bypass of feed, Isothermal PFR, Non-isothermal PFR, CSTR, Isothermal PFR) may be required to get the highest yield of the desired intermediate. The proposed method involves only elementary calculus. The detailed solution algorithm has been described using analogy with highways. Three cases with the values of reaction constants reported in the literature have been solved.

Whole-body phase plane analysis for standard maximum vertical jump assessment

2021 ◽  
Vol 90 ◽  
pp. 203-204
Author(s):  
C. Rodrigues ◽  
M. Correia ◽  
J. Abrantes ◽  
B. Rodrigues ◽  
J. Nadal
Keyword(s):  
Phase Plane ◽  
Vertical Jump ◽  
Whole Body ◽  
Phase Plane Analysis ◽  
Plane Analysis

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Phase-plane analysis of driven multi-lane exclusion models

2012 ◽  
Vol 2012 (04) ◽  
pp. P04004 ◽  
Author(s):  
Vandana Yadav ◽  
Rajesh Singh ◽  
Sutapa Mukherji
Keyword(s):  
Phase Plane ◽  
Phase Plane Analysis ◽  
Plane Analysis

scholarly journals Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanfan Chen ◽  
Dingbian Qian ◽  
Xiying Sun ◽  
Yinyin Wu
Keyword(s):  
Hamiltonian Systems ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Zero Eigenvalue ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Plane Analysis ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Twist Theorem

<p style='text-indent:20px;'>We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.</p>

scholarly journals Bees Algorithm for multimodal function optimisation

2015 ◽  
Vol 230 (5) ◽  
pp. 867-884 ◽  
Author(s):  
ZD Zhou ◽  
YQ Xie ◽  
DT Pham ◽  
S Kamsani ◽  
M Castellani
Keyword(s):  
Global Optimum ◽  
Bees Algorithm ◽  
Benchmark Problems ◽  
Search Technique ◽  
Local Optima ◽  
Multimodal Function ◽  
Real World Applications ◽  
Speed Up ◽  
Search Approach ◽  
Optimisation Procedure

The aim of multimodal optimisation is to find significant optima of a multimodal objective function including its global optimum. Many real-world applications are multimodal optimisation problems requiring multiple optimal solutions. The Bees Algorithm is a global optimisation procedure inspired by the foraging behaviour of honeybees. In this paper, several procedures are introduced to enhance the algorithm’s capability to find multiple optima in multimodal optimisation problems. In the proposed Bees Algorithm for multimodal optimisation, dynamic colony size is permitted to automatically adapt the search effort to different objective functions. A local search approach called balanced search technique is also proposed to speed up the algorithm. In addition, two procedures of radius estimation and optima elitism are added, to respectively enhance the Bees Algorithm’s ability to locate unevenly distributed optima, and eliminate insignificant local optima. The performance of the modified Bees Algorithm is evaluated on well-known benchmark problems, and the results are compared with those obtained by several other state-of-the-art algorithms. The results indicate that the proposed algorithm inherits excellent properties from the standard Bees Algorithm, obtaining notable efficiency for solving multimodal optimisation problems due to the introduced modifications.

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