Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences

This chapter provides a short overview of the most significant research work that has been conducted regarding the solution of computationally expensive multi-objective optimization problems. The approaches that are briefly discussed include problem approximation, function approximation (i.e., surrogates) and evolutionary approximation (i.e., clustering and fitness inheritance). Additionally, the use of alternative approaches such as cultural algorithms, small population sizes and hybrids that use a few solutions (generated with optimizers that sacrifice diversity for the sake of a faster convergence) to reconstruct the Pareto front with powerful local search engines are also briefly discussed. In the final part of the chapter, some topics that (from the author’s perspective) deserve more research, are provided.

In this paper we will present some hybrid methodologies applied tooptimization of complex systems. The paper is divided in two parts. The first part presents several automatic switching concepts among constituent optimizers in hybrid optimization, where different heuristic and deterministic techniques are combined to speed up the optimization task. In the second part, several high dimensional response surface generation algorithms are presented, where some very basic hybridization concepts are introduced.

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. We consider the case where the design variables are the coordinates of

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points in a region of the plane and we look for the optimal configuration of the points under some constraints. Arising from a concrete situation, concerning the ARGO-YBJ experiments, the goal is to find the optimal configuration of the detector, consisting of a single layer of resistive plate counters. Theoretical and computational results are presented for this location problem.

This paper reviews the combination of Artificial Neural Networks (ANN) and Evolutionary Optimisation (EO) to solve challenging problems for the academia and the industry. Both methodologies has been mixed in several ways in the last decade with more or less degree of success, but most of the contributions can be classified into the two following groups: the use of EO techniques for optimizing the learning of ANN (EOANN) and the developing of ANNs to increase the efficiency of EO processes (ANNEO). The number of contributions shows that the combination of both methodologies is nowadays a mature field but some new trends and the advances in computer science permits to affirm that there is still room for noticeable improvements.

This paper presents an approach to optimization under uncertainty that is very well and naturally suited to reliability-based design optimization problems and it is a possible alternative to traditional approaches to robust design based on the optimization of statistical moments. The approach shown here is based on the direct use of the generalized inverse distribution function estimated using the empirical cumulative distribution function (ECDF). The optimization approach presented is illustrated with the application to some test functions for both robust optimization and reliability-based design optimization. In the robust optimization test case, the bootstrap statistical technique is used to estimate the error introduced by the usage of the ECDF for quantile estimation.

The objective of this study is to propose a methodology which aims at reducing the memory size of hierarchical multilevel models while satisfying both a given accuracy and a maximum computational time, and keeping the initial multilevel structure. In this paper, we propose to construct a new multilevel model satisfying such requirements, based on a choice among available surrogates associated with each submodel. We show how this metamodel assignments can be formulated in an optimal manner through an integer programming problem. The proposed methodology is illustrated on a drag performance model, with surrogates based on High Dimensional Model Representation (HDMR).

This work illustrates a practical and efficient method for performing multi-objective optimization using high-order statistics. It is based on a Polynomial Chaos framework, and evolutionary algorithms. In particular, the interest of considering high-order statistics for reducing the number of uncertainties is studied. The feasibility of the proposed method is proved on a Computational Fluid-Dynamics (CFD) real-case application.

The one-shot approach has proven to be very efficient in optimization and control with steady partial differential equations (PDEs) which are solved by fixed-point iterations. The purpose of this paper is to extend the one-shot method to unsteady problems and to make it as efficient as in steady cases. We derive a framework for optimization and control with unsteady PDEs, whose structure is the same as in the steady one-shot method. First results in the direction of one-shot optimization with unsteady Reynolds-averaged Navier-Stokes equations (URANS) are presented. With the Van der Pol oscillator as a generic model problem, we investigate an adaptive time scaling approach, which demonstrates the classical one-shot efficiency on unsteady problems.

We state and analyze one-shot optimization methods in a function space setting for optimal control problems, for which the state equation is given in terms of a fixed-point equation. Further, we concentrate on the application of a design optimization problem incorporating the solution of the compressible Navier-Stokes equations using a discontinuous Galerkin method. For the given primal fixed-point solver an appropriate adjoint solver is constructed. For the following design update we compute the shape derivative analytically based on the weak formulation of the governing equations. The primal, adjoint and design updates are performed in a one-shot manner, i.e., the corresponding equations are not fully solved, instead only a few iteration steps are performed. Finally, we add an additional adaptive step. During the optimization routine we refine or coarsen the grid to obtain a better accuracy.

