Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I: Mathematical Derivation of Adjoint Lattice Boltzmann Equations

2014 ◽  
Vol 6 (5) ◽  
pp. 570-589 ◽  
Author(s):  
Mohamad Hamed Hekmat ◽  
Masoud Mirzaei
Keyword(s):  
Cost Function ◽  
Lattice Boltzmann ◽  
Optimization Problems ◽  
General Procedure ◽  
Main Idea ◽  
Distribution Functions ◽  
Adjoint Equations ◽  
Aerodynamic Optimization ◽  
Discrete Adjoint ◽  
The Cost

AbstractThe significance of flow optimization utilizing the lattice Boltzmann (LB) method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques. These unique characteristics of the LB method form the main idea of its application to optimization problems. In this research, for the first time, both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost. The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector. Moreover, this approach was not limited to flow fields and could be employed for steady as well as unsteady flows. Initially, the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time, respectively. Meanwhile, new adjoint concepts in lattice space were introduced. Finally, the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

scholarly journals Development of Discrete Adjoint Approach Based on the Lattice Boltzmann Method

2014 ◽  
Vol 6 ◽  
pp. 230854 ◽  
Author(s):  
Mohamad Hamed Hekmat ◽  
Masoud Mirzaei
Keyword(s):  
Cost Function ◽  
Optimization Problems ◽  
General Procedure ◽  
Adjoint Equation ◽  
Adjoint Equations ◽  
Test Case ◽  
Inverse Optimization Problem ◽  
Discrete Adjoint ◽  
Adjoint Approach ◽  
The Cost

The purpose of this research is to present a general procedure with low implementation cost to develop the discrete adjoint approach for solving optimization problems based on the LB method. Initially, the macroscopic and microscopic discrete adjoint equations and the cost function gradient vector are derived mathematically, in detail, using the discrete LB equation. Meanwhile, for an elementary case, the analytical evaluation of the macroscopic and microscopic adjoint variables and the cost function gradients are presented. The investigation of the derivation procedure shows that the simplicity of the Boltzmann equation, as an alternative for the Navier-Stokes (NS) equations, can facilitate the process of extracting the discrete adjoint equation. Therefore, the implementation of the discrete adjoint equation based on the LB method needs fewer attempts than that of the NS equations. Finally, this approach is validated for the sample test case, and the results gained from the macroscopic and microscopic discrete adjoint equations are compared in an inverse optimization problem. The results show that the convergence rate of the optimization algorithm using both equations is identical and the evaluated gradients have a very good agreement with each other.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

An Efficient Unsteady Adjoint Optimization System for Multistage Turbomachinery

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance Method ◽  
Adjoint Equations ◽  
Aerodynamic Optimization ◽  
Flow Equations ◽  
Optimization System ◽  
Unsteady Aerodynamic ◽  
Flow Features ◽  
The Cost ◽  
Unsteady Adjoint

Unsteady blade row interactions play an important role in the performance of multistage turbomachinery. However, most aerodynamic optimizations of multistage turbomachinery are based on mixing-plane steady flow simulations. To take into account the unsteady flow features in the optimization cycle, this paper develops an adjoint-based unsteady aerodynamic optimization system for multistage turbomachinery. To the authors' best knowledge, this is the first work in the literature conducting the unsteady adjoint aerodynamic optimization of multistage turbomachinery. The unsteady flow equations and the discrete adjoint equations are solved using a finite volume code, with the harmonic balance method adopted to reduce the cost of unsteady simulations. The system is applied to the unsteady aerodynamic optimization of a 1.5-stage compressor. Results show the efficiency and capability of the proposed framework for the unsteady aerodynamic optimization of multistage turbomachinery.

A Novel Modified Artificial Bee Colony for DOA Estimation

2019 ◽  
Vol 09 ◽  
Author(s):  
Seyed Ahmadreza Hashemi Parsa ◽  
Ataolah Ebrahim Zadeh ◽  
Seyed Javad Kazemitabar
Keyword(s):  
Cost Function ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Main Idea ◽  
Doa Estimation ◽  
Second Order ◽  
Bee Colony ◽  
Non Linear ◽  
Code Division Multiple

: We consider the direction of arrival (DOA) estimation for code division multiple access (CDMA) signals. Solving this problem requires non-linear optimization and thus, speed of convergence becomes crucial. Evolutionary methods have proven to be effective in solving non-linear optimization problems. In this paper a novel modified artificial bee colony (MABC) has been proposed. We use second order Taylor series expansion of the cost function to ameliorate the search ability of artificial bee colony (ABC) for finding the globally optimal solution. The main idea is to harness the exploration and exploitation features. The optimum points of second order Taylor expansion of cost function is used as velocity factor of the ABC algorithm. The proposed technique is used for solving the DOA estimation problem of a CDMA system. Simulation results confirm the performance improvement of our proposed algorithm.

