Surrogate-assisted Genetic Algorithm Research Articles

Optimization of a High Pressure Turbine Blade and Sector-Based Annular Rig Design for Supercritical CO2 Power Cycle Representative Testing

Abstract As part of the ongoing research into the design of hardware for zero emission cycles, a first-stage high-pressure turbine (HPT) blade is optimized for a 300 MWe supercritical CO2 (sCO2) power cycle using the surrogate-assisted genetic algorithm optimizer in Numeca FINE/Design three-dimensional with objectives of increasing efficiency and decreasing heat load to the blade. Supercritical CO2 property tables are constructed from NIST REFPROP data for the condensable gas simulation in FINE/Turbo. A detailed mesh sensitivity study is performed for a baseline design to identify the proper-grid refinement and efficiently allocate resources for the optimization. Seventy design variables are selected for the initial population generation. Self-organizing maps are then used to focus the design variables on the most important ones affecting the objective functions. The optimization results in approximately 3000 three-dimensional Reynolds Averaged Navier Stokes simulations of different blade shapes with increases in efficiency of up to 0.85% and decreases in heat load of 14%. Families of blade shapes are identified for experimental testing in an annular rig at the Purdue Experimental Turbine Aerothermal Laboratory. A design to adapt the annular cascade for testing optimized geometries is introduced, which features eccentric radius sectors allowing for scaled-up geometries of sCO2 optimized blade profiles to be tested at design cycle representative conditions at high Reynolds numbers in dry air. Analysis into the effects of Reynolds number, working fluid, and geometric relations are presented to prove the efficacy of the test method.

Optimizing additive manufacturing path pattern for Ti-6Al-4V thin rods using a combinatorial radial basis function surrogate-assisted genetic algorithm

Path pattern is one of the most significant parameters in the additive manufacturing (AM) process because it influences the specimen's final shape and residual stress distribution. Generally, the optimal path pattern is a computationally expensive, high-dimensional, and black-box permutation optimization problem. In this paper, we propose a combinatorial radial basis function surrogate-assisted genetic algorithm (CRBF-GA) to effectively generate the optimal path pattern by integrating the combinatorial radial basis function surrogate model (CRBF) with the genetic algorithm (GA). To demonstrate the effectiveness of the proposed CRBF-GA, a Ti-6Al-4V thin rod, a component of lattice, is chosen as the research object. Through numerical simulation, experimental verification, and error comparison analysis, the RBF-GA pattern is demonstrated to be the best path pattern among the random forest-assisted evolutionary algorithm (RF-EA), GA, spiral, and zigzag patterns, and it excels in achieving a more precise rod shape compared to the other patterns examined.

Bottom-up approaches for rapid on-demand design of modular metaporous structures with tailored absorption

As a new trend in the studies on sound-absorbing structures design, customizable metaporous structures (MPSs) have drawn a great deal of interest due to their distinct advantages, which include designable broadband absorption, light weight, and low thickness. Conventional finite element-based design methods, such as trial-and-error and iterative optimization, are inefficient and expensive in terms of computational resources. Inspired by the widely used bottom-up method, in this study, we develop a data-driven metaheuristic optimization framework to accomplish the rapid on-demand design for a novel modular metaporous structure (MMPS) of only 30mm thickness from the local to the global level. Two cascade variants of the genetic algorithm (GA) are employed for local optimization and global customized design, accordingly. The local design level involves the development of a surrogate-assisted genetic algorithm (SAGA) for design space optimization. On the basis of the structural dataset, a well-tuned convolutional neural network (CNN) model is developed for expediting the forward prediction of the acoustic properties of the two-dimensional (2D) MPS. In the subsequent phase, the validated CNN model is combined with SAGA to expedite the fitness evaluation for optimizing the structural units. At the global design stage, the developed SAGA is coupled with the population initialization process of an elitist genetic algorithm (EGA) to achieve inverse design for the MMPS with customizable broadband absorption based on the optimized design space. Furthermore, an acoustic measurement is performed on the fabricated MMPS samples to validate the finite element method (FEM) simulation and impedance design method. The utilization of this optimization method opens up fresh possibilities not solely for the customized design of sound-absorbing structures, but also for optimization processes in various other domains. Meanwhile, the proposed MMPS with customizable broadband absorption in a thickness of 30mm could well be utilized for noise reduction in a variety of practical applications.