This paper presents the development and application of the unsteady continuous adjoint method to the incompressible Navier-Stokes equations and its use in two different optimization problems. The first is the computation of the optimal setting of a flow control system, based on pulsating jets located along the surface of a square cylinder, in order to minimize the time-averaged drag. The second is dealing with unsteady topology optimization of a duct system with four fixed inlets and a single outlet, with periodic in time inlet velocity profiles, where the target is to minimize the time-averaged viscous losses. The presentation of the adjoint formulation is kept as general as possible and can thus be used to other optimization problems governed by the unsteady Navier-Stokes equations. Though in the examined problems the flow is laminar, the extension to turbulent flows is doable.

Engineers are often challenged by designing new equipment without any prior knowledge or guidance from an existing similar product. The large degree of freedom that this generates can become a bottleneck as it could lead to a loss of global oversight and may even lead to wrong, uninformed choices. It is essential to have a large exploration of the design space to allow for innovative solutions, on the other hand it is important to introduce a high level of detail as early as possible in the design process to increase the reliability of the model predictions, which drive the decision process. This leads to a well-known conflict where more knowledge is needed upfront in the design process in the early stages of the design, and a larger degree of freedom is needed near the end of the design process where typically more knowledge is available. In this work it is demonstrated how modern design optimization tools can be effectively used to integrate the preliminary with the detailed design process. The key to achieve a good balance between design exploration and detailed design is obtained by reducing the parameters that are fixed during the preliminary design to an absolute minimum, such that the detailed design phase has still a large degree of freedom. The parameters that are fixed in the preliminary design phase are moreover those parameters that have a pronounced influence on the design performance and can be reliably predicted by a lower detail analysis code. Both preliminary and detailed design processes rely heavily on optimization techniques. Due to the larger computational cost in the detailed design phase, a surrogate model based optimization is used opposed to an evolutionary algorithm in the preliminary design phase. The application within this paper is the design of a liquid-metal pump for the primary cooling system of the advanced nuclear reactor MYRRHA conceived by the Belgian research center (SCK

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CEN). This single stage axial-flow pump has unique design requirements not met by any previously designed pump, and hence demands for a novel approach.

Secondary flow features of turbine blade flows are only assessable by 3D computational fluid dynamics (CFD) which is a time-consuming task. In this paper a fast automatic optimization process for the aerodynamic improvement of three-dimensional turbine blades is described and applied to a two-stage turbine rig. Basically, standard tools are used where the 3D CFD analysis, however, is significantly accelerated by a novel CFD solver running on graphics processing units (GPU) and the entire blade is parameterized in 3D. This approach shows that three-dimensional optimization of turbine blades is feasible within days of runtime and finds an improved blade design.

Surrogate models are used to approximate complex problems in order to reduce the final cost of the design process. This study has evaluated the potential for employing surrogate modelling methods in turbo-machinery component design optimization. Specifically four types of surrogate models are assessed and compared, namely: neural networks, Radial Basis Function (RBF) Networks, polynomial models and Kriging models. Guidelines and automated setting procedures are proposed to set the surrogate models, which are applied to two turbo-machinery application case studies.

The work reported in this paper deals with the development of a design system for the robust aerodynamic design optimization of horizontal axis wind turbine rotors. The system developed is here used to design a 126-m diameter, three-bladed rotor, featuring minimal sensitivity to uncertainty associated with blade manufacturing tolerances. In particular, the uncertainty affecting the rotor geometry is associated with the radial distributions of blade chord and twist, and the airfoil thickness. In this study, both geometric and operative design variables are treated as part of the optimization. Airfoil aerodynamics and rotor aeroelasticity are predicted by means of XFOIL and FAST codes, respectively, and a novel deterministic method, the Univariate Reduced Quadrature, is used for uncertainty propagation. The optimization is performed by means of a two-stage multi-objective evolution-based algorithm, aiming to maximize the rotor expected annual energy production and minimize its standard deviation. The design optimization is subjected to a single structural constrain associated with the maximum out-of-plane blade tip deflection. The results of this research highlight that a lower sensitivity to uncertainty tied to manufacturing tolerances can be achieved by lowering the angular speed of the rotor.

