Metamodel-assisted Evolutionary Algorithms Research Articles

Multilevel design optimization of hydraulic turbines based on hierarchical metamodel-assisted evolutionary algorithms

In this paper, an efficient hydraulic optimization procedure is presented and applied to the design of hydraulic turbines. For computationally expensive industrial design optimization problems, an advanced optimization tool (EASY software) and a fast CFD evaluation tool are required. EASY optimization software is a Hierarchical Metamodel-Assisted Evolutionary Algorithm (HMAEA) that can be used in both single-(SOO) and multi-objective optimization (MOO) problems. In order to minimize the CFD solver calls during the optimization design, the MAEA rely on local metamodels, trained on the fly, that are used to identify the most promising members in each population and then only these are to be re-evaluated by the CPU costly CFD solver. For additional economy in the CPU cost, the hierarchical (two-level) optimization scheme is used in this paper, where at each level, a different evaluation tool, a low and a high fidelity specific software, can be linked. The low level utilizes a low-CPU cost and low-accuracy tool to explore the design space with a minimum impact to the wall clock time and the high level, using the high fidelity, high-CPU cost tool is used to exploit the information from the low level. For the applications presented in this paper, the high fidelity model is an incompressible Navier-Stokes equation solver and the low fidelity model is based on the solution of the incompressible Euler equations. In order to optimize the geometry of hydraulic machines, an in-house automatic geometry and mesh generation tool has been integrated in the optimization tool chain. In what follows, 2 three-objective design optimization problems of 3D Francis hydraulic turbines are presented. The optimization objective functions concern the ‘quality’ of the runner outlet velocity profile, the cavitation behavior and efficiency of the runner. The optimization results of the hydraulic turbine components along with the performance of the presented optimization procedure are shown in the paper.

Evolutionary multi-objective optimization assisted by metamodels, kernel PCA and multi-criteria decision making techniques with applications in aerodynamics

This paper presents two methods which aim at improving the efficiency of evolutionary algorithms (EAs) and metamodel-assisted EAs (MAEAs) used to solve multi-objective optimization problems with computationally expensive evaluation tools. The EAs and MAEAs are accelerated by implementing the kernel principal component analysis (KPCA) during: (a) the application of the evolution operators, by processing the population members in a new/feature, rather than the standard design, space and/or (b) the metamodel training, to reduce the number of input units and, thus, get more accurate predictions. Over and above, a variant of EA (or MAEA) which takes the decision maker's (DM) preferences into consideration during the evolution is proposed. In contrast to standard multi-objective EAs which may insufficiently populate the preferred area(s) of the objective space, more non-dominated solutions are now driven towards them. This is achieved by using the multi-criteria decision making (MCDM) Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), which affects the parent selection and the non-dominated front trimming operators. The combined use of KPCA and TOPSIS is implemented, too. The proposed methods are evaluated by solving two computationally demanding aerodynamic shape optimization problems, with two objectives each.

Efficient PCA-driven EAs and metamodel-assisted EAs, with applications in turbomachinery

This article presents methods to enhance the efficiency of Evolutionary Algorithms (EAs), particularly those assisted by surrogate evaluation models or metamodels. The gain in efficiency becomes important in applications related to industrial optimization problems with a great number of design variables. The development is based on the principal components analysis of the elite members of the evolving EA population, the outcome of which is used to guide the application of evolution operators and/or train dependable metamodels/artificial neural networks by reducing the number of sensory units. Regarding the latter, the metamodels are trained with less computing cost and yield more relevant objective function predictions. The proposed methods are applied to constrained, single- and two-objective optimization of thermal and hydraulic turbomachines.

Design of a matrix hydraulic turbine using a metamodel-assisted evolutionary algorithm with PCA-driven evolution operators

To overcome the excessive CPU cost of evolutionary algorithms (EAs) which make use of demanding evaluation models, metamodel-assisted EAs (MAEAs) have been devised and used in either single-objective (SOO) or multi-objective (MOO) problems. MAEAs are based on low-cost surrogate evaluation models that screen out non-promising individuals during the evolution and exclude them from the expensive, problem-specific evaluation. This paper proposes a new technique that further reduces the computational cost of MAEAs. This technique is based on the principal-component-analysis (PCA) of the non-dominated individuals (in MOO) within each generation, to identify dependences among the design variables and, through appropriate rotations, use this piece of information to efficiently ‘drive’ the application of the evolution operators. The proposed technique is used to perform the multi-operating point design of a matrix hydraulic turbine, where each evaluation is based on a 3D computational fluid dynamics (CFD) code; this is a highly constrained optimisation problem with many objectives, which is herein handled as a two-objective one. Some convincing mathematical function minimisation problems are also worked out using PCA-driven EAs; it is, thus, shown that the PCA-driven evolution operators can be used with or without metamodels.

