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At least 55 records · Page 3

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator

JAXtronomy: A JAX port of lenstronomy

Gravitational lensing is a phenomenon where light bends around massive objects, resulting in distorted images seen by an observer. Studying gravitationally lensed systems provides insights into cosmology and astrophysics, including constraints of the expansion rate of the Universe and the distribution of dark matter. Thus, we introduce JAXtronomy, a re-implementation of the gravitational lensing software package lenstronomy (Birrer, 2021; Birrer & Amara, 2018) using JAX (Bradbury et al., 2018). JAX is a Python library that uses an accelerated linear algebra (XLA) compiler to improve the performance of computing software. Our core design principle of JAXtronomy is to maintain an identical API to that of lenstronomy. The main JAX features utilized in JAXtronomy are just-in-time compilation, which can lead to significant reductions in execution time, and automatic differentiation, which allows for the implementation of gradient-based algorithms that were previously impossible. Additionally, JAX allows code to be run on GPUs or parallelized across CPU cores, further boosting the performance of JAXtronomy.

astronomy

Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks

We explore the practicability of optimal shape design for flows modeled by the Euler equations. We define a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a co-state equation. The optimization problem is then examined by comparing the performance of several gradient-based optimization algorithms. In this formulation, the flow field can be computed to an arbitrary order of accuracy. Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.

Iollo, Angelo

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Samareh, Jamshid A.

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Taylor, Arthur C., III

HDBind: encoding of molecular structure with hyperdimensional binary representations

Traditional methods for identifying “hit” molecules from a large collection of potential drug-like candidates rely on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have a significant limitation in that they require exceptional computing capabilities for even relatively small collections of molecules. Increasingly large and complex state-of-the-art deep learning approaches have gained popularity with the promise to improve the productivity of drug design, notorious for its numerous failures. However, as deep learning models increase in their size and complexity, their acceleration at the hardware level becomes more challenging. Hyperdimensional Computing (HDC) has recently gained attention in the computer hardware community due to its algorithmic simplicity relative to deep learning approaches. The HDC learning paradigm, which represents data with high-dimension binary vectors, allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas (computer vision, bioinformatics, mass spectrometery, remote sensing, edge devices, etc.). To the best of our knowledge, our work is the first to consider HDC for the task of fast and efficient screening of modern drug-like compound libraries. We also propose the first HDC graph-based encoding methods for molecular data, demonstrating consistent and substantial improvement over previous work. We compare our approaches to alternative approaches on the well-studied MoleculeNet dataset and the recently proposed LIT-PCBA dataset derived from high quality PubChem assays. We demonstrate our methods on multiple target hardware platforms, including Graphics Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs), showing at least an order of magnitude improvement in energy efficiency versus even our smallest neural network baseline model with a single hidden layer. Our work thus motivates further investigation into molecular representation learning to develop ultra-efficient pre-screening tools. We make our code publicly available at https://github.com/LLNL/hdbind.

59 BASIC BIOLOGICAL SCIENCES

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full-Waveform Inversion

Concrete is a vital material in construction—especially in the nuclear industry, where it is used in critical structures such as containment vessels. Over time, concrete can degrade due to harsh operational and environmental conditions, necessitating that its elastic properties be accurately evaluated to ensure structural integrity and safety. Traditional nondestructive evaluation methods such as ultrasound-based techniques often rely on simplifying assumptions that may not hold true for concrete. This paper presents an advanced ultrasound-based method that uses elastic full-waveform inversion (EFWI) to create detailed images of concrete’s mechanical properties. By accurately modeling wave behaviors such as scattering and reflection, we aim to overcome the limitations of conventional ultrasonic-based methods. In this work, the imaging problem involved reconstructing the various elastic properties of a heterogenous concrete block with three steel rebars embedded in it. The ultrasonic measurements were synthetically generated from multiple sources and receivers, and the reconstruction process was performed using a gradient-based optimization algorithm. Our approach leveraged EFWI to reconstruct high-resolution images of the pressure wave speed, shear wave speed, and density. Multiple misfit functions—including L2-norm, cross-correlation (CC), and L1-norm—combined with total variation (TV) regularization and parameter constraints using a Sigmoid function—were explored for the reconstruction. The results demonstrated that using the L1-norm misfit function in conjunction with TV regularization and Sigmoid constraints significantly improved the reconstruction quality in comparison to traditional methods. This approach provided clearer images with fewer artifacts and better captured background heterogeneity. Our findings highlight that, when properly designed, EFWI carries great potential for providing comprehensive, more accurate, and more reliable assessments of concrete conditions, as is crucial for the maintenance and safety of nuclear power plant structures.