The present work concerns the optimization of the shroud of an horizontal axis hydro turbine (HAHT). The main aim is to improve the hydro-turbine efficiency by designing a new shroud airfoil through an optimization process that maximize, as objective function, the power coefficient. The optimization process is carried out by MATLAB on the supercomputing infrastructure SCoPE of the University of Naples, “Federico II”. Results are obtained with CFD calculations, namely by STARCCM+ for an axisymmetric model, taking advantage of the symmetry of the problem, to minimize the computational time; in addition the HAHT is simulated with an actuator disk that gave reliable results in good agreement with previous works, developed with different software, and with experimental results. The original airfoil was designed for high-lift regimes, so it already gave excellent performance in these kind of applications. For that reason, is not expected a very high increase of the power coefficient. Nevertheless the optimization process results into a power coefficient increase of 4.5 %, with respect to the original airfoil.

Due to raising demands from aviation industry concerning weight reduction and increased efficiency, compressor front stages of jet engines are designed as blade integrated disks (blisks). However, a major drawback of blisks is that small cracks from foreign object impacts occurring in service may propagate into the whole disk causing burst at worst case which is unacceptable. As a damaged blade of a blisk cannot easily be replaced, there is a need for repair. For example, borescope blisk blending may be applied on-wing to ensure safe on-going operation. To determine best solutions for the blending shape, process integration and optimisation tools are used which modify a parametric model and examine its impact on fatigue criteria by FEM.

Designing complex and challenging machines demands the use of sophisticated methods such as multi-objective optimization. In this paper the aerodynamic design process of a jet engine compressor is used to demonstrate how process automation and optimization may support engineers to find better designs. The design process is divided into four sub-processes starting with a correlation-based 1D meanline code and ending with a 3D CFD analysis. These sub-processes of different fidelity are automated and coupled to enable a cascaded, sequential optimization. This approach allows to start with few basic assumptions and ends with a complete 3D geometry and flow field of an axial jet engine compressor.

This paper presents the design/optimization of turbomachinery blades using synchronous and asynchronous metamodel-assisted evolutionary algorithms on a GPU cluster. Asynchronous EAs overcome the synchronization barrier at the end of each generation and exploit better all available computational resources. Radial basis function networks are used as on-line trained surrogate evaluation models (metamodels) according to the inexact pre-evaluation (IPE) concept. With the exception of a few initial evaluations, which are based on the exact evaluation tool, each new candidate solution is approximately evaluated using local metamodels and only the most promising among them are, then, re-evaluated using the exact tool. Suggestions about the number of population members to be re-evaluated on the CFD tool, in the framework of the IPE scheme, are provided. The effect of using more than one GPUs to evaluate each candidate solution in the optimization turnaround time is discussed.

The paper is devoted to applications of two bio-inspired methods: artificial immune systems and particle swarm optimizers to selected shape and topology optimization problems of structures. It contains numerical examples and comparisons of immune and swarm approaches with evolutionary optimization.

While the handling of optimization variables directly expressed by numbers (continuous, discrete, or integer) is abundantly investigated in the literature, the use of nominal variables is generally overlooked, despite its practical interest in plenty of scientific and industrial applications. For example, in civil engineering, the designers of a structure made out of beams might have to select the best cross-section shapes among a list of available geometries (square, circular, rectangular, etc.), which can be modeled by nominal data. Therefore, in the context of single- and multi-objective evolutionary optimization for mixed variables, this study investigates three genetic encodings (binary, real, and real-simplex) for the representation of mixed variables involving both continuous and nominal parameters. The comparison of the genotypes combined with the instances of crossover is performed on six analytical benchmark test functions, as well as on the multi-objective design optimization of a six-storey rigid frame, showing that for mixed variables, real (and to a lesser extent: real-simplex) coding provides the best results, especially when combined with a uniform crossover.

In this paper we deal with solving inverse problems in structural engineering (both the reconstruction inverse problem and the fully stressed design problem are considered). We apply a game-theory based Nash-evolutionary algorithm and compare it with the standard panmictic evolutionary algorithm. The procedure performance is analyzed on a ten bar sized test case of discrete real cross-section types structural frame, where a significant increase of performance is achieved using the Nash approach, even achieving super-linear speed-up.

