Global minimization of total exergy loss of multicomponent distillation configurations
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Global optimization of multicomponent distillation configurations: Global minimization of total cost for multicomponent mixture separations
We introduce a global optimization framework for determining the minimum cost required to distill any ideal or near-ideal multicomponent mixture into its individual constituents using a sequence of columns. This new framework extends the Global Minimization Algorithm (GMA) previously introduced by Nallasivam et al. (2016); and we refer to the new framework as the Global Minimization Algorithm for Cost (GMAC). GMAC guarantees global optimality by formulating a nonlinear program (NLP) for each and every distillation configuration in the search space and solving it using global optimization solvers. In conclusion, the case study presented in this work not only demonstrates the need for developing such an algorithm, but also shows the flexibility and effectiveness of GMAC, which enables process engineers to design and retrofit energy efficient and cost-effective distillation configurations.
42 ENGINEERING↗
Global optimization of multicomponent distillation configurations: 2. Enumeration based global minimization algorithm
We present a general Global Minimization Algorithm (GMA) to identify basic or thermally coupled distillation configurations that require the least vapor duty under minimum reflux conditions for separating any ideal or near-ideal multicomponent mixture into a desired number of product streams. In this algorithm, global optimality is guaranteed by modeling the system using Underwood equations and reformulating the resulting constraints to bilinear inequalities. The speed of convergence to the globally optimal solution is increased by using appropriate feasibility and optimality based variable-range reduction techniques and by developing valid inequalities. As a result, the GMA can be coupled with already developed techniques that enumerate basic and thermally coupled distillation configurations, to provide for the first time, a global optimization based rank-list of distillation configurations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Experimental observation of chimera and cluster states in a minimal globally coupled network
A “chimera state” is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Global minimization via classical tunneling assisted by collective force field formation
Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a “Lyapunov force,” which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.
97 MATHEMATICS AND COMPUTING↗
A filled function method for global optimization with inequality constraints
In this paper, we propose a new filled function method for finding a global minimizer of global optimization with inequality constraints. The proposed filled function is a continuously differentiable function with only one parameter. Then, we can use classical local optimization methods to find a better minimizer of the proposed filled function with a few parameter adjustment. The numerical experiments are made and the results show that the proposed filled function method is effective.
97 MATHEMATICS AND COMPUTING↗
Adversarial classification via distributional robustness with Wasserstein ambiguity
Abstract We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification, and we explore links to adversarial classification models proposed earlier and to maximum-margin classifiers. We also provide a reformulation of the distributionally robust model for linear classification, and show it is equivalent to minimizing a regularized ramp loss objective. Numerical experiments show that, despite the nonconvexity of this formulation, standard descent methods appear to converge to the global minimizer for this problem. Inspired by this observation, we show that, for a certain class of distributions, the only stationary point of the regularized ramp loss minimization problem is the global minimizer.
Ho-Nguyen, Nam (ORCID:0000000344647730)↗
A GPU-based Approach for Path Planning Optimization via Travel Length Reduction
Typically, before constructing an object with an additive manufacturing system, the 3D object must be sent through a process called slicing. Slicing converts a 3D object commonly in the form of an STL file into a set of layers by horizontally intersecting a plane with the object at various heights. At each height, called a layer, multiple 2D polygons can be generated. Each polygon represents a boundary for solid geometry and is called an island. Each island is then comprised of multiple path types in an attempt to optimally fill the polygon. To move between each island and each islands’ paths, travels are inserted. Travels are simply motion by the system to move from one area of construction to another. Travels do not contribute to the construction of the object, and so, are considered wasted motion. In large-scale additive manufacturing, objects can be quite large and the distance between islands can be large as well. As a result, these travels can waste a significant amount of time. Ideally, travels would be as short as possible, however, computing global minimal travel paths is computationally expensive. To combat this problem, researchers at Oak Ridge National Lab developed a GPU-based approach to travel insertion based on a unique factoradic representation. This representation was then utilized by the GPU to solve the Traveling Salesman Problem (TSP). This algorithm was able to compute global minimal travel paths quickly resulting in faster object construction. A general investigation was also carried out to determine when a GPU vs CPU implementation would be beneficial.
Borish, Michael↗
FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration
Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.