97 - MATHEMATICS AND COMPUTING

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Adaptive Cybersecurity for Distributed Energy Resources (AdCyDER): Online Reinforcement Learning with Stackelberg-Optimized Defenses — Pipeline Architecture, Evaluation Methodology, and Findings from a Synthetic-Data Evaluation

This report documents the design and evaluation of an integrated online-learning pipeline developed within the AdCyDER project for Distributed Energy Resource (DER) cybersecurity. The pipeline couples a Reinforcement Learning (RL) attack classifier — which produces an attack-type probability distribution — with a Stackelberg game-theoretic (GT) defense selector that consumes those distributions alongside SME-encoded priors over (defense, attack) effectiveness pairings and perdefense costs to choose grid-health-preserving defenses. The objective is not attack classification per se but production of distributions that drive effective defense selection through the Stackelberg layer, learned from delayed grid-health feedback rather than labeled attack data. AdCyDER as a whole is broader than the work presented here; this report covers the specific RL/GT loop integration and its evaluation. We present the integrated pipeline (SCADA telemetry with Fronius inverter physics, Suricata IDS, time-windowed aggregation, per-facility LSTM classifier, Stackelberg optimizer, OpenC2 actuators), an experimental campaign of 28 eight-hour iterations across three baseline modes, and a pipeline-ordered diagnostic protocol. The protocol identifies two distinct failure modes within the loop: paired supervised ceilings on the same features establish that the deployed online RL classifier (macro F1 ≈ 0.07) sits at least 4.7× below a same-architecture supervised LSTM (≈ 0.34) and 10–11× below a linear feature-signal ceiling (≈ 0.70–0.79 depending on per-facility isolation), localizing the dominant failure to the training procedure; and the reward signal driving online updates carries weak directional coupling with classifier correctness in the methodology-expected direction (multi-lens convergent: top-decile P(true) records produce more frequent state changes and slightly larger improvements, top-vs-bot Cohen’s 𝑑 ≈ −0.19), but at effect magnitudes too small to drive gradient-based learning at the campaign sample size. The original learning hypothesis is not supported by the data. The primary contributions are the diagnostic methodology — proposed as a transferable falsification protocol for online RL/GT defense pipelines learning from delayed environmental reward — and the open, reproducible experimental infrastructure. We outline reward reformulation as the highest-priority aspirational next step given the underpowered-but-aligned Q6 reading, with hardware-in-the-loop evaluation as the broadest scope-expansion option.

Blakely, Benjamin [Argonne National Laboratory (AN

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY

Multidisciplinary Design Techniques Applied to Conceptual Aerospace Vehicle Design

Multidisciplinary design optimization (MDO) is an emerging discipline within aerospace engineering. Its goal is to bring structure and efficiency to the complex design process associated with advanced aerospace launch vehicles. Aerospace vehicles generally require input from a variety of traditional aerospace disciplines - aerodynamics, structures, performance, etc. As such, traditional optimization methods cannot always be applied. Several multidisciplinary techniques and methods were proposed as potentially applicable to this class of design problem. Among the candidate options are calculus-based (or gradient-based) optimization schemes and parametric schemes based on design of experiments theory. A brief overview of several applicable multidisciplinary design optimization methods is included. Methods from the calculus-based class and the parametric class are reviewed, but the research application reported focuses on methods from the parametric class. A vehicle of current interest was chosen as a test application for this research. The rocket-based combined-cycle (RBCC) single-stage-to-orbit (SSTO) launch vehicle combines elements of rocket and airbreathing propulsion in an attempt to produce an attractive option for launching medium sized payloads into low earth orbit. The RBCC SSTO presents a particularly difficult problem for traditional one-variable-at-a-time optimization methods because of the lack of an adequate experience base and the highly coupled nature of the design variables. MDO, however, with it's structured approach to design, is well suited to this problem. The result of the application of Taguchi methods, central composite designs, and response surface methods to the design optimization of the RBCC SSTO are presented. Attention is given to the aspect of Taguchi methods that attempts to locate a 'robust' design - that is, a design that is least sensitive to uncontrollable influences on the design. Near-optimum minimum dry weight solutions are determined for the vehicle. A summary and evaluation of the various parametric MDO methods employed in the research are included. Recommendations for additional research are provided.

Olds, John Robert

Wing-section optimization for supersonic viscous flow

To improve the shape of a supersonic wing, an automated method that also includes higher fidelity to the flow physics is desirable. With this impetus, an aerodynamic optimization methodology incorporating thin-layer Navier-Stokes equations and sensitivity analysis had been previously developed. Prior to embarking upon the wind design task, the present investigation concentrated on testing the feasibility of the methodology, and the identification of adequate problem formulations, by defining two-dimensional, cost-effective test cases. Starting with two distinctly different initial airfoils, two independent shape optimizations resulted in shapes with similar features: slightly cambered, parabolic profiles with sharp leading- and trailing-edges. Secondly, the normal section to the subsonic portion of the leading edge, which had a high normal angle-of-attack, was considered. The optimization resulted in a shape with twist and camber which eliminated the adverse pressure gradient, hence, exploiting the leading-edge thrust. The wing section shapes obtained in all the test cases had the features predicted by previous studies. Therefore, it was concluded that the flowfield analyses and sensitivity coefficients were computed and fed to the present gradient-based optimizer correctly. Also, as a result of the present two-dimensional study, suggestions were made for the problem formulations which should contribute to an effective wing shape optimization.

Item, Cem C.