Metamodel-assisted evolutionary algorithms for the unit commitment problem with probabilistic outages

An efficient method for solving power generating unit commitment ( UC) problems with probabilistic unit outages is proposed. It is based on a two-level evolutionary algorithm ( EA) minimizing the expected total operating cost ( TOC) of a system of power generating units over a scheduling period, with known failure and repair rates of each unit. To compute the cost function value of each EA population member, namely a candidate UC schedule, a Monte Carlo simulation must be carried out. Some thousands of replicates are generated according to the units’ outage and repair rates and the corresponding probabilities. Each replicate is represented by a series of randomly generated availability and unavailability periods of time for each unit and the UC schedule under consideration accordingly. The expected TOC is the average of the TOCs of all Monte Carlo replicates. Therefore, the CPU cost per Monte Carlo evaluation increases noticeably and so does the CPU cost of running the EA. To reduce it, the use of a metamodel-assisted EA ( MAEA) with on-line trained surrogate evaluation models or metamodels (namely, radial-basis function networks) is proposed. A novelty of this method is that the metamodels are trained on a few “representative” unit outage scenarios selected among the Monte Carlo replicates generated once during the optimization and, then, used to predict the expected TOC. Based on this low cost, approximate pre-evaluation, only a few top individuals within each generation undergo Monte Carlo simulations. The proposed MAEA is demonstrated on test problems and shown to drastically reduce the CPU cost, compared to EAs which are exclusively based on Monte Carlo simulations.

A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement

Metamodel-assisted evolutionary algorithms are low-cost optimization methods for CPU-demanding problems. Memetic algorithms combine global and local search methods, aiming at improving the quality of promising solutions. This article proposes a metamodel-assisted memetic algorithm which combines and extends the capabilities of the aforementioned techniques. Herein, metamodels undertake a dual role: they perform a low-cost pre-evaluation of population members during the global search and the gradient-based refinement of promising solutions. This reduces significantly the number of calls to the evaluation tool and overcomes the need for computing the objective function gradients. In multi-objective problems, the selection of individuals for refinement is based on domination and distance criteria. During refinement, a scalar strength function is maximized and this proves to be beneficial in constrained optimization. The proposed metamodel-assisted memetic algorithm employs principles of Lamarckian learning and is demonstrated on mathematical and engineering applications.

Grid enabled, hierarchical distributed metamodel-assisted evolutionary algorithms for aerodynamic shape optimization

A Grid-enabled optimization environment is presented. It is based on Metamodel-Assisted Evolutionary Algorithms ( MAEAs), where radial basis function networks, trained on the fly on selected subsets of the previously evaluated individuals, are used to pre-evaluate the population members. The search follows a Hierarchical and Distributed scheme ( HDMAEA), with more than one search level, each of which is associated with a different problem-specific evaluation tool and a different number of semi-isolated demes. Irrespective of the use of cluster or Grid computing, the HDMAEA drastically reduces the number of evaluations required to reach the optimal solution(s). The Grid-enabled HDMAEA, based on the master–slave model with simultaneously evaluated population members, aims at solving large scale optimization problems in affordable wall clock time. In the proposed Grid–computing setup, Condor is used as the local resource manager on each contributing cluster, authentication and interfacing is carried out via the Globus Toolkit and the unification of Grid resources under a common queue is undertaken by the Gridway metascheduler. If more than one search level are used (hierarchical search), the optimization of Grid resources’ allocation relies on the distinction between computationally demanding, high-accuracy and less demanding, low-accuracy evaluation tools. The proposed Grid-enabled problem solving environment is demonstrated on three aerodynamic shape optimization problems, namely the design of a compressor cascade and two 3D elbow ducts, on three remote clusters.