Universal Optimization Research Articles

Method with batching for stochastic finite-sum variational inequalities in non-Euclidean setting

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this paper, we present an analysis of a method that gives optimal convergence estimates for monotone stochastic finite-sum variational inequalities. In contrast to the previous works, our method supports batching, does not lose the oracle complexity optimality and uses an arbitrary Bregman distance to take into account geometry of the problem. Paper provides experimental confirmation to algorithm’s effectiveness.

Waste heat-driven water generator with optimized multi-cycle strategy for high water yield

Water scarcity and energy crisis have recently become two severe global problems. Low-grade waste heat, a substantial byproduct of energy consumption, promises to provide safe water by driving sorption-based atmospheric water harvesting (SAWH) device. Herein, a low-grade waste heat-driven atmospheric water generator (LWG) is constructed with rapid kinetics at the system level. Solely in 3 h, the device obtains 1.766 g g−1 of water productivity and up to 98 % of water recovery ratio driven by 120 °C of waste heat. Further, an optimized multi-cycle operation strategy is proposed to guide LWG's daily water harvesting, enabling it to predictably obtain over 15 kg m−2 day−1 water productivity by maximizing systemic sorption and desorption-condensation rates. The strategy not only is widely suitable for all SAWH devices, but also provides a universal optimization guideline for sorption-based dehumidification, thermal storage, and electric thermal management.

The Universal Optimism of the Self-Evidencing Mind.

Karl Friston's free-energy principle casts agents as self-evidencing through active inference. This implies that decision-making, planning and information-seeking are, in a generic sense, 'wishful'. We take an interdisciplinary perspective on this perplexing aspect of the free-energy principle and unpack the epistemological implications of wishful thinking under the free-energy principle. We use this epistemic framing to discuss the emergence of biases for self-evidencing agents. In particular, we argue that this elucidates an optimism bias as a foundational tenet of self-evidencing. We allude to a historical precursor to some of these themes, interestingly found in Machiavelli's oeuvre, to contextualise the universal optimism of the free-energy principle.

Maximal Polarization for Periodic Configurations on the Real Line

Abstract We prove that among all 1-periodic configurations $\Gamma $ of points on the real line $\mathbb{R}$ the quantities $\min _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ and $\max _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number of points $n$ per period is sufficiently large (depending on $\alpha $). This solves the polarization problem for periodic configurations with a Gaussian weight on $\mathbb{R}$ for large $n$. The first result is shown using Fourier series. The second result follows from the work of Cohn and Kumar on universal optimality and holds for all $n$ (independent of $\alpha $).

Insight into the Dependence of Photovoltaic Performance on Interfacial Energy Alignment in Solar Cells with Mobile Ions

A key aspect in the optimization of perovskite (PVK) solar cells is the mitigation of interface losses, which are determined by energy band offsets and recombination. Counterintuitively, recent experimental evidence on inorganic PVK solar cells shows that increasing band offsets may improve open‐circuit voltage at efficiency levels over 20%. In order to improve the knowledge of the impact of interfaces, the authors model solar cells consisting of an intrinsic absorber material containing mobile ions, sandwiched between two wide‐gap charge transport layers. The results show that minimizing band offsets decreases interface losses in various scenarios, but cannot be adopted as a universal optimization rule. For instance, even in the absence of interface recombination, unequal majority carrier band offsets avoid high injection conditions. Moreover, assuming a fixed band offset at one interface, the band offset at the opposite interface should be reduced if it shows the highest interface recombination, or increased if it shows the lowest recombination. Remarkably, it is found that solar cells with mobile ions hold the potential to outperform of ion‐free counterparts, depending on the extent to which the interplay between band offsets and Debye layers result in the establishment of a majority carrier concentration in the intrinsic absorber.