Investigation on the Performance of Surrogate-assisted Genetic Algorithms According to Changes in Learning Model and Data

Investigation on the Performance of Surrogate-assisted Genetic Algorithms According to Changes in Learning Model and Data

Evolutionary neural architecture search on transformers for RUL prediction

ABSTRACT Remaining useful life (RUL) predictions are a key enabler for predictive maintenance. Data-driven approaches, typically based on deep neural networks (DNNs), have shown success in RUL prediction. However, DNNs are usually handcrafted via a labor-intensive design process. To overcome this issue, we propose a neural architecture search (NAS) technique based on a surrogate-assisted genetic algorithm that automatically discovers the optimal architectures of Transformers. To our knowledge, this is the first work to optimize the architecture of Transformers for RUL predictions using evolutionary computation. We evaluate the performance of the proposed method (in terms of RMSE and -score) on the well-known CMAPSS benchmark dataset. Compared with the state-of-the-art, the Transformers obtained by our NAS method outperform other recent handcrafted DNNs in terms of RMSE and are comparable regarding the -score. Our results demonstrate that the proposed method provides better prediction accuracy with less human effort compared to other data-driven approaches.

Interpretable Calibration of Crystal Plasticity Model Using a Bayesian Surrogate-Assisted Genetic Algorithm

The accurate calibration of material parameters in crystal plasticity models is essential for applying crystal plasticity (CP) simulations. Identifying these parameters usually requires unfeasible single-crystal experiments or expensive time costs due to the use of traditional genetic algorithm (GA) optimization. This study proposed an efficient and interpretable method for calibrating the constitutive parameters with macroscopic mechanical tests. This approach utilized the Bayesian neural network (BNN)-based surrogate-assisted GA (SGA) optimization method to identify a group of constitutive parameters that can reproduce the experimental stress–strain curve and crystallographic orientation by crystal plasticity simulation. The proposed approach was performed on the calibration of typical high-entropy alloy material parameters in two different CP models. The use of the surrogate model reduces the call count of simulation in the parameter searching process and speeds up the calibration significantly. With the help of infill sampling, the accuracy of this optimization method is consistent with the CP simulation and not limited by the accuracy of the surrogate model. Another merit of this method is that the pattern that the BNN surrogate found in the model parameters can be interpreted with its integrated gradients, which helps us to understand the relationship between constitutive parameters and the output mechanical response. The interpretation of BNN can guide further experiment design to decouple particular parameters and add constraints provided by the attached experiment or prior knowledge.

Optimal Agent Search Using Surrogate-Assisted Genetic Algorithms

An intelligent agent is a program that can make decisions or perform a service based on its environment, user input, and experiences. Due to the complexity of its state and action spaces, agents are approximated by deep neural networks (DNNs), and it can be optimized using methods such as deep reinforcement learning and evolution strategies. However, these methods include simulation-based evaluations in the optimization process, and they are inefficient if the simulation cost is high. In this study, we propose surrogate-assisted genetic algorithms (SGAs), whose surrogate models are used in the fitness evaluation of genetic algorithms, and the surrogates also predict cumulative rewards for an agent’s DNN parameters. To improve the SGAs, we applied stepwise improvements that included multiple surrogates, data standardization, and sampling with dimensional reduction. We conducted experiments using the proposed SGAs in benchmark environments such as cart-pole balancing and lunar lander, and successfully found optimal solutions and significantly reduced computing time. The computing time was reduced by 38% and 95%, in the cart-pole balancing and lunar lander problems, respectively. For the lunar lander problem, an agent with approximately 4% better quality than that found by a gradient-based method was even found.

Surrogate-assisted evolutionary multi-objective optimisation applied to a pressure swing adsorption system

The complexity of chemical plant systems (CPS) makes optimising their design and operation challenging tasks. This complexity also results in analytical and numerical simulation models of these systems having high computational costs. Research demonstrates the benefits of using machine learning models as surrogates or substitutes for these computationally expensive simulation models during CPS optimisation. This paper presents the results of our study, extending recent research into optimising chemical plant design and operation. The study explored the original surrogate-assisted genetic algorithms (SA-GA) in more complex variants of the plant design and operation optimisation problem. The more complex plant design variants include additional parallel and feedback components. The study also proposes a novel multivariate extension, surrogate-assisted NSGA (SA-NSGA), to the original univariate SA-GA algorithm. The study evaluated the SA-NSGA extension on the popular pressure swing adsorption (PSA) system. This paper outlines our extensive experimentation, comparing various meta-heuristic optimisation techniques and numerous machine learning models as surrogates. The results in both more complex plant design variants and the PSA case show the suitability of genetic algorithms combined with surrogate models as an optimisation framework for CPS design and operation in single and multi-objective scenarios. The analysis further confirms that combining a genetic algorithm framework with machine learning surrogate models as a substitute for long-running simulation models yields significant computational efficiency improvements, 1.7–1.84 times speedup for the increased complexity examples and a 2.7 times speedup for the pressure swing adsorption system. The discussion successfully concludes that surrogate-assisted evolutionary algorithms can be scaled to increasingly complex CPS with parallel and feedback components.