Feng, Xue [University of California, Davis]↗
A framework and tool for designing cost-effective, resilient, and circular net-zero supply chains under uncertainty with an application to multilayer plastic films
While 55% of Fortune 500 companies have committed to achieving net-zero emissions and/or zero-waste operations by 2035, only 2% are currently on track, revealing a critical gap between ambition and action. Designing supply chains that reduce both emissions and waste is a complex non-intuitive, multi-objective challenge, compounded by the high costs of new technologies and the need for resilient, profitable solutions. This paper aims to address this challenge by presenting a generic framework and multi-objective optimization formulation for designing cost-effective, circular, and resilient supply chains under uncertainty, implemented through a user-friendly decision-support tool with intuitive data visualization capabilities, enabling communication of results to both technical and non-technical stakeholders. We demonstrate the application of this framework in the context of multilayer plastic films (barrier films), which are widely used in food packaging and composite materials. The model quantifies trade-offs across three objectives: minimizing global warming potential, maximizing circularity, and minimizing cost. A key contribution of this work is the explicit modeling of technological resilience, the ability of supply chains to maintain function under disruption. In the cost-minimization case, the resilience constraint makes the design approximately three times more expensive in the short-term metric, but shifts the system from relying on a single recovery pathway to a portfolio of four recovery pathways, improving the robustness of the optimization solution under uncertainty. Lastly, we introduce TranZero, a decision-support tool that integrates material flow analysis, hotspot identification, and optimization-based scenario planning to support net-zero and circularity decisions.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems
We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists of choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to the nonconvex AC power flow constraints, and bilevel solution approaches commonly apply a convex relaxation or approximation to allow for tractable bilevel reformulations at the cost of underestimating some power system vulnerabilities. Our main contribution is to provide an alternative branch-and-bound algorithm whose upper bounding mechanism (in a maximization context) is based on a reformulation that avoids relaxation of the AC power flow constraints in the lower-level defender problem. Lower bounding is provided with semidefinite programming (SDP) relaxed solutions to the lower-level problem. We establish finite termination with guarantees of either a globally optimal solution to the original bilevel problem, or a globally optimal solution to the SDP-relaxed bilevel problem which is included in a vetted list of upper-level attack solutions, at least one of which is a globally optimal solution to the bilevel problem. We demonstrate through computational experiments applied to IEEE case instances both the relevance of our contribution, and the effectiveness of our contributed algorithm for identifying power system vulnerabilities without resorting to convex relaxations of the lower-level problem. We conclude with a discussion of future extensions and improvements.
97 MATHEMATICS AND COMPUTING↗
An Evaluation of the Effect of Network Cost Optimization for Leadership Class Supercomputers
Dragonfly-based networks are an extensively deployed network topology in large-scale high-performance computing due to their cost-effectiveness and efficiency. The US will soon have three Exascale supercomputers for leadership class workloads deployed using dragonfly networks. Compared to indirect networks of similar scale, the dragonfly network has considerably reduced cable lengths, cable counts, and switch counts, resulting in significant network cost savings for a given system size, however, these cost reductions result in reduced global minimal paths and more challenging routing. Additionally, large scale dragonfly networks often require a taper at the global link level, resulting in less bisection bandwidth than is achievable in other traditional non-blocking topologies of equivalent scale. While dragonfly networks have been extensively studied, they have yet to be fully evaluated in an extreme scale (i.e., exascale) system that targets capability workloads. In this paper, we present the results of the first large scale evaluation of a dragonfly network on an exascale system (Frontier) and compare its behavior to a similar scale fat-tree network on a previous generation TOP500 system (Summit). This evaluation aims to determine the effect of network cost optimizations by measuring a tapered topology’s impact on capability workloads. Our evaluation is based on a collection of synthetic microbenchmarks, mini-apps, and full scale applications. It compares the scaling efficiencies of each benchmark between the dragonfly-based Frontier and the fat-tree-based Summit systems. Our results show that a dragonfly network is $\sim \mathbf{3 0 \%}$ more cost efficient than a fat-tree topology, which amortizes to $\sim 3 \%$ of an exascale system cost. Furthermore, while tapered dragonfly networks impose significant tradeoffs, the impacts are not as broad as initially thought and are mostly seen in applications with global communication patterns, particularly all-to-all (e.g., FFT-based algorithms), but also local communication patterns (e.g., nearest-neighbor algorithms) that are sensitive to network performance variability.
Khan, Awais↗
Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1
The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.