Universal optimality and robust utility bounds for metric differential privacy1

We study the privacy-utility trade-off in the context of metric differential privacy. Ghosh et al. introduced the idea of universal optimality to characterise the “best” mechanism for a certain query that simultaneously satisfies (a fixed) ε-differential privacy constraint whilst at the same time providing better utility compared to any other ε-differentially private mechanism for the same query. They showed that the Geometric mechanism is universally optimal for the class of counting queries. On the other hand, Brenner and Nissim showed that outside the space of counting queries, and for the Bayes risk loss function, no such universally optimal mechanisms exist. Except for the universal optimality of the Laplace mechanism, there have been no generalisations of these universally optimal results to other classes of differentially-private mechanisms. In this paper, we use metric differential privacy and quantitative information flow as the fundamental principle for studying universal optimality. Metric differential privacy is a generalisation of both standard (i.e., central) differential privacy and local differential privacy, and it is increasingly being used in various application domains, for instance in location privacy and in privacy-preserving machine learning. Similar to the approaches adopted by Ghosh et al. and Brenner and Nissim, we measure utility in terms of loss functions, and we interpret the notion of a privacy mechanism as an information-theoretic channel satisfying constraints defined by ε-differential privacy and a metric meaningful to the underlying state space. Using this framework we are able to clarify Nissim and Brenner’s negative results by (a) that in fact all privacy types contain optimal mechanisms relative to certain kinds of non-trivial loss functions, and (b) extending and generalising their negative results beyond Bayes risk specifically to a wide class of non-trivial loss functions. Our exploration suggests that universally optimal mechanisms are indeed rare within privacy types. We therefore propose weaker universal benchmarks of utility called privacy type capacities. We show that such capacities always exist and can be computed using a convex optimisation algorithm. Further, we illustrate these ideas on a selection of examples with several different underlying metrics.

A Universal Optimization Framework for Learning-based Image Codec

Recently, machine learning-based image compression has attracted increasing interests and is approaching the state-of-the-art compression ratio. But unlike traditional codec, it lacks a universal optimization method to seek efficient representation for different images. In this paper, we develop a plug-and-play optimization framework for seeking higher compression ratio, which can be flexibly applied to existing and potential future compression networks. To make the latent representation more efficient, we propose a novel latent optimization algorithm to adaptively remove the redundancy for each image. Additionally, inspired by the potential of side information for traditional codecs, we introduce side information into our framework, and integrate side information optimization with latent optimization to further enhance the compression ratio. In particular, with the joint side information and latent optimization, we can achieve fine rate control using only single model instead of training different models for different rate-distortion trade-offs, which significantly reduces the training and storage cost to support multiple bit rates. Experimental results demonstrate that our proposed framework can remarkably boost the machine learning-based compression ratio, achieving more than 10% additional bit rate saving on three different representative network structures. With the proposed optimization framework, we can achieve 7.6% bit rate saving against the latest traditional coding standard VVC on Kodak dataset, yielding the state-of-the-art compression ratio.

Component-Based Test Case Generation and Prioritization Using an Improved Genetic Algorithm

Developing test cases is the most challenging and crucial step in the software testing process. The initial test data must be optimized using a strong optimization technique due to many testing scenarios and poor testing effectiveness. Test prioritization is essential for testing the developed software products in a production line with a restricted budget in terms of time and money. A good understanding of the trade-off between costs (e.g. time and resources needed) and efficiency (e.g. component coverage) is necessary to prioritize test case scenarios for one or more software products. So, this paper proposes an efficient Multi-objective Test Case Generation and Prioritization using an Improved Genetic Algorithm (MTCGP-IGA) in Component-based Software Development (CSD). A random search-based method for creating and prioritizing multi-objective tests has been employed utilizing numerous cost and efficacy criteria. Specifically, the multi-objective optimization comprises maximizing the Prioritized Range of test cases (PR), Pairwise Coverage of Characteristics (PCC), Fault-Finding Capability (FFC), and minimizing Total Implementation Cost (TIC). For this test prioritizing problem, a unique fitness function is constructed with cost-effectiveness metrics. IGA is a robust search technique that exhibits excellent benefits and significant efficacy in resolving challenging issues, including ample space, multiple-peak, stochastic, and universal optimization. Relying on the use of IGA, this paper classifies, computes the objective function, introduces the Nondominated Sorting Genetic Algorithm-II (NSGA-II) method, evaluates each branch’s proximity on the handling route, and arranges the path set to get the best answer. The outcomes demonstrate that the proposed MTCGP-IGA with NSGA-II performed the best than other baseline algorithms in terms of prioritizing the test cases (mean value of 195.2), PCC (mean score of 0.7828), and FFC (mean score of 0.8136).

