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

Risk is usually a criteria which involves the world’s state; for instance the best policy to extract oil from a well of finite resource depends on the price of oil which in turn depends on how much the world’s oil extractors produce. Many optimization of systems with respect to profit and risk involve a very large number of players who optimize the same criteria. Then the profit is the result of a global optimization problem, which is coupled with a each player’s system design where price appears as a passive variable. Meanfield type control is a mathematical tool which can help solve such problem in the presence of randomness, an aspect essential for the modeling of risk. We shall give a few examples and compare solutions by calculus of variations plus gradient algorithms with extended dynamic programming and fixed point.

Recent progresses in aircraft aerodynamics have witnessed the introduction of surrogate-based approaches in design analysis and optimization as an alternative to address the challenges posed by the complex objective functions, constraints, the high-dimensionality of the aerodynamic design space, the computational burden, etc. The present review revisits the most popular sampling strategies used in conducting physical and simulation-based experiments in aircraft aerodynamics. Moreover, a comprehensive and state-of-the art survey on numerous surrogate modeling techniques for aerodynamic analysis and surrogate-based optimization (SBO) is presented, with an emphasis on models selection and validation, sensitivity analysis, infill criterion, constraints handling, etc. Closing remarks foster on the drawbacks and challenges linked with SBO aircraft aerodynamic industrial applications, despite its increased interest among the academic community.

The application of surrogate-based methods to the constrained optimization of aerodynamic shapes is nowadays a very active research field due to the potential of these methods to reduce the number of actual computational fluid dynamics simulation runs, and therefore drastically speed-up the design process. However, their feasibility when handling a large number of design parameters, which in fact is the case in industrial configurations, remains unclear and needs further efforts, as demonstrated by recent research on design space reduction techniques and adaptive sampling strategies. This paper presents the results of applying surrogate-based optimization to the three-dimensional, constrained aerodynamic shape design of the DPW-W1 wing, involving both inviscid and viscous transonic flow. The wing geometry is parameterized by a control box with 36 design variables and the applied approach is based on the use of Support Vector Machines (SVMs) as the surrogate model for estimating the objective function, in combination with an Evolutionary Algorithm (EA) and an adaptive sampling technique focused on optimization, called the Intelligent Estimation Search with Sequential Learning (IES-SL).

We present an approach for shape optimization of large-scale aerodynamic problems, combining free-form deformation and POD based reduced-order modeling. An extension of the classical Free-Form Deformation techniques is derived in order to handle efficiently constraints regarding fixed and deformable portions of the geometry and to impose the smoothness at the interface between the two different regions. The second aspect concerns the development of a hybrid model, combining a POD-based reduced order model and a industrial CFD solver using a domain-decomposition approach. A method on how determining automatically a suitable domain decomposition is discussed. The effectiveness and drawback of the above techniques are highlighted on a large-scale aerodynamic shape optimization and control problem, i.e. the mainsail thrust optimization of a sailing boat.

The paper proposes the application of evolutionary-based optimization coupled with physics-based and adaptively-trained surrogate model to the solution of both two- and three-dimensional aerodynamic optimization problems. The shape parameterization approach consists of the Class-Shape Transformation (CST) method with a sufficient degree of Bernstein polynomials to cover a wide range of shapes. The in-house ZEN flow solver is used for RANS aerodynamic solution. Results show that, thanks to the combined usage of surrogate models and smart training, optimal candidates may be located in the design space even with limited computational resources with respect to standard global optimization approaches.

In the frame of an investigation about surrogate models employed in aerodynamic optimization problems, this work aims at illustrating the suitability of adapted design space sampling to evolutionary optimization. The adaptive sampling algorithm is based on the Weighted Expected Improvement idea applied to a Kriging-based meta-model. A multipoint airfoil optimization is set as test case. A deep investigation is devoted to the tuning of the weights of Expected Improvement function to enhance the performance of the optimization process. A comparison between a pure genetic optimization and a Weighted Expected Improvement approach is proposed. Efficiency and quality of the obtained results are discussed.

Gradient-based optimisation using adjoints is an increasingly common approach for industrial flow applications. For cases where the flow is largely unsteady however, the adjoint method is still not widely used, in particular because of its prohibitive computational cost and memory footprint. Several methods have been proposed to reduce the peak memory usage, such as checkpointing schemes or checkpoint compression, at the price of increasing the computational cost even further. We investigate incomplete checkpointing as an alternative, which reduces memory usage at almost no extra computational cost, but instead offers a trade-off between memory footprint and the fidelity of the model. The method works by storing only selected physical time steps and using interpolation to reconstruct time steps that have not been stored. We show that this is enough to compute sufficiently accurate adjoint sensitivities for many relevant cases, and does not add significantly to the computational cost. The method works for general cases and does not require to identify periodic cycles in the flow.

