Optimal control of the Sabatier process in microchannel reactors

AbstractWe consider the optimization of a chemical microchannel reactor by means of PDE-constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software package cashocs which implements the adjoint approach and facilitates the numerical solution of the subsequent optimization problems. We solve a parameter identification problem numerically to determine necessary kinetic parameters for the models from experimental data given in the literature. The obtained results show excellent agreement to the measurements. Finally, we present two optimization problems for optimizing the reactor’s product yield. First, we use a tracking-type cost functional to maximize the reactant conversion, keep the flow rate of the reactor fixed, and use its wall temperature as optimization variable. Second, we consider the wall temperature and the inlet gas velocity as optimization variables, use an objective functional for maximizing the flow rate in the reactor, and ensure the quality of the product by means of a state constraint. The results obtained from solving these problems numerically show great potential for improving the design of the microreactor.

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Truss geometry and topology optimization with global stability constraints

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-020-02634-z ◽

2020 ◽

Vol 62 (4) ◽

pp. 1721-1737

Author(s):

Alemseged Gebrehiwot Weldeyesus ◽

Jacek Gondzio ◽

Linwei He ◽

Matthew Gilbert ◽

Paul Shepherd ◽

...

Keyword(s):

Topology Optimization ◽

Global Stability ◽

Optimization Problems ◽

Optimization Techniques ◽

Truss Structures ◽

Cross Sectional ◽

And Topology ◽

Highly Nonlinear ◽

Primal Dual ◽

The Cross

Abstract In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the cross-sectional areas of the bars and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal-dual interior point implementation. During the solution process, both the cross-sectional areas of the bars and the coordinates of the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and to improve the quality of the optimal designs.

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A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

Volume 2A: 42nd Design Automation Conference ◽

10.1115/detc2016-59151 ◽

2016 ◽

Author(s):

Po Ting Lin ◽

Wei-Hao Lu ◽

Shu-Ping Lin

Keyword(s):

Design Optimization ◽

Design Space ◽

Optimization Problems ◽

Nonlinear Problems ◽

Kernel Functions ◽

Sensitivity Analyses ◽

Normal Space ◽

Highly Nonlinear ◽

Standard Normal ◽

Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

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Joint Optimization on Trajectory, Cache Placement, and Transmission Power for Minimum Mission Time in UAV-Aided Wireless Networks

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi10070426 ◽

2021 ◽

Vol 10 (7) ◽

pp. 426

Author(s):

Tingting Lan ◽

Danyang Qin ◽

Guanyu Sun

Keyword(s):

Wireless Communication ◽

Power Allocation ◽

Optimization Problems ◽

Base Station ◽

Optimization Techniques ◽

Joint Optimization ◽

Transmission Power ◽

Wireless Backhaul ◽

Mission Time ◽

Cache Placement

In recent years, due to the strong mobility, easy deployment, and low cost of unmanned aerial vehicles (UAV), great interest has arisen in utilizing UAVs to assist in wireless communication, especially for on-demand deployment in emergency situations and temporary events. However, UAVs can only provide users with data transmission services through wireless backhaul links established with a ground base station, and the limited capacity of the wireless backhaul link would limit the transmission speed of UAVs. Therefore, this paper designed a UAV-assisted wireless communication system that used cache technology and realized the transmission of multi-user data by using the mobility of UAVs and wireless cache technology. Considering the limited storage space and energy of UAVs, the joint optimization problem of the UAV’s trajectory, cache placement, and transmission power was established to minimize the mission time of the UAV. Since this problem was a non-convex problem, it was decomposed into three sub-problems: trajectory optimization, cache placement optimization, and power allocation optimization. An iterative algorithm based on the successive convex approximation and alternate optimization techniques was proposed to solve these three optimization problems. Finally, in the power allocation optimization, the proposed algorithm was improved by changing the optimization objective function. Numerical results showed that the algorithm had good performance and could effectively reduce the task completion time of the UAV.