Generalized entransy dissipation and its application in heat conduction optimizations with arbitrary boundary conditions

Heat conduction optimization with arbitrary boundary conditions is a challenging problem that lacks a universal optimization criterion. In the present work, the concept of generalized entransy dissipation (GED) is proposed through transforming heat conduction optimization problems with arbitrary boundaries into their homogeneous counterparts. It is demonstrated that minimizing GED leads to optimal thermal performance of heat conduction problems with arbitrary boundary conditions. In addition, GED-based continuous optimization problems are convex, guaranteeing the uniqueness and global optimality of the solution and benefitting numerical calculations. Two typical problems with complex boundary conditions are studied by applying the minimum principle of GED, and the results are compared with other optimization objectives. The numerical results show that GED achieves better thermal performance than entropy generation- (EG) and entransy dissipation- (ED) based optimizations. For the optimization of boundary average temperature under the given input heat flux of ▪, GED achieves the best result, where the optimized average temperature is ▪ and ▪ lower compared with EG and ED optimizations, respectively. In general, GED offers a reasonable and easy to implement optimization principle for heat conduction processes with arbitrary boundaries and may provide new insights for heat conduction optimization.

Autonomous Behavioral Decision for Vehicular Agents Based on Cyber-Physical Social Intelligence

In future smart cities supported by cyber-physical social intelligence, autonomous behavioral decision for vehicular agents is going to become a general demand. Despite much progress achieved in autonomous behavioral decision of vehicular agents, the existing works can just be used in scenarios of short-distance behavioral decision. Naturally, they are not well suitable for long-distance behavioral decision tasks, posing much challenge in realistic cyber-physical environment. To bridge the existing gaps, this article proposes an autonomous behavioral decision framework for vehicular agents using cyber-physical social intelligence. First, it is expected to establish a dynamic planning model with multiple objectives and constraints. This can be embedded into the control unit of a vehicular agent to endow it with proper social intelligence. On this basis, an iterative search algorithm is specifically designed for it to find the optimal solutions from the whole solution space. Finally, two typical situation cases are implemented with use of simulation modeling to display the working architecture of the proposed method. In addition, a universal optimization search algorithm is selected as the baseline to be compared with the proposed method. The comparison results reveal both planning utility and running efficiency of the proposed method.

FedFTHA: A Fine-Tuning and Head Aggregation Method in Federated Learning

Personalized federated learning is a sub-field of federated learning. Contrary to conventional federated learning that expects to find a general global model, personalized federated learning generates a personalized model adapted to its local data distribution for each client. Some existing personalized federated learning methods only consider improving the client-side personalization ability, discarding the server-side generalization capacity. To address this issue, we propose a fine-tuning and head aggregation method in federated learning (FedFTHA). It allows each client to maintain a personalized model head and fine-tune it after each local update to generate a local model containing the personalized head. Specifically, during FedFTHA training, these personalized heads are aggregated to generate a generalized head for the global model. FedFTHA meets the needs of both client-side model personalization and server-side model generalization. In addition, a universal optimization framework is employed to prove its convergence under convex and non-convex conditions. We verify the personalization ability and generalization performance of FedFTHA under heterogeneous settings with benchmark datasets. The comparative analysis authenticates the significance of our proposal.

Socio-cognitive caste-based optimization

Metaheuristics are universal optimization algorithms that are used to solve difficult problems, which are unsolvable by classic approaches. In this paper, we aim to construct a novel class of socio-cognitive metaheuristics based on the caste metaphor. We focus on classic evolutionary and agent-based metaheuristics, adding a sociologically inspired structure of the population and cognitively inspired variation operators. In addition to giving the background and details of the proposed algorithms, we apply them to the optimization of a variety of difficult benchmark problems.