The inclusion of sound barriers for abating road traffic noise is a broadly used strategy that is often constrained by the requirements associated with its effective height. Due to this fact, the searching process has to deal with compromise solutions between the effective height and the acoustic efficiency of the barrier, assessed by the insertion loss (IL) in this paper. Two different barrier designs are studied herein for two different receivers configurations and for three clearly distinguishable regions in terms of closeness to the barrier. These models are based on the optimization of the IL of thin-cross section profiles proposed by an Evolutionary Algorithm. The special nature of these sorts of barriers makes necessary the implementation of a dual BEM formulation in the optimization process. Results obtained show the usefulness of representing complex thin-cross section barrier configurations as null boundary thickness-like models.

In this paper, we present a discrete adjoint-based optimization framework to obtain the optimal distribution of the porous material over the trailing edge of a 3-D flat plate. The near-body strength of the noise source generated by the unsteady turbulent flow field is computed using a high-fidelity large-eddy simulation (LES). By optimally controlling the material porosity and permeability, it is possible to minimize the turbulence intensity responsible for noise generation at the trailing edge and thus significantly reduce the radiated noise. We demonstrate, using a simple geometry as a first step, the efficacy of the discrete adjoint method in achieving minimum-noise design via optimal distribution of porous media, with future applications to aircraft high-lift devices.

A single-stage launch vehicle with hybrid rocket engine has been conceptually designed by using design informatics, which has three points of view as problem definition, optimization, and data mining. The primary objective of the design in the present study is that the sufficient down range and the duration time in the lower thermosphere are achieved for aurora scientific observation whereas the initial gross weight is held down. Multidisciplinary design optimization and data mining were performed by using evolutionary hybrid computation under the conditions that polypropylene as solid fuel and liquid oxygen as liquid oxidizer were adopted and that single-time ignition is implemented in sequence. Consequently, the design information regarding the tradeoffs and the behaviors of the design variables in the design space was obtained in order to quantitatively differentiate the advantage of hybrid rocket engine.

A robust optimization technique is developed for the aerodynamic shape optimization of a helicopter rotor airfoil considering uncertain operating conditions. Both a CFD model and a coupled panel/integral boundary layer model of the aerodynamics are coupled with an optimization code based on Genetic Algorithms. In order to reduce the computational cost of the robust optimization, a multi-fidelity strategy is developed which employs both aerodynamic models inside the optimization loop.

In this paper we present a computational methodology to solve the problem of the proper design of the test matrix for an envelope expansion test campaign, where both flutter and systems testing are required (i.e. a new store integration). There are two different stakeholders involved: Structural Engineers (StE), who want to verify their predictions about the flutter free area, and the Systems Engineers (SyE), who want to investigate environmental aspects in the entire operational flight envelope. The test matrix, representing the test points distribution in the flight envelope, can be found solving an optimization problem with hard constraints (flight envelope boundaries) and different objective functions for the two stakeholders StE and SyE. Given the goals of the two stakeholders, the problem is formulated as a noncooperative game, where StE control M distribution and SyE control H distribution, according to their respective strategies. The two players make their decision about test points location simultaneously, playing a spatial competition game and a genetic algorithm is adopted to estimate the Nash equilibrium solutions to the multiple test points location problem. Results for a multiple test points location problem are shown.

Flow separation on the flap of a high-lift device degrades the overall aerodynamic performance and hence results in a drop in the lift coefficient. However, by employing the active flow control techniques, separation can be delayed and thus the lift can be enhanced. In these methods, the flow is controlled by varying the parameters of actuation. In the present work, the optimal set of actuation parameters is found using the gradient-based optimisation algorithms combined with an accurate and robust discrete adjoint method for unsteady RANS. Numerical results are presented for the optimal separation control on the flap of a high-lift configuration over a large time interval.

Safety (S) improvement of industrial installations leans on the optimal allocation of designs that use equipment that is more reliable and testing and maintenance activities to assure a high level of reliability, availability and maintainability (RAM) for their safety-related systems. However, this also requires assigning a certain amount of resources (C) that are usually limited. Therefore, the decision-maker in this context faces in general a multiple-objective optimization problem (MOP) based on RAMS+C criteria where the parameters of design, testing and maintenance act as decision variables. A general framework for such MOP based on RAMS+C criteria was proposed in [

1

]. There, a number of alternatives were proposed based on the use of a combination of RAMS+S formulation and Genetic Algorithms (GAs) based optimization to solve the problem of testing and maintenance optimization based only on system unavailablity and cost criteria. The results showed the capabilities and limitations of alternatives. Based on them, challenges were identified in this field and guidelines were provided for further research. In [