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Assessing the performances of recent global search algorithms using analytic objective functions and seismic optimization problems

Geophysics ◽

10.1190/geo2019-0111.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. R767-R781 ◽

Cited By ~ 1

Author(s):

Mattia Aleardi ◽

Silvio Pierini ◽

Angelo Sajeva

Keyword(s):

Particle Swarm Optimization ◽

Optimization Problems ◽

Particle Swarm ◽

Model Space ◽

Global Search ◽

Objective Functions ◽

Swarm Optimization ◽

Fireworks Algorithm ◽

Highly Nonlinear ◽

Whale Optimization

We have compared the performances of six recently developed global optimization algorithms: imperialist competitive algorithm, firefly algorithm (FA), water cycle algorithm (WCA), whale optimization algorithm (WOA), fireworks algorithm (FWA), and quantum particle swarm optimization (QPSO). These methods have been introduced in the past few years and have found very limited or no applications to geophysical exploration problems thus far. We benchmark the algorithms’ results against the particle swarm optimization (PSO), which is a popular and well-established global search method. In particular, we are interested in assessing the exploration and exploitation capabilities of each method as the dimension of the model space increases. First, we test the different algorithms on two multiminima and two convex analytic objective functions. Then, we compare them using the residual statics corrections and 1D elastic full-waveform inversion, which are highly nonlinear geophysical optimization problems. Our results demonstrate that FA, FWA, and WOA are characterized by optimal exploration capabilities because they outperform the other approaches in the case of optimization problems with multiminima objective functions. Differently, QPSO and PSO have good exploitation capabilities because they easily solve ill-conditioned optimizations characterized by a nearly flat valley in the objective function. QPSO, PSO, and WCA offer a good compromise between exploitation and exploration.

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Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.215-216.133 ◽

2012 ◽

Vol 215-216 ◽

pp. 133-137

Author(s):

Guo Shao Su ◽

Yan Zhang ◽

Zhen Xing Wu ◽

Liu Bin Yan

Keyword(s):

Stochastic Optimization ◽

Covariance Matrix ◽

Optimization Problems ◽

Fitness Function ◽

Optimization Methods ◽

Evolution Strategy ◽

Covariance Matrix Adaptation ◽

Study Results ◽

Highly Nonlinear ◽

Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

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Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

ACM Transactions on Evolutionary Learning and Optimization ◽

10.1145/3469801 ◽

2021 ◽

Vol 1 (4) ◽

pp. 1-26

Author(s):

Faramarz Khosravi ◽

Alexander Rass ◽

Jürgen Teich

Keyword(s):

Optimization Problems ◽

Statistical Tests ◽

Optimization Techniques ◽

Simultaneous Optimization ◽

Sampled Data ◽

Efficient Computation ◽

Multi Objective Optimization ◽

Multi Objective ◽

Conflicting Objectives ◽

Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

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Evolutionary Algorithms for Constrained Parameter Optimization Problems

Evolutionary Computation ◽

10.1162/evco.1996.4.1.1 ◽

1996 ◽

Vol 4 (1) ◽

pp. 1-32 ◽

Cited By ~ 1027

Author(s):

Zbigniew Michalewicz ◽

Marc Schoenauer

Keyword(s):

Nonlinear Programming ◽

Evolutionary Algorithms ◽

Evolutionary Computation ◽

Numerical Optimization ◽

Optimization Problems ◽

Optimization Techniques ◽

Test Cases ◽

Nonlinear Constraints ◽

Nonlinear Programming Problem ◽

General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

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Comparative Study of Optimization Algorithms for The Optimal Reservoir Operation

MATEC Web of Conferences ◽

10.1051/matecconf/201824601003 ◽

2018 ◽

Vol 246 ◽

pp. 01003

Author(s):

Xinyuan Liu ◽

Yonghui Zhu ◽

Lingyun Li ◽

Lu Chen

Keyword(s):