Brown, Aaron J.↗
Detailed analysis of excited-state systematics in a lattice QCD calculation of 𝑔 𝐴
Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations ≳ 1 fm are commonly used to combat these issues. In this work, focusing on g A , we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Active control of sound transmission/radiation from elastic plates by vibration inputs. II - Experiments
Actively controlled harmonic force inputs were applied experimentally to reduce the sound transmitted through an elastic circular plate. The control implementation used a time domain least mean square adaptive algorithm with two error sensors. The control forces were applied directly to the plate by point force vibration inputs, while the error information and performance were measured in the radiated acoustic field by microphones. Test cases were also performed in which the error sensors were accelerometers mounted on the plate. When accelerometers were used as error sensors, the controller performance was degraded; leading to the conclusion that minimizing plate motion does not necessarily lead to an associated decrease in radiated sound levels. In contrast, the results show excellent attenuation of the transmitted sound field when microphone error sensors were used. This result was consistent over a range of frequencies. In addition, the experimental results are compared to previously derived analytical results and the effect of using a point or global minimization scheme is discussed.
Metcalf, V. L.↗
Stratospheric Aerosol Injection Can Reduce Risks to Antarctic Ice Loss Depending on Injection Location and Amount
Owing to increasing greenhouse gas emissions, the Antarctic Ice Sheet is vulnerable to rapid ice loss in the upcoming decades and centuries. Here this study examines the effectiveness of using stratospheric aerosol injection (SAI) that minimizes global mean temperature (GMT) change to slow projected 21st century Antarctic ice loss. We simulate 11 different SAI cases which vary by the latitudinal location(s) and the amount(s) of the injection(s) to examine the climatic response near Antarctica in each case as compared to the reference climate at the turn of the last century. We demonstrate that injecting at a single latitude in the northern hemisphere or at the Equator increases Antarctic shelf ocean temperatures pertinent to ice shelf basal melt, while injecting only in the southern hemisphere minimizes this temperature change. We use these results to analyze the results of more complex multi-latitude injection strategies that maintain GMT at or below 1.5°C above the pre-industrial. All these multi-latitude cases will slow Antarctic ice loss relative to the mid-to-late 21st century SSP2-4.5 emissions pathway. Yet, to avoid a GMT threshold estimated by previous studies pertaining to rapid West Antarctic ice loss (1.5°C above the pre-industrial GMT, though large uncertainty), our study suggests SAI would need to cool about 1.0°C below this threshold and predominately inject at low southern hemisphere latitudes (~15°S - 30°S). These results highlight the complexity of factors impacting the Antarctic response to SAI and the critical role of the injection strategy in preventing future ice loss.
54 ENVIRONMENTAL SCIENCES↗
Short-cut Methods versus Rigorous Methods for Performance-evaluation of Distillation Configurations
Here, this study demonstrates the efficacy of a short-cut method such as the Global Minimization Algorithm (GMA), that uses assumptions of ideal mixtures, constant molar overflow (CMO) and pinched columns, in pruning the search-space of distillation column configurations for zeotropic multicomponent separation, to provide a small subset of attractive configurations with low minimum heat duties. The short-cut method, due to its simplifying assumptions, is computationally efficient, yet reliable in identifying the small subset of useful configurations for further detailed process evaluation. This two-tier approach allows expedient search of the configuration space containing hundreds to thousands of candidate configurations for a given application.
42 ENGINEERING↗
Addressing Criticality in Rare Earth Elements via Permanent Magnets Recycling
Rare earth elements (REEs) are critical for many advanced technologies and are faced with potential supply disruptions. Recycling of permanent magnets (PMs) can be good sources for REEs which can help minimize global dependence on freshly mined REEs, but PMs are rarely recycled. Recycling of PMs has been discussed with respect to improving REEs resource sustainability. Some challenges to be addressed in order to establish industrially deployable technologies for PMs recycling have also been discussed, including profitability, energy efficiency and environmental impacts. Key considerations for promoting circular economy via PMs recycling is proposed with the focus on deciding the target points in the supply chain at which the recycled products will be inserted. Important technical considerations for recycling different forms of waste PMs, including swarfs, slags, shredded and intact hard disk drives magnets, have been presented. Lastly, the aspects of circular economy considered include reusing magnets, remanufacturing magnets and recovering of REEs from waste PMs.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