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

Optimal Control of a Compound Rotorcraft for Engine Performance Enhancement

Abstract Demands for rotorcraft with increased flight speed, improved operational performance and reduced environmental impact have led to a drive in research and development of alternative concepts. Compound rotorcraft overcome the flight speed limitations of conventional helicopters with additional lifting and propulsive components. Further to operational benefits, these augmentations provide additional flight control parameters, resulting in control redundancy. This work aims to investigate the impact of optimal control strategies for a generic coaxial compound rotorcraft, equipped with turboshaft engines, targeting the minimization of mission fuel burn and gaseous emissions. The direct redundant controls considered are: (a) main rotor speed, (b) propeller speed, and (c) fuselage pitch attitude. A simulation tool for coaxial compound rotorcraft analysis has been developed and coupled to a zero-dimensional engine performance model and a stirred-reactor combustor model. First, experimental and flight test data were used to provide extensive validation of the developed models. A parametric analysis was then carried out to gain insight into the effect of the redundant controls. This was followed by the derivation of a generalized set of optimal redundant control allocations using a surrogate-assisted genetic algorithm. Application of the optimal redundant control allocations during realistic operational scenarios has demonstrated reductions in fuel burn and NOx of up to 6.93% and 8.74%, respectively. The developed method constitutes a rigorous approach to guide the design of control systems for future advanced rotorcraft.

Bi-objective traffic count location model for mean and covariance of origin–destination estimation

This paper describes a bi-objective optimization model for the traffic count location problem in stochastic origin–destination (OD) traffic demand estimation. Two measures are defined to capture the maximum possible absolute error of the mean and the covariance of the estimated OD demand. The bounds of these two measures are mathematically deduced, and then the bi-objective optimization model is formulated to minimize the two upper bounds simultaneously. A surrogate-assisted genetic algorithm is proposed to solve this model, and a series of numerical examples are presented to demonstrate the applicability of the proposed model and the efficiency of the proposed algorithm.

Automatic clustering-based surrogate-assisted genetic algorithm for groundwater remediation system design

Simulation-optimization techniques in support of groundwater management are computationally expensive. To tackle such computational burden, a variety of surrogate modeling-frameworks have been proposed, where a cheaper-to-run model referred to as a surrogate is used in lieu of a computationally intensive model. These frameworks are generally based on what referred herein to as ‘global surrogate modelling’ where a single surrogate approximates the underlying response surface of a model. Such classic frameworks, however, are sub-optimal when the response surface is complex and/or high-dimensional. This paper proposes a novel ‘local surrogate modelling’ framework that simultaneously builds and evolves multiple local surrogates, guided by an automatic clustering method. Unlike traditional clustering methods that select the number of clusters a priori, the proposed automatic clustering method concurrently determines the optimum number of clusters and the clustering scheme itself. To serve as the surrogate, Artificial Neural Networks (ANNs) are used. The proposed framework is applied to solve a computationally intensive groundwater remediation optimization problem. This study shows that the proposed automatic clustering-based local surrogate modeling is effective and reliable while reducing at least 60 percent of the computational burden.

Vibration-based delamination detection in curved composite plates

Delamination is one of common damages in fibre-reinforced composite laminates. It is known to cause changes in the vibration characteristics of the laminates, which allows for the use of vibration-based indicators for assessing structural health conditions and identifying potential risk of catastrophic failures. This paper presents a vibration-based approach to assess delamination in fibre reinforced composite curved plates through frequency shifts as indicative parameters. Two algorithms based on computational intelligence, namely artificial neural network (ANN) and surrogate assisted genetic algorithm (SAGA), were employed as inverse algorithms for predicting the location, size and interface of the delamination. The validation of the two algorithms is realized numerically through finite element (FE) studies conducted using a structured selection of parameters of genetic algorithms, number of frequency shifts and database size. Experimental modal testing was conducted using scanning laser vibrometer on five carbon fibre reinforced polymer (CFRP) curved plates. Among these, one was intact and the other four were manufactured with artificially induced laminations. It was confirmed that the two inverse algorithms were able to reasonably predict delamination parameters in curved composite plates. Among the two, SAGA’s performance was observed to be better. A sensitivity analysis was further conducted by adding artificial noise to the numerical data to simulate measurement errors for investigating the influence of noise on the accuracy of the two algorithms.

