Linear Rule Research Articles

SPF-CA-1.2: an enhanced version of cellular automata-based block cipher system

In this article, an enhanced version of SPF is presented. SPF is a previously developed cellular automata-based block cipher that combines Substitution-Permutation Networks (SPN) with a Feistel scheme using key-dependent S-boxes. SPF system has satisfying cryptographic properties against attacks. However, the rule 30 used in the Feistel round function was subject to an attack by Meier and Staffelbach (MS-attack). In order to avoid this attack, a new construction of SPF, namely SPF-CA 1.2, is proposed using a new ruleset combining linear and non-linear rules. In addition, a robust and fast key scheduling algorithm is employed to improve key efficiency. Moreover, the number of rounds has been reduced while conserving the high confusion and diffusion properties of the previous version. A thorough security analysis reveals the efficiency and robustness of the proposed construction.

The Multi-Focus-Image-Fusion Method Based on Convolutional Neural Network and Sparse Representation.

Multi-focus-image-fusion is a crucial embranchment of image processing. Many methods have been developed from different perspectives to solve this problem. Among them, the sparse representation (SR)-based and convolutional neural network (CNN)-based fusion methods have been widely used. Fusing the source image patches, the SR-based model is essentially a local method with a nonlinear fusion rule. On the other hand, the direct mapping between the source images follows the decision map which is learned via CNN. The fusion is a global one with a linear fusion rule. Combining the advantages of the above two methods, a novel fusion method that applies CNN to assist SR is proposed for the purpose of gaining a fused image with more precise and abundant information. In the proposed method, source image patches were fused based on SR and the new weight obtained by CNN. Experimental results demonstrate that the proposed method clearly outperforms existing state-of-the-art methods in addition to SR and CNN in terms of both visual perception and objective evaluation metrics, and the computational complexity is greatly reduced. Experimental results demonstrate that the proposed method not only clearly outperforms the SR and CNN methods in terms of visual perception and objective evaluation indicators, but is also significantly better than other state-of-the-art methods since our computational complexity is greatly reduced.

Optimizing makespan and resource utilization for multi-DNN training in GPU cluster

Deep neural network (DNN) has been widely applied in many fields of artificial intelligence (AI), gaining great popularity both in industry and academia. Increasing the size of DNN models does dramatically improve the learning accuracy. However, training large-scale DNN models on a single GPU takes unacceptable waiting time. In order to speed up the training process, many distributed deep learning (DL) systems and frameworks have been published and designed for parallel DNN training with multiple GPUs. However, most of the existing studies concentrate only on improving the training speed of a single DNN model under centralized or decentralized systems with synchronous or asynchronous approaches. Few works consider the issue of multi-DNN training on the GPU cluster, which is the joint optimization problem of job scheduling and resource allocation. This paper proposes an optimizing makespan and resource utilization (OMRU) approach to minimize job completion time and improve resource utilization for multi-DNN training in a GPU cluster. Specifically, we first collect the training speed/time data of all DNN models by running a job for one epoch on a different number of GPUs. The OMRU algorithm, integrating job scheduling, resource allocation, and GPU reuse strategies, is then devised to minimize the total job completion time (also called makespan) and improve GPU cluster resource utilization. The linear scaling rule (LSR) is adopted for adjusting the learning rate when a DNN model is trained on multiple GPUs with large minibatch size, which can guarantee model accuracy without the other hyper-parameters tune-up. We implement the OMRU algorithm on the Pytorch with Ring-Allreduce communication architecture and a GPU cluster with 8 nodes, each of which has 4 NVIDIA V100 GPUs. Experimental results on image classification and action recognition show that OMRU achieves a makespan reduction of up to 30% compared to the baseline scheduling algorithms and reach an average of 98.4% and 99.2% resource utilization on image classification and action recognition, respectively, with the state-of-the-art model accuracy.

Multiaxial fatigue assessment for outer cylinder of landing gear by critical plane method

The in-service loadings on the landing gear are usually complex and from different directions, which lead to the fatigue critical locations in the landing gear structure mostly in multiaxial stress state. A methodology based on the critical plane method was proposed for estimating the fatigue lifetime of outer cylinder of the main landing gear undergoing variable amplitude (VA) multiaxial proportional loading. The orientation of the critical plane was determined by the so-called maximum variance method. The Bannantine–Socie’s cycle counting method and Miner’s linear rule were applied with Zhang–Yao’s criterion in this research. The calculated results on the fatigue lifetime of the outer cylinder were compared with the experimental data. The results indicate that the methodology proposed in this article is a sound method for fatigue life prediction of engineering components bearing complex VA multiaxial fatigue loading.

Sample Robust Scheduling of Electricity-Gas Systems Under Wind Power Uncertainty

Bulk integrated electricity and gas systems (IEGSs) introduce complex coupling relations and induce synergistic operation challenges. The growing uncertainty arising from the renewable power generation in the IEGS further aggravates the synergistic problems. Considering the availability of historical wind power generation data, this paper adopts a two-stage sample robust optimization (SRO) model, which is equivalent to the two-stage distributionally robust optimization (DRO) model with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{type}} - \infty $</tex-math></inline-formula> Wasserstein ambiguity set, to address the wind power penetrated unit commitment optimal energy flow (UC-OEF) problem for the IEGS. Compared to the equivalent DRO model, the two-stage SRO model can be approximately transformed into a computationally efficient form. Specifically, we employ linear decision rules to simplify the proposed UC-OEF model. Moreover, we further enhance the tractability of the simplified model by exploring its structural features and, accordingly, develop a solution method. Simulation results on two IEGSs validate the effectiveness of the proposed model and solution method.