This paper presents the development and application of the continuous adjoint method for the shape optimization of wind turbine blades aiming at maximum power output. A RANS solver, coupled with the Spalart-Allmaras turbulence model, is the flow (primal) model based on which the adjoint system of equations is derived. The latter includes the adjoint to the turbulence model equation. The primal and adjoint fields are used for the computation of the objective function gradient w.r.t. the design variables. A volumetric Non-Uniform Rational B-Splines (NURBS) model is used to parameterize the shape to be designed. The latter is also used for deforming the computational mesh at each optimization cycle. In order to reduce the computational cost, the aforementioned tools, developed in the CUDA environment, run on a cluster of Graphics Processing Units (GPUs) using the MPI protocol. Optimized GPU memory handling and GPU dedicated algorithmic techniques make the overall optimization process up to 50x faster than the same process running on a CPU. The developed software is used for the shape optimization of an horizontal axis wind turbine blade for maximum power output.

This paper presents the development and application of the truncated Newton (TN) method in aerodynamic shape optimization problems. The development is made for problems governed by the laminar flow equations of incompressible fluids. The method was developed in OpenFOAM$$^{\copyright }$$© with the aim to stress its advantages over standard gradient-based optimization algorithms. The Newton equations are solved using the Conjugate Gradient (CG) method which requires the computation of the product of the Hessian of the objective function and a vector, escaping thus the need for computing the Hessian itself. The latter has a computational cost that scales with the number of design variables and becomes unaffordable in large-scale problems with many design variables. A combination of the continuous adjoint method and direct differentiation is used to compute all Hessian-vector products. A grid displacement PDE (Laplace equation) is also used to compute the necessary derivatives of grid displacements w.r.t. the design variables. The programmed method is used to optimize the sidewall shapes of 2D ducts for minimum total pressure losses.

Hydraulic phenomena in open-channel flows are usually described by means of the shallow water equations. This hyperbolic non-linear system can be used for predictive purposes provided that initial and boundary conditions are supplied and the roughness coefficient is calibrated. When calibration is required to fully pose the problem, several strategies can be adopted. In the present work, an inverse technique, useful for any of such purposes, based on the adjoint system and gradient descent is presented. It is used to find the optimal time evolution of the inlet boundary condition required to meet the 20 measured water depth data in an experimental test case of unsteady flow on a beach. The partial differential systems are solved using an upwind finite volume scheme. Several subsets of probes were selected and the quality of the reconstructed boundary tested against the experimental results. The results show that the adjoint technique is useful and robust for these problems, and exhibits some sensitivity to the choice of probes, which can be used to properly select probes in real applications.

This paper presents the application of the continuous adjoint method, programmed in OpenFOAM$$^{\copyright }$$©, combined with an RBF-based morpher to the aerodynamic optimization of a generic car model. The continuous adjoint method produces accurate sensitivities by utilizing the full differentiation of the Spalart–Allmaras turbulence model, based on wall functions, while the RBF-based morpher provides a fast and versatile way to deform both the surface of the car and the interior mesh nodes. The integrated software is used to minimize the drag force exerted on the surface of the DrivAer car model.

The paper presents an overview of parameter-based geometric modeling as used for shape optimization with respect to fluid-dynamic performance. Parametric modeling is well established in Computer Aided Design, particularly in the phases of detailed design and production. However, production-centric models often require considerable effort, e.g. de-featuring, to prepare them for simulation, above all for Computational Fluid Dynamics. Consequently, to investigate a large number of design variants special engineering models are built, deliberately omitting certain details, especially if they cannot be captured by the simulation within reasonable effort anyway. In the context of aero- and hydrodynamic design dedicated parametric models are utilized that define shapes of high quality with as few parameters as possible. Parametric modeling for shape optimization can be subdivided into fully-parametric and partially-parametric modeling. In fully-parametric modeling the entire shape is defined and realized by means of parameters while in partially-parametric modeling only the changes to an existing shape are described parametrically. Prominent techniques of partially-parametric modeling are free-form deformation, shift transformations and morphing. The most popular techniques are summarized, giving some of their mathematical background while discussing advantages and drawbacks. Examples are drawn from the maritime and aerospace industries, turbomachinery and automotive design.