Reservoir Operation ◽

Optimization Problems ◽

Optimization Algorithms ◽

Complex Problem ◽

Optimization Techniques ◽

Decision Variables ◽

Handling Methods ◽

Optimality Algorithm ◽

Parameter Values

Apart from traditional optimization techniques, e.g. progressive optimality algorithm (POA), modern intelligence algorithms, like genetic algorithms, differential evolution have been widely used to solve optimization problems. This paper deals with comparative analysis of POA, GA and DE and their applications in a reservoir operation problem. The results show that both GA and DES are feasible to reservoir operation optimization, but they display different features. GA and DE have many parameters and are difficult in determination of these parameter values. For simple problems with mall number of decision variables, GA and DE are better than POA when adopting appropriate parameter values and constraint handling methods. But for complex problem with large number of variables, POA combined with simplex method are much superior to GA and DE in time-assuming and quality of optimal solutions. This study helps to select proper optimization algorithms and parameter values in reservoir operation.

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Virtual Machine Placement Using Energy Efficient Particle Swarm Optimization in Cloud Datacenter

Cybernetics and Information Technologies ◽

10.2478/cait-2021-0005 ◽

2021 ◽

Vol 21 (1) ◽

pp. 62-72

Author(s):

R. B. Madhumala ◽

Harshvardhan Tiwari ◽

Verma C. Devaraj

Keyword(s):

Particle Swarm Optimization ◽

Virtual Machine ◽

Optimization Problems ◽

Particle Swarm ◽

Pso Algorithm ◽

Optimization Techniques ◽

Virtual Machine Placement ◽

Placement Problem ◽

Swarm Optimization ◽

Cloud Datacenter

Abstract Efficient resource allocation through Virtual machine placement in a cloud datacenter is an ever-growing demand. Different Virtual Machine optimization techniques are constructed for different optimization problems. Particle Swam Optimization (PSO) Algorithm is one of the optimization techniques to solve the multidimensional virtual machine placement problem. In the algorithm being proposed we use the combination of Modified First Fit Decreasing Algorithm (MFFD) with Particle Swarm Optimization Algorithm, used to solve the best Virtual Machine packing in active Physical Machines to reduce energy consumption; we first screen all Physical Machines for possible accommodation in each Physical Machine and then the Modified Particle Swam Optimization (MPSO) Algorithm is used to get the best fit solution.. In our paper, we discuss how to improve the efficiency of Particle Swarm Intelligence by adapting the efficient mechanism being proposed. The obtained result shows that the proposed algorithm provides an optimized solution compared to the existing algorithms.

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A Survey on Dragonfly Algorithm and its Applications in Engineering

10.36227/techrxiv.11811768.v2 ◽

2020 ◽

Author(s):

Chnoor M. Rahman ◽

Tarik A. Rashid

Keyword(s):

Review Paper ◽

Optimization Problems ◽

Optimization Techniques ◽

Superior Performance ◽

Test Functions ◽

Dragonfly Algorithm ◽

Engineering Problems ◽

Complex Optimization ◽

Metaheuristic Techniques ◽

Benchmark Test Functions

Dragonfly algorithm developed in 2016. It is one of the algorithms used by the researchers to optimize an extensive series of uses and applications in various areas. At times, it offers superior performance compared to the most well-known optimization techniques. However, this algorithm faces several difficulties when it is utilized to enhance complex optimization problems. This work addressed the robustness of the method to solve real-world optimization issues, and its deficiency to improve complex optimization problems. This review paper shows a comprehensive investigation of the dragonfly algorithm in the engineering area. First, an overview of the algorithm is discussed. Besides, we also examine the modifications of the algorithm. The merged forms of this algorithm with different techniques and the modifications that have been done to make the algorithm perform better are addressed. Additionally, a survey on applications in the engineering area that used the dragonfly algorithm is offered. A comparison is made between the algorithm and other metaheuristic techniques to show its ability to enhance various problems. The outcomes of the algorithm from the works that utilized the dragonfly algorithm previously and the outcomes of the benchmark test functions proved that in comparison with some techniques, the dragonfly algorithm owns an excellent performance, especially for small to intermediate applications. Moreover, the congestion facts of the technique and some future works are presented. The authors conducted this research to help other researchers who want to study the algorithm and utilize it to optimize engineering problems.

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