A Novel Sequential-Stage Optimization Strategy for an Interior Permanent Magnet Synchronous Generator Design

For an optimal design of an interior permanent magnet synchronous generator (IPMSG) for range the extended electric vehicle (REEV), many design variables and objective functions should be considered. Conventional optimization methods like the Taguchi method and multiobjective optimization algorithm have completeness or calculation time problems when solving the many design variables and objectives problems. To address these problems, a sequential-stage optimization strategy (SSOS) is proposed. In the first stage of the SSOS, the initial design result considering the various objective functions is derived by using the Taguchi method. In addition, the sensitive design variables are sorted through the calculation of synthetic signal to noise. In the second stage, the optimal solution for the sensitive design variables is derived using the surrogate assisted genetic algorithm (SAGA). The SAGA not only obtains an accurate and well-distributed Pareto front set but considerably reduces the number of function calls as well. In the last stage, the uncertainty consideration based on the worst-case scenario is applied to derive the robust optimal solution. By applying the proposed optimization strategy to the optimal design of IPMSG for REEV, an optimal solution is derived with fewer function calls, and the feasibility of the proposed optimization is verified by experimental results of manufactured generator.

A surrogate-assisted genetic algorithm for the selection and design of highway safety and travel time improvement projects

Measures to improve highway safety can affect travel times, just like measures to reduce travel times can affect highway safety. For this reason, the models used in the process of allocating funds across different highway improvement projects should simultaneously consider the safety and travel time effects of the project alternatives. In this paper, an optimization model is presented for the joint selection and design of highway safety and travel time improvement projects. The model is formulated as a bi-objective, mixed-integer optimization problem with constraints on project costs and on the types of improvement combinations admissible at project sites. By incorporating travel behavior models within the optimization process, the model accounts for the potential network-level effects of highway improvement schemes. Given that the model systems needed in this process are time-consuming, a genetic algorithm is proposed that utilizes surrogate models to accelerate the discovery of good solutions to the presented optimization model. In this algorithm, the surrogate models are used to generate computationally inexpensive approximations to computationally expensive functions that quantify a decision-maker’s safety and travel time objectives. Like the problem formulation, the proposed heuristic can be employed in conjunction with computer-based travel demand models commonly used by transportation planning agencies. An illustrative application of the model and its solution heuristic is presented using a hypothetical planning scenario in Southwest Puerto Rico. Besides illustrating the application of the model, the example was used to test the surrogates’ predictive accuracy and the impact of different parameter values on the algorithm’s performance.

Aerodynamic Optimization of Near-future High-wing Aircraft

This paper discusses aerodynamic optimization of the high-wing configuration to explore fuselage-wing shapes for the high-wing configurations of near-future aircraft, in which it will be possible to install fuel-efficient, ultrahigh-bypass ratio engines, using computational fluid dynamics simulation and the Kriging surrogate-assisted genetic algorithm. First, optimization of the fuselage upper surface is performed, with exploration of the fairing shape suitable for the high-wing configuration. Second, the aircraft nose shape is also optimized, in addition to the fuselage upper surface, to confirm the possibility of generating higher lift by the fuselage itself. Finally, both the fuselage and the wing shape are optimized to improve the lift-to-drag ratio by alleviating the shock wave over the wing, while sustaining the high lift generation of the high-wing configuration. The final optimized configuration achieves not only a lift-to-drag ratio comparable to the DLR-F6, but also a CL approximately 1.5 times higher than the DLR-F6. These results indicate the possibility of producing high-wing aircraft that not only employ fuel-efficient ultrahigh-bypass ratio engines, but also have much better aerodynamic performance than low-wing configurations.

An efficient evolutionary optimisation framework applied to turbine blade firtree root local profiles

In this paper, an efficient evolutionary optimisation of a turbine blade firtree root local profile is presented. The firtree geometry is designed using an intelligent rule-based computer-aided design system (ICAD) and analysed using an industrial-strength finite element code. A large number of geometric and mechanical constraints drawn from past experience are incorporated in the design of the model. The high computational cost associated with finding optimal designs using high-fidelity codes is addressed using a surrogate-assisted genetic algorithm. The initial surrogate model is first built based on points sampled with a design-of-experiment method. A database of designs analysed using the high-fidelity code is built and augmented while the genetic algorithm progresses. In the procedure for deciding whether the high-fidelity code should be run, a simple 3σ principle is used instead of searching for the point with maximum expected improvement. This is combined with an appropriate ranking of the design points within the database. Some benchmark test problems are first used to illustrate the effectiveness and efficiency of the framework. When applied to the problem of local shape optimisation of a turbine blade firtree root, significant improvement is achieved using a limited computational budget.