Wing-section optimization for supersonic viscous flows

The recent interest in High Speed Civil Transport (HSCT) has resulted in renewed research studies of optimized supersonic cruise transport configurations. Incorporation of flow viscosity effects in the design process of such a supersonic wing is currently under investigation. This may lead to more accurate problem formulations and, in turn, greater aerodynamic efficiency than can be obtained by the traditional, inviscid, linear theories. In this context, for a design code to be a candidate for a complex optimization problem, such as three-dimensional viscous supersonic wing design, it should be validated using simpler building-block shapes. To optimize the shape of a supersonic wing, an automated method that also includes higher fidelity to the flow physics is desirable. With this impetus, an aerodynamic optimization methodology incorporating Navier-Stokes equations and sensitivity analysis had been previously developed. Prior to embarking upon the wing design task, the present investigation concentrated on testing the flexibility of the methodology, and the identification of adequate problem formulations, by defining two-dimensional, cost-effective test cases. Starting with two distinctly different initial airfoils, two independent shape optimizations resulted in shapes with very similar features. Secondly, the normal section to the subsonic portion of the leading edge, which had a high normal angle-of-attack, was considered. The optimization resulted in a shape with twist and camber, which eliminated the adverse pressure gradient, hence, exploiting the leading-edge thrust. The wing section shapes obtained in all the test cases had the features predicted by previous studies. Therefore, it was concluded that the flowfield analyses and the sensitivity coefficients were computed and fed to the present gradient-based optimizer correctly. Also, as a result of the present two-dimensional study, suggestions were made for problem formulations which should contribute to an effective wing shape optimization.

Item, Cem C.

Three-Dimensional Viscous Alternating Direction Implicit Algorithm and Strategies for Shape Optimization

A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.

Pandya, Mohagna J.

Aerothermal Shape Optimization of Actively-Cooled Battery Packs using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

thermal management

A Modular Conjugate Heat Transfer Optimization Framework for Thermal Management of Electric Aircraft

Conjugate heat transfer (CHT) analysis and optimization is a powerful method for improving thermal management, as it simultaneously resolves the temperature distribution in both fluid and solid domains. This paper presents a modular, discrete adjoint-based CHT optimization capability integrated within the OpenMDAO/MPhys framework. A unique feature of the proposed framework is its flexibility to extend to multidisciplinary optimization, including aero-structural-thermal applications. The fluid domain is modeled using a finite-volume Computational Fluid Dynamics (CFD) solver, and the solid domain with a conduction heat transfer solver. A mixed Neumann-Dirichlet boundary condition is developed to enable full submersion of the solid geometry within the fluid domain, while ensuring consistent temperature and heat flux coupling at the CHT interface. Gradient-based optimization is performed; the gradients are efficiently computed using the discrete adjoint solvers implemented in DAFoam. To demonstrate the method, this paper considers two cases related to electric aircraft thermal management: a U-bend heat exchanger and an actively cooled battery pack. The U-bend case aims to minimize pressure loss while maximizing heat flux by changing the pipe geometry. The optimized design reduces pressure loss by 52.7% and increases total heat flux by 2.3%. In the battery pack case, a 3-by-3 cell configuration is cooled by ambient airflow, with constant heat generation prescribed in the cells. The battery casing shape serves as the design variable, and the objective function is a weighted sum of pressure loss and pack weight, subject to a maximum temperature constraint. The optimized design achieves a 44.6% reduction in pressure loss and a 1.5% reduction in weight, while satisfying the thermal constraint. To ensure the reliability of the optimized designs, this study validates coarse-mesh, steady-state predictions against fine-mesh unsteady simulations, demonstrating consistency within acceptable errors. This work demonstrates the potential of the developed framework to enable rapid, high-fidelity design of thermal management systems for electric aircraft.

heat transfer

DEVELOPMENT AND APPLICATION OF RISK ANALYSIS TOOLKIT FOR PLANT RESOURCE OPTIMIZATION

This paper presents the development of methods and tools that are being designed to optimize plant operations (e.g., maintenance/replacement schedules and optimal maintenance postures for plant components) in a manner that is more cost effective than current approaches and makes better use of available component health and cost data. These methods include both data- and model-based optimization methods. Model-based optimization methods directly include reliability and cost models to determine an optimal plant operational strategy. We consider gradient-based and evolutionary (based on genetic algorithms) optimization methods. The second class of methods target more specific use cases (e.g., project schedule optimization) and are not based on reliability models directly, but they require specific component reliability and cost data. This class of methods is based on variants of the knapsack problem with an aim to determine an optimal project schedule that maximizes the overall NPV. This paper also presents multi-objective methods designed to identify an optimal maintenance posture based on a Pareto frontier analysis. Rather than dictating the “right” tradeoff (i.e., identify the absolute best posture), we show how it is possible to perform a trade space exploration approach (i.e., identify value and costs of several postures and let the analysis account for desired value and cost metrics). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space. For all these methods we present detailed applicative examples that show their validity from a decision-making perspective.

97 - MATHEMATICS AND COMPUTING