scholarly journals FINDING MINIMA IN COMPLEX LANDSCAPES: ANNEALED, GREEDY AND RELUCTANT ALGORITHMS

2005 ◽  
Vol 15 (09) ◽  
pp. 1349-1369 ◽  
Author(s):  
PIERLUIGI CONTUCCI ◽  
CRISTIAN GIARDINÀ ◽  
CLAUDIO GIBERTI ◽  
CECILIA VERNIA
Keyword(s):  
Complex Systems ◽  
Cost Function ◽  
Spin Glasses ◽  
Optimization Problems ◽  
New Class ◽  
Kirkpatrick Model ◽  
Annealing Procedure ◽  
The Cost ◽  
Complex Landscapes

We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced greedy-reluctant strategy drive the systems towards the deepest minimum of the cost function. Results are presented for the Sherrington–Kirkpatrick model of spin-glasses.

Genetic Algorithm for the Optimization of Collaborative Systems

2007 ◽  
Vol 11 (7) ◽  
pp. 793-802
Author(s):  
Tad Gonsalves ◽  
◽  
Shinichiro Baba ◽  
Kiyoshi Itoh ◽  
Keyword(s):  
Genetic Algorithm ◽  
Cost Function ◽  
Job Scheduling ◽  
Optimization Problems ◽  
Collaborative Systems ◽  
Service Cost ◽  
Combinatorial Optimization Problems ◽  
Operational Optimization ◽  
Waiting Cost ◽  
The Cost

The “survival of the fittest” strategy of the Genetic Algorithm has been found to be robust and is widely used in solving combinatorial optimization problems like job scheduling, circuit design, antenna array design, etc. In this paper, we discuss the application of the Genetic Algorithm to the operational optimization of collaborative systems, illustrating our strategy with a practical example of a clinic system. Collaborative systems (also known as co-operative systems) are modeled as server-client systems in which a group of collaborators come together to provide service to end-users. The cost function to be optimized is the sum of the service cost and the waiting cost. Service cost is due to hiring professionals and/or renting equipment that provide service to customers in the collaborative system. Waiting cost is incurred when customers who are made to wait in long queues balk, renege or do not come to the system for service a second time. The number of servers operating at each of the collaborative places, and the average service time of each of the servers are the decision variables, while server utilization is a constraint. The Genetic Algorithm tailored to collaborative systems finds the minimum value of the cost function under these operational constraints.

scholarly journals Self-Tuning Lam Annealing: Learning Hyperparameters While Problem Solving

2021 ◽  
Vol 11 (21) ◽  
pp. 9828
Author(s):  
Vincent A. Cicirello
Keyword(s):  
Cost Function ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Target Behavior ◽  
Discrete And Continuous Optimization ◽  
Self Tuning ◽  
Continuous Optimization Problems ◽  
The Cost ◽  
Java Library ◽  
Self Adaptive

The runtime behavior of Simulated Annealing (SA), similar to other metaheuristics, is controlled by hyperparameters. For SA, hyperparameters affect how “temperature” varies over time, and “temperature” in turn affects SA’s decisions on whether or not to transition to neighboring states. It is typically necessary to tune the hyperparameters ahead of time. However, there are adaptive annealing schedules that use search feedback to evolve the “temperature” during the search. A classic and generally effective adaptive annealing schedule is the Modified Lam. Although effective, the Modified Lam can be sensitive to the scale of the cost function, and is sometimes slow to converge to its target behavior. In this paper, we present a novel variation of the Modified Lam that we call Self-Tuning Lam, which uses early search feedback to auto-adjust its self-adaptive behavior. Using a variety of discrete and continuous optimization problems, we demonstrate the ability of the Self-Tuning Lam to nearly instantaneously converge to its target behavior independent of the scale of the cost function, as well as its run length. Our implementation is integrated into Chips-n-Salsa, an open-source Java library for parallel and self-adaptive local search.

Discrete Adjoint Solution of Unsteady Turbulent Flow in Compressor

2015 ◽  
Author(s):  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Adjoint Equations ◽  
Navier Stokes ◽  
Aerodynamic Optimization ◽  
Flow Equations ◽  
Discrete Adjoint ◽  
Continuous Adjoint ◽  
Unsteady Flow Simulation

Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.

A STUDY OF DISCRETE ADJOINT-BASED GRADIENT METHOD IMPLEMENTATION FOR AERODYNAMIC OPTIMIZATION

2020 ◽  
Author(s):  
Gilberto Bueno Luque Filho ◽  
Marco Aurélio Leonel Matunaga ◽  
João Luiz F. Azevedo
Keyword(s):  
Gradient Method ◽  
Aerodynamic Optimization ◽  
Discrete Adjoint
Sign in / Sign up

Export Citation Format

Share Document