A universal optimization framework for commercial building loads using DERs from utility tariff perspective with tariff change impacts analysis

To accommodate the changes in the nature and the pattern of electricity consumption with the available resources, utilities have introduced variety of tariffs over the years. This paper develops a comprehensive optimization framework that addresses the challenges associated with the diversity of utility tariffs for commercial loads. Optimization of commercial building net load through Battery Energy Storage System (BESS) and renewable energy resources is modeled and explored for minimizing billing cost for different tariffs. Cost functions are formulated for each possible commercial utility tariff type, engendering the universal cost function format. An algorithm is developed to apply the optimization model and generate the desired optimal outputs (e.g., optimal net load and BESS power, costs and savings, etc.). The results for several building loads and all tariff types are compared and analyzed to present the findings. An impacts analysis is performed to observe how different changes in tariffs affect the optimizations results. Results exhibit that for same building load and renewable generation, the tariff type can have an overwhelming impact on costs and savings. Tariffs without Time of Use (TOU) charges or peak demand charge components offer lower savings opportunity from BESS optimization. Price change sensitivities showed the complicated dynamics among TOU price components on savings and historical trend analysis as an effective tool to predict future savings. Tradeoff between energy and demand charge heavy tariff options are also discussed for user benefit. The recent change in TOU time periods presents limited desired benefits while the modified tariff proposed in this paper exhibit significant improvement in terms of utility operation.

A Genetic Algorithm for Universal Optimization of Ultrasensitive Surface Plasmon Resonance Sensors with 2D Materials.

We present a general optimization technique for surface plasmon resonance, (SPR) yielding a range of ultrasensitive SPR sensors from a materials database with an enhancement of ∼100%. Applying the algorithm, we propose and demonstrate a novel dual-mode SPR structure coupling SPP and a waveguide mode within GeO2 featuring an anticrossing behavior and an unprecedented sensitivity of 1364 deg/RIU. An SPR sensor operating at wavelengths of 633 nm having a bimetal Al/Ag structure sandwiched between hBN can achieve a sensitivity of 578 deg/RIU. For a wavelength of 785 nm, we optimized a sensor as a Ag layer sandwiched between hBN/MoS2/hBN heterostructures achieving a sensitivity of 676 deg/RIU. Our work provides a guideline and general technique for the design and optimization of high sensitivity SPR sensors for various sensing applications in the future.

Universal Optimization Framework: Leader-Centered Learning Team Formation Based on Fuzzy Evaluations of Learners and E-CARGO

Building the right learning teams is a key to the success of collaborative learning in online and offline learning environments. However, existing research on learning team formation (LTF) ignores the uncertainty of learners’ abilities and lacks a common problem modeling and optimization approach. Aiming at the characteristics of two typical types of leader-centered (LC) LTF problems, a universal optimization framework of LC-LTF is proposed by introducing role-based collaboration (RBC) theory. This framework evaluates the comprehensive ability of learners via a fuzzy description mechanism; applies the environments–classes, agents, roles, groups, and objects (E-CARGO) model to formulate the LC-LTF problem; and employs an optimization platform to obtain an optimal solution. A case study demonstrates the effectiveness and feasibility of the proposed framework.

Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies

We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H. Montgomery, Minimal theta functions. Glasgow Mathematical Journal, 30 (1988), 75–85]. The studied theta functions are generalizations of the Jacobi theta-2 and theta-4 functions. Contrary to Montgomery’s result, we show that, among lattices, the hexagonal lattice is the unique maximizer of both families of theta functions. As an immediate consequence, we obtain a new universal optimality result for the hexagonal lattice among two-dimensional alternating charged lattices and lattices shifted by the center of their unit cell.