A pharmacokinetic simulation study to assess the performance of a sparse blood sampling approach to quantify early drug exposure.

Estimating early exposure of drugs used for the treatment of emergent conditions is challenging because blood sampling to measure concentrations is difficult. The objective of this work was to evaluate predictive performance of two early concentrations and prior pharmacokinetic (PK) information for estimating early exposure. The performance of a modeling approach was compared with a noncompartmental analysis (NCA). A simulation study was performed using literature‐based models for phenytoin (PHT), levetiracetam (LEV), and valproic acid (VPA). These models were used to simulate rich concentration‐time profiles from 0 to 2 h. Profiles without residual unexplained variability (RUV) were used to obtain the true partial area under the curve (pAUC) until 2 h after the start of drug infusion. From the profiles with the RUV, two concentrations per patient were randomly selected. These concentrations were analyzed under a population model to obtain individual population PK (PopPK) pAUCs. The NCA pAUCs were calculated using a linear trapezoidal rule. Percent prediction errors (PPEs) for the PopPK pAUCs and NCA pAUCs were calculated. A PPE within ±20% of the true value was considered a success and the number of successes was obtained for 100 simulated datasets. For PHT, LEV, and VPA, respectively, the median value of the success statistics obtained using the PopPK approach of 81%, 92%, and 88% were significantly higher than the 72%, 80%, and 67% using the NCA approach (p < 0.05; Mann–Whitney U test). This study provides a means by which early exposure can be estimated with good precision from two concentrations and a PopPK approach. It can be applied to other settings in which early exposures are of interest.

A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty

Currently, optimization models for the safe and reliable operation of power systems deal with two major challenges: the first one is the reduction of the computational load when considering N−1 contingencies; the second one is the adequate modeling of the uncertainty of intermittent generation and demand. This paper proposes a new affinely adjustable robust model to solve the security constrained unit commitment problem considering these sources of uncertainty. Linear decision rules, which take into account the forecasts and forecast errors of the different sources of uncertainty, are used for the affine formulation of the dispatch variables, thus allowing the tractability of the model. Another major novelty is that the evaluation of the N−1 security constraints is performed by incorporating a novel method, proposed in the literature, based on the user-cuts concept. This method efficiently and dynamically adds only the binding N−1 security constraints, increasing the computational efficiency of the model when transmission line contingencies are considered. Finally, Monte Carlo simulations on the post-optimization results were run to demonstrate the effectiveness, feasibility and robustness of the solutions provided by the proposed model.

Some issues in creep-fatigue research

In the component operated at elevated temperatures, the life evaluation should be made in consideration of both creep and fatigue (creep-fatigue) such as the linear damage summation rule. However, the concept of creep-fatigue life evaluation has not spread well in the industry. In order to consider the reason, a series of past creep-fatigue research was surveyed, namely experimental methods, life evaluation procedures and strength design guidelines. As a result, it was revealed that the mechanism of creep-fatigue interaction has not been fully clarified yet, which results in obscuring the necessity of creep-fatigue life evaluation. The necessity of creep-fatigue life evaluation was reviewed and consequently it proved to be necessary in two cases. One is the case where the creep-fatigue interaction is significant for some kinds of material, loading modes and temperatures. The other is one where the amount of creep damage is almost the same as that of fatigue damage even though the creep-fatigue interaction is insignificant.

Technical Note—Two-Stage Sample Robust Optimization

In “Two-Stage Sample Robust Optimization,” Bertsimas, Shtern, and Sturt investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-infinity Wasserstein ambiguity set. Their main result establishes that this approximation scheme is asymptotically optimal for two-stage stochastic linear optimization problems; that is, under mild assumptions, the optimal cost and optimal first-stage decisions obtained by approximating the robust optimization problem converge to those of the underlying stochastic problem as the number of data points grows to infinity. These guarantees notably apply to two-stage stochastic problems that do not have relatively complete recourse, which arise frequently in applications. In this context, the authors show through numerical experiments that the approximation scheme is practically tractable and produces decisions that significantly outperform those obtained from state-of-the-art data-driven alternatives.

Density, refractive index, and derived properties of binary mixtures of water + ionic liquid 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate

The density and refractive index were experimentally determined for binary mixtures of water + ionic liquid 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate throughout the ionic liquid mass fraction range, at atmospheric pressure and various temperatures between 293.15 K and 323.15 K. The refractive index was measured at five wavelengths between 589.2 nm and 935 nm. From the experimental data on density, volumetric properties such as the excess molar volume and thermal expansion coefficient were calculated. The excess molar volume was negative throughout the ionic liquid mass fraction range and its magnitude decreased with temperature. From the experimental data on the refractive index, the deviation in the refractive index and its coefficients of concentration, temperature and chromatic dispersion were obtained. The values