The paper presents a global method for simulation-based design optimization (SBDO) which combines a dynamic radial basis function (DRBF) surrogate model with a sequential multi-criterion adaptive sampling (MCAS) technique. Starting from an initial training set, groups of new samples are sequentially selected aiming at both the improvement of the surrogate model global accuracy and the reduction of the objective function. The objective prediction and the associated uncertainty provided by the DRBF model are used by a multi-objective particle swarm optimization algorithm to identify Pareto-optimal solutions. These are used by the MCAS technique, which selects new samples by down-sampling the Pareto front, allowing for a parallel infill of an arbitrary number of points at each iteration. The method is applied to a set of 28 unconstrained global optimization test problems and a six-variable SBDO of the DTMB 5415 hull-form in calm water, based on potential flow simulations. Results show the effectiveness of the method in reducing the computational cost of the SBDO, providing the background for further developments and application to more complex ship hydrodynamic problems.

The recent years have seen an evolution of traditional approaches in ship design. Raising fuel costs, tough and volatile market conditions, the constant societal pressure for a «green» environmental footprint combined with ever demanding international safety regulations pose a new challenge for today’s Naval Architect. As a result of this current status of shipping commercial ship design is shifting towards new approaches where holistic approaches are deemed necessary. Apart from considering all the interrelationships between the subsystems that consist the vessel, lifecycle and supply chain considerations are the key in successful and «operator-oriented» designs. The paper presents a methodology within the parametric design software CAESES® for the optimization of the basic design of a new vessel and the operation of an existing one with regards to the maximization of the efficiency, safety and competitiveness of the final design. A case study with the design optimization was undertaken based on the simulation of the anticipated operation of a vessel engaged in the supply chain of Iron Ore. The target was the minimization of costs, fuel consumptions as well as of the Energy Efficiency Operating Index (EEOI) under conditions of uncertainty.

In this paper we present a cooperative game for a network design. The game model adopts for the cooperating players the profit maximizing requirement. Since the players may use different paths, there is the possibility to cooperate and design the optimal network satisfying the requests of all the players and minimizing the cost. The solution of the game is determined by the core concept, well known in cooperative game literature. By means of several examples, both analytical and numerical solutions are proposed. Concerning the computational procedure, in this work an algorithmic approach based on ant colony model is employed. Finally, an application to the airline network design is discussed, providing a numerical example for intercontinental air traffic routes.

An approach to the resolution of inequality constrained potential games based on a dual problem is here presented. The dual problem is solved by using a two-level optimization iterative scheme based on a linear program for the dual problem and a classical hybrid evolutionary approach for the primal problem. An application to a facility location problem in presence of obstacles is described.

Game-theory based Nash–evolutionary algorithms are efficient to speed-up and parallelize the optimum design procedure. They have been applied in several fields of engineering and sciences, mainly, in aeronautical and structural engineering. The influence of the search space player territory has been shown as having an important role in the algorithm performance. Here we present a study where a diversity enhanced dynamic player territory is introduced and its behavior is tested in a reconstruction problem in structural engineering. The proposed diversity dynamic territory seems to increase the optimization procedure robustness, and improves the results from a classical dynamic territory, in a structural frame test case.

An interactive version of the inverse modeling based multiobjective evolutionary algorithm is presented. Instead of generating a representation of the whole Pareto optimal front, the algorithm aims at producing solutions in the regions where the decision maker is interested in. This is facilitated through an interactive solution process where the decision maker iteratively evaluates a set of solutions shown to her/him and the preference information obtained is used to adapt the search process of the algorithm.