Quantitative Information Flow Techniques for Studying Optimality in Differential Privacy

Universal optimality for differential privacy seeks to characterise the "best" mechanisms, which are the ones that provide the most utility to some class of consumers whilst simultaneously satisfying a fixed ε-differential privacy constraint. The study of universal optimality was initiated in 2009 in two important papers: the first by Ghosh et al., who discovered a universally optimal mechanism for a large class of consumers within the differential privacy constraint context of "counting queries" on statistical datasets; the second by Brenner and Nissim who found that outside of this context, no such universally optimal mechanisms exist. Since those remarkable results, there have been few advances in this field. In this article we detail some recent work which sheds new light on these results using Quantitative Information Flow (QIF), a mathematical framework for quantifying information leaks under a Bayesian adversarial model. Using standard QIF reasoning we show how the earlier results can be both generalised and extended, opening up new avenues for exploring optimality in a wide variety of differential privacy contexts.

Universal optimality of the $E_8$ and Leech lattices and interpolation formulas

We prove that the $E_8$ root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions eight and twenty-four, respectively. In other words, they minimize energy for every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians), which is a strong form of robustness not previously known for any configuration in more than one dimension. This theorem implies their recently shown optimality as sphere packings, and broadly generalizes it to allow for long-range interactions. The proof uses sharp linear programming bounds for energy. To construct the optimal auxiliary functions used to attain these bounds, we prove a new interpolation theorem, which is of independent interest. It reconstructs a radial Schwartz function $f$ from the values and radial derivatives of $f$ and its Fourier transform $\hat{f}$ at the radii $\sqrt{2n}$ for integers $n\ge 1$ in $\mathbb{R}^8$ and $n\ge 2$ in $\mathbb{R}^{24}$. To prove this theorem, we construct an interpolation basis using integral transforms of quasimodular forms, generalizing Viazovska's work on sphere packing and placing it in the context of a more conceptual theory.

Evolutionary Design of Machining Fixture Layout for Thin-Walled Structure

Fixture layout for machining thin-walled structures plays an important role in fixture performance. This work focuses on the optimization design of machining fixture layout including clamp layout and the layout of support heads. A universal optimization methodology that can automatically generate the optimal machining fixture layout is proposed. The optimization of fixture layout is implemented based on the criteria of minimizing maximum deflection of the thin-walled workpiece while remain relatively small torque caused by the clamping tables. An evolutionary algorithm is employed to solve the fixture layout optimization for the optimal solution. The optimal position of the support heads and the layout of clamping tables obtained from this work vary along with the change of cutting force. To validate the proposed optimization methodology, a fixture layout design for a typical thin-walled structure is optimized as an example. The case study demonstrates the application of the proposed approach in the fixture layout design for thin-walled structures, which is beneficial to design an optimal fixture layout.

Segmentation on remote sensing imagery for atmospheric air pollution using divergent differential evolution algorithm.

Air pollution is a global issue causing major health hazards. By proper monitoring of air quality, actions can be taken to control air pollution. Satellite remote sensing is an effective way to monitor global atmosphere. Various sensors and instruments fitted to satellites and airplanes are used to obtain the radar images. These images are quite complex with various wavelength differentiated by very close color differences. Clustering of such images based on its wavelengths can provide the much-needed relief in better understanding of these complex images. Such task related to image segmentation is a universal optimization issue that can be resolved with evolutionary techniques. Differential Evolution (DE) is a fairly fast and operative parallel search algorithm. Though classical DE algorithm is popular, there is a need for varying the mutation strategy for enhancing the performance for varied applications. Several alternatives of classical DE are considered by altering the trial vector and control parameter. In this work, a new alteration of DE technique labeled as DiDE (Divergent Differential Evolution Algorithm) is anticipated. The outcomes of this algorithm were tested and verified with the traditional DE techniques using fifteen benchmark functions. The new variant DiDE exhibited much superior outcomes compared to traditional approaches. The novel approach was then applied on remote sensing imagery collected form TEMIS, a web based service for atmospheric satellite images and the image was segmented. Fuzzy Tsallis entropy method of multi-level thresholding technique is applied over DiDE to develop image segmentation. The outcomes obtained were related with the segmented results using traditional DE and the outcome attained was found to be improved profoundly. Experimental results illustrate that by acquainting DiDE in multilevel thresholding, the computational delay was greatly condensed and the image quality was significantly improved.