A method for determining the optimal delivered hydrogen pressure for fuel cell electric vehicles
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Results for “optimality”
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Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method
Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.
bundle method↗
Optimization of global model composed of radial basis functions using the term-ranking approach
A term-ranking method is put forward to optimize the global model composed of radial basis functions to improve the predictability of the model. The effectiveness of the proposed method is examined by numerical simulation and experimental data. Numerical simulations indicate that this method can significantly lengthen the prediction time and decrease the Bayesian information criterion of the model. The application to real voice signal shows that the optimized global model can capture more predictable component in chaos-like voice data and simultaneously reduce the predictable component (periodic pitch) in the residual signal.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids
This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flow equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow
In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Dendrite-Free and Performance-Enhanced Lithium Metal Batteries through Optimizing Solvent Compositions and Adding Combinational Additives
The instability of lithium (Li) metal anode due to the dendritic growth and low Coulombic efficiency hinders the practical application of the well-regarded high-energy-density Li metal batteries. Here we report the systematic studies of improving the stability of Li metal anode and the electrochemical performances of the related Li metal batteries through the addition of combinational additives and the optimization of solvent compositions in dual-salt/carbonate electrolytes. A dendrite-free and high Coulombic efficiency of 98.1% for Li metal anode is achieved. The well protection of the Li metal anode and the excellent cyclability and rate capability of the 4-V Li metal batteries have been obtained. This is attributed to the formation of a robust, denser, more polymeric and higher ionic conductive surface film on the Li metal anode via the electrochemical reductive decompositions of the electrolyte components and the ring-opening polymerization of additives and cyclic carbonate solvents. The key findings of this work emphasize that the optimization of solvent compositions and the manipulation of the additives are facile and effective to enhance the Li metal battery performances.
Li metal batteries, dual-salt electrolyte, additiv↗
An optimization-based web application for synthesis and analysis of biomass-to-fuel strategies: An optimization-based web application for synthesis and analysis of biomass-to-fuel strategies
We develop an optimization-based web application for assessing biomass-to-fuels strategies based on the Biomass Utilization Superstructure (BUS) framework. This web application allows researchers with limited knowledge of optimization to assess different technologies employed at different strategies and identify the major cost drivers. The user must only provide the necessary parameters and create an optimization run after identifying the question to be addressed and the assessment metric. The web application generates visual representations of the results once the optimal solution is obtained. Finally, we demonstrate the applicability of the web application through an example.
09 BIOMASS FUELS↗
Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]
In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.
42 ENGINEERING↗
Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.
97 MATHEMATICS AND COMPUTING↗
Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget
Full configuration interaction (FCI) solvers are limited to small basis sets due to their expensive computational costs. An optimal orbital selection for FCI (OptOrbFCI) is proposed to boost the power of existing FCI solvers to pursue the basis set limit under a computational budget. The optimization problem coincides with that of the complete active space SCF method (CASSCF), while OptOrbFCI is algorithmically quite different. OptOrbFCI effectively finds an optimal rotation matrix via solving a constrained optimization problem directly to compress the orbitals of large basis sets to one with a manageable size, conducts FCI calculations only on rotated orbital sets, and produces a variational ground-state energy and its wave function. Coupled with coordinate descent full configuration interaction (CDFCI), we demonstrate the efficiency and accuracy of the method on the carbon dimer and nitrogen dimer under basis sets up to cc-pV5Z. We also benchmark the binding curve of the nitrogen dimer under the cc-pVQZ basis set with 28 selected orbitals, which provide consistently lower ground-state energies than the FCI results under the cc-pVDZ basis set. Furthermore, the dissociation energy in this case is found to be of higher accuracy.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Communication: Optimal parameters for basin-hopping global optimization based on Tsallis statistics
A fundamental problem associated with global optimization is the large free energy barrier for the corresponding solid-solid phase transitions for systems with multi-funnel energy landscapes. To address this issue we consider the Tsallis weight instead of the Boltzmann weight to define the acceptance ratio for basin-hopping global optimization. Benchmarks for atomic clusters show that using the optimal Tsallis weight can improve the efficiency by roughly a factor of two. We present a theory that connects the optimal parameters for the Tsallis weighting, and demonstrate that the predictions are verified for each of the test cases.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Use Conditions and Efficiency Measurements of DC Power Optimizers for Photovoltaic Systems
No consensus standard exists for estimating annual conversion efficiency of DC-DC converters or power optimizers in photovoltaic (PV) applications. The performance benefits of PV power electronics including per-panel DC-DC converters depend in large part on the operating conditions of the PV system, along with the performance characteristics of the power optimizer itself. This work presents acase study of three system configurations that take advantage of the capabilities of DC power optimizers. Measured conversion efficiencies of DC-DC converters are applied to these scenarios to determine the annual weighted operating efficiency. A simplified general method of reporting weighted efficiency is given, based on the California Energy Commission's CEC efficiency rating and severalinput / output voltage ratios. Efficiency measurements of commercial power optimizer products are presented using the new performance metric, along with a description of the limitations of the approach.
14 SOLAR ENERGY↗
Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion
In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.
Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗
Analysis and Optimization of a Multi-Layer Integrated Organic Substrate for High Current GaN HEMT-Based Power Module
In this paper, analysis and optimization of a multi-layer organic substrate for high current GaN HEMT based power module are discussed. The organic multi-layer substrates can provide high electrical performance in terms of low parasitic inductance in the power loop by providing vertical layout, and shielding for reduction of common-mode noise, a common problem in fast switching power converters. Furthermore, high performance cooling solutions, such as micro-channel heat sinks, can be directly bonded to the substrate for optimum thermal management. The structure of the proposed architecture, thermal analysis and optimization of layer thickness, thermo-mechanical stress analysis of the GaN HEMT and development of a high-performance heat sink are discussed.
47 OTHER INSTRUMENTATION↗
WE-AB-209-09: Optimization of Rotational Arc Station Parameter Optimized Radiation Therapy
Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of improving VMAT in both plan quality and delivery efficiency. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based Proximal Operator Graph Solver (POGS) within seconds. Apertures with zero or low weight were thrown out. To avoid being trapped in a local minimum, a stochastic gradient descent method was employed which also greatly increased the convergence rate of the objective function. The above procedure repeated until the plan could not be improved any further. A weighting factor associated with the total plan MU also indirectly controlled the complexities of aperture shapes. The number of apertures for VMAT and SPORT was confined to 180. The SPORT allowed the coexistence of multiple apertures in a single SP. The optimization technique was assessed by using three clinical cases (prostate, H&N and brain). Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. Prostate case: the volume of the 50% prescription dose was decreased by 22% for the rectum. H&N case: SPORT improved the mean dose for the left and right parotids by 15% each. Brain case: the doses to the eyes, chiasm and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the H&N case. Conclusion: The superior dosimetric quality and delivery efficiency presented here indicates that SPORT is an intriguing alternative treatment modality.
60 APPLIED LIFE SCIENCES↗
Optimization of rotational arc station parameter optimized radiation therapy
Purpose: To develop a fast optimization method for station parameter optimized radiation therapy (SPORT) and show that SPORT is capable of matching VMAT in both plan quality and delivery efficiency by using three clinical cases of different disease sites. Methods: The angular space from 0° to 360° was divided into 180 station points (SPs). A candidate aperture was assigned to each of the SPs based on the calculation results using a column generation algorithm. The weights of the apertures were then obtained by optimizing the objective function using a state-of-the-art GPU based proximal operator graph solver. To avoid being trapped in a local minimum in beamlet-based aperture selection using the gradient descent algorithm, a stochastic gradient descent was employed here. Apertures with zero or low weight were thrown out. To find out whether there was room to further improve the plan by adding more apertures or SPs, the authors repeated the above procedure with consideration of the existing dose distribution from the last iteration. At the end of the second iteration, the weights of all the apertures were reoptimized, including those of the first iteration. The above procedure was repeated until the plan could not be improved any further. The optimization technique was assessed by using three clinical cases (prostate, head and neck, and brain) with the results compared to that obtained using conventional VMAT in terms of dosimetric properties, treatment time, and total MU. Results: Marked dosimetric quality improvement was demonstrated in the SPORT plans for all three studied cases. For the prostate case, the volume of the 50% prescription dose was decreased by 22% for the rectum and 6% for the bladder. For the head and neck case, SPORT improved the mean dose for the left and right parotids by 15% each. The maximum dose was lowered from 72.7 to 71.7 Gy for the mandible, and from 30.7 to 27.3 Gy for the spinal cord. The mean dose for the pharynx and larynx was reduced by 8% and 6%, respectively. For the brain case, the doses to the eyes, chiasm, and inner ears were all improved. SPORT shortened the treatment time by ∼1 min for the prostate case, ∼0.5 min for brain case, and ∼0.2 min for the head and neck case. Conclusions: The dosimetric quality and delivery efficiency presented here indicate that SPORT is an intriguing alternative treatment modality. With the widespread adoption of digital linac, SPORT should lead to improved patient care in the future.
60 APPLIED LIFE SCIENCES↗
A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles
The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion. Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Toward “optimal” integration of terrestrial biosphere models
Multimodel ensembles (MME) are commonplace in Earth system modeling. Here we perform MME integration using a 10-member ensemble of terrestrial biosphere models (TBMs) from the Multiscale synthesis and Terrestrial Model Intercomparison Project (MsTMIP). We contrast optimal (skill based for present-day carbon cycling) versus naive (one model-one vote) integration. MsTMIP optimal and naive mean land sink strength estimates (-1.16 versus -1.15 Pg C per annum respectively) are statistically indistinguishable. This holds also for grid cell values and extends to gross uptake, biomass, and net ecosystem productivity. TBM skill is similarly indistinguishable. The added complexity of skill-based integration does not materially change MME values. This suggests that carbon metabolism has predictability limits and/or that all models and references are misspecified. Finally, resolving this issue requires addressing specific uncertainty types (initial conditions, structure, and references) and a change in model development paradigms currently dominant in the TBM community.
54 ENVIRONMENTAL SCIENCES↗