The design integration of a supersonic combustion ramjet engine (SCRAMJET) with an airframe remains a critical task for guarantying a successful mission of trans atmospheric or hypersonic cruise vehicles. For this purpose, the operational efficiency has to be established by the effective specific impulse and the thrust to weight ratio of the accelerating vehicle. In order to analyze the foregoing problems, a design methodology based on Evolutionary Algorithms (EAs) and Game Strategies (GS) is developed. In this study, Evolutionary Algorithms (EAs) are used to solve MDO problems. The proposed methodology is tested and its performances and quality design evaluated for optimizing a 2-D air-breathing hypersonic vehicle shape at cruise flight conditions: Euler flow, Mach number = 8; angle of attack = 0°; flight altitude = 30 km, involving aerodynamics, thermodynamics and propulsion disciplines. The set up of an operational flight corridor requires a compromise among air-breathing engine performance, vehicle aerodynamic performance, and structural thermal load limit resulting from aero-heating. For this purpose, the operational efficiency is established by the effective specific impulse and thrust to weight ratio of the accelerating vehicle. In order to analyze the foregoing problems, a methodology is developed, which permits a quick performance evaluation of an idealized, integrated SCRAMJET vehicle for preliminary design analysis. A Pareto-EAs methodology is used to find design and off design solutions of an integrated vehicle consisting of the fore body inlet, the supersonic flow combustor and the after body expansion nozzle. From preliminary numerical experiments on a generic test case 2-D air breathing vehicle and analysis of results, the Pareto-EAs numerical approach is a promising methodology with game coalition for its use in industrial aeronautical design and well suited for its implementation on HPCs for increasing its efficiency.

This paper describes the methodologies that have been developed by ESTECO during the first phase of UMRIDA European Project, in the field of Uncertainty Management and Robust Design Optimization, and that have been implemented in the software platform modeFRONTIER. In particular, in the first part there are proposed two methodologies, one based on SS-ANOVA regression applied directly to the uncertainties variables and one based on a stepwise regression methodology applied to the Polynomial Chaos terms used for the uncertainty quantification. Aeronautical test cases proposed by UMRIDA consortium are used to verify the validity of the methodologies. In the second part, the state of art methodologies for Robust Design Optimization are compared with a new proposed approach, based on a min-max definition of the objectives, and the application of Polynomial Chaos coefficients for an accurate definition of percentiles (reliability-based robust design optimization). Also in this case an Aeronautical CFD test case is proposed to validate the methodologies.

Proposed is a novel method for inverse uncertainty propagation, ultimately aiming to facilitate the wider uncertainty allocation problem. The approach is enabled by techniques for the reversal of computational workflows and for the efficient propagation of uncertainty. The method is validated with analytical and numerical examples. Also a representative aircraft sizing code is used to illustrate the application in a more realistic setting.

An aerodynamic configuration of a supersonic business jet wing-body is proposed as baseline for a robust aerodynamic shape design problem. This configuration has been analyzed to identify the main dependencies and interactions of the parameters that describe the uncertainty sources in the robust design problem. Subsequent steps of the research activity will be related to the robust natural laminar flow design optimization of this configuration.

We apply the concept of robustness to multi-objective optimization for finding robust Pareto optimal solutions. The multi-objective optimization and robustness problem is solved by using the $$\varepsilon $$ε-constraint method combined with the non-intrusive polynomial chaos approach for uncertainty quantification. The resulting single-objective optimization problems are solved with a deterministic method using algorithmic differentiation for the needed derivatives. The proposed method is applied to an aerodynamic shape optimization problem for minimizing drag and maximizing lift in a steady Euler flow. We consider aleatory uncertainties in flight conditions and in the geometry separately to find robust solutions. In the case of geometrical uncertainties we apply a Karhunen-Loeve expansion to approximate the random field and make use of a dimension-adaptive quadrature based on sparse grid methods for the numerical integration in random space.

A novel formulation for design under uncertainty is presented, which is based on the computation of the mean value and the minimum of the function. The aim of the method is to exert a stronger control on the system output variability in the optimization loop at a moderate cost. This would reduce post-processing analysis of the PDF of the resulting optimal designs, by converging rapidly to the interesting individuals. In other words, in the set of designs resulting from the optimization, the new approach should be capable of discarding poor-performance design. Also, no a priori assumption of optimal PDF is made. The preliminary results presented in the paper proves the benefit of the new formulation.

This chapter introduces an approach to capture unmodelled components in dynamical systems through a hierarchical polynomial expansion in the state space. This approach is reminiscent of the empirical acceleration approach commonly used in precise orbit determination to account for unmodelled components in the force model.

This paper presents a new archiving strategy and some modified search heuristics for the Multi Agent Collaborative Search algorithm (MACS). MACS is a memetic scheme for multi-objective optimisation that combines the local exploration of the neighbourhood of some virtual agents with social actions to advance towards the Pareto front. The new archiving strategy is based on the physical concept of minimising the potential energy of a cloud of points each of which repels the others. Social actions have been modified to better exploit the information in the archive and local actions dynamically adapt the maximum number of coordinates explored in the pattern search heuristic. The impact of these modifications is tested on a standard benchmark and the results are compared against MOEA/D and a previous version of MACS. Finally, a real space related problem is tackled.