2

], a full scope application of RAMS+S based optimization using GAs was reported. Since then, the reliability and risk based optimization of design and operation of equipment and facilities has evolved into a set of technical documents, conference contributions and technical papers published elsewhere. Many of them have already addressed to some extent the effect of both random and epistemic uncertainties within this reliability and risk informed decision-making framework. This paper discusses the importance of appropriate formulation, treatment and analysis of model and parameter uncertainties in reliability and risk informed decision-making. It faces on how treatment and analysis of uncertainties should be integrated within an approach for evaluation of reliability and risk impact of safety issues, i.e. equipment design, operational requirements, etc. The approach would consist of modeling, assessment and analysis of the safety concern, which is intended to be used within an optimization context to support the decision-making on the most effective safety requirements. The paper focuses on Reliability and Risk of Nuclear Installations, where particular attention is paid to address the effect of uncertainties in the reliability and risk informed optimization of testing and maintenance of safety related equipment. Similar challenges can be observed for many other complex installations, such as energy generation and distributions, process industry, aeronautics, etc.

In this paper we deal with a variant of the VRPTW that is oriented to the quality of service to customers. In this model, we incorporate a measure of quality associated with the time the vehicles reach customers within their time window as an objective. We apply a bi-objective discrete PSO to deal with the problem. The procedure performance is analyzed on classical and real data based instances.

This paper presents an approach for the evaluation of risk impact of Surveillance Requirement changes addressing identification, treatment and analysis of uncertainties in an integrated manner, which is intended to be used in an optimization context. It is also presented an example of application of the methodology to study a SF change of the Reactor Protection System of a Nuclear Power Plant.

Transportation planning is central activity in logistic network design. In this study, we examine the deployment of optimization methodology to transportation planning. More specifically, we examine the adoption of system solving the well-known combinatorial optimization problem, the vehicle routing problem (VRP). Its application has resulted in efficiency gains in transportation logistics, but they have not been very widespread, and especially small-scale operators have not yet benefited from these systems. In this paper, we present a prospective case study on the issues during deployment of optimization, especially in the context of small and medium enterprises (SMEs). We propose a novel perspective to analyzing vehicle routing systems (VRSs), and complement the previous research on real-life aspects of commercial routing. In this study, we suggest a framework for analyzing VRS deployment, from a viewpoint frequently identified in enterprise architecture (EA) theory. To our knowledge, EA theory has not been applied to study the requirements of VRP solution methods. This new viewpoint allows us to identify new needs for widespread adoption of vehicle routing systems, and to derive additional requirements for the optimization methodology for SMEs. In practice, we identify several adoption barriers for VRSs and suggest potential strategies for lowering them.

Historical data of electricity demand in La Palma island (Spain) were collected and electricity demand estimates conducted by different organizations were sought. Some factors that could affect these data were studied and its predictions by the next years were looked for. The idea was to use these factors as explanatory variables in order to predict the values of electricity demand in the next years. Moreover, with the aim of minimizing the limitation of predicting the future based only on relationships between variables that occurred in the past, it has been considered the annual demand forecast for various scenarios, taking into account, for each of them, different variations of the explanatory variables. All that with the goal that the estimate band of the demand for each year includes the real future demand with high probability. This provided a prediction model that takes into account population and gross domestic product. Results and their graphical representation along with the other estimates found are presented. A similar approach was carried out to predict peak powers.

In this paper a micro genetic algorithm for multi-objective optimization (AMGA) is used to minimize the number of function evaluations of the dimensionless model of an electrostatic microswitch. A non-dimensional dynamic model is proposed, and three objective functions are defined: the closing dimensionless time of the first impact, the maximum dimensionless speed and the maximum dimensionless displacement of the first impact. This work has been carried out using dimensional analysis. Results demonstrate an interesting methodology based on AMGA for optimizing the closing time and displacement of the first impact in a microswitch.

In this paper we obtain new detection codes, to determine whether a GPS satellite in particular is visible, using NSGA-II as multi-objective optimization engine. Our approach takes into consideration the length of the code and the sampling frequency in comparison with other approaches found in the literature that fix those design parameters. The obtained new detection codes produce an improvement of the 19 % in terms of CPU execution time. Results demonstrate that both design parameters must be taken in consideration to obtain high quality detection codes.