The multi-objective optimization approach has a large influence in the industrial production scheduling. The goal of such optimization is to find a production schedule that satisfies different, usually contradictory, production and business constraints. In the paper, memetic versions of three multi-objective algorithms with different approaches to problem solving are implemented. The customized reproduction operators and local search procedures are also used. These memetic algorithms are applied to real order-lists from a production company. It is shown that the multi-objective approaches are able to find high-quality solutions, also when quick respond is required to adapt to dynamic business conditions. According to the results it is concluded that for the two tested real-world problems the IBEA confirmed its superiority over the NSGA-II and SPEA2.

The stratum-type association analysis as a new data mining technique has been applied to the conceptual design of a single-stage launch vehicle with hybrid rocket engine. The conceptual design was performed by using design informatics, which has three points of view, i.e., problem definition, optimization, and data mining. The primary objective of the present design is that the down range and the duration time in the lower thermosphere are sufficiently secured for the aurora scientific observation, whereas the initial gross weight is held down to the extent possible. The multidisciplinary design optimization was performed by using a hybrid evolutionary computation. Data mining was also implemented by using the stratum-type association analysis. Consequently, the design information regarding the tradeoffs has been revealed. The hierarchical dendrogram generated by using the stratum-type association analysis indicates the structure of the design space in order to improve the objective functions. Furthermore, the assignments of the stratum-type association analysis have been obtained.

The routing of employees who provide services such as home health or social care is a complex problem. When sending an employee between two addresses, there may exist more than one travel option, e.g. public transport or car. In this paper we examine the optimisation of travel plans, supporting the provision of health and social services, with respect to objectives of travel times and estimated CO$$_2$$2 produced. We include modal choice, either car or public transport as a decision variable. Car travel is normally quicker, but has a higher CO$$_2$$2 cost, whereas public transport may have longer journey times, but produces less CO$$_2$$2. We examine a set of problems involving real city and transport network data based in the UK cities of Edinburgh and London. We show that a multi-objective Evolutionary Algorithm can produces Pareto sets of solutions that allow a trade off between CO$$_2$$2 and travel time through the use of the decision variable.

We describe a new rich VRP model that captures many real-world constraints, following a recently proposed taxonomy that addresses both scenario and problem physical characteristics. The model is used to generate 4800 new instances of rich VRPs which is made freely available. To the best of our knowledge this represents the most comprehensive resource of rich VRP problems available, and provides a platform for researchers to conduct rigorous comparisons of new methods and solvers, moving academic research much closer to real practice in the future.

The conceptual design of a multi-stage launch vehicle (LV) using a clustered hybrid rocket engine (HRE) is carried out through multi-disciplinary design optimization. This LV designed in this study can deliver micro-satellites to sunsynchronous orbits (SSO). The optimum size of each component, such as an oxidizer tank containing liquid oxidizer, a combustion chamber containing solid fuel, a pressurizing tank, and a nozzle, should be strictly optimized because of the combustion mechanism is different from existent liquid/solid rocket engines. In this study, the semi-empirical based evaluation is applied to the design optimization of the multi-stage LV. For clustered HRE, paraffin (FT-0070) is used as a propellant for the HRE, and three cases are compared to examine the commonization effect of the engine for each stage: In the first case, HREs are optimized for each stage. In the second case, HREs are optimized together for the first and second stages but separately for the third stage. In the third case, HREs are optimized together for each stage. The optimization results show that the performance of the design case that uses the same HREs in all stages is 40% reduced compared with the design case that uses optimized HREs for each stage.

A global optimization method for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the global topology optimization method in flow problems, this research works on two single-objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and the multi-objective optimization problem, which combines these two problems. The shape of flow channels is represented by the level set function, and the pressure loss and the temperature of the channels are evaluated by the Building-Cube Method (BCM), which is a Cartesian-mesh CFD approach. The proposed method resulted in an agreement with previous study in the single-objective problems in its topology, and achieved global exploration of non-dominated solutions in the multi-objective problem.

In this paper we present a matrix-free geometric multigrid method for solving a linear system of equations needed at every iteration of the topology optimization process. The multigrid solver is parallelized on an Nvidia graphics card using CUDA, therefore reducing simulation time drastically. This enables users to derive optimal topologies represented with a high number of elements while having low execution time. Computational domain is discretized with a regular structured hexahedral mesh. To improve the accuracy of the non-conformal discretizazion, the Dirichlet boundary conditions are imposed in a weak form using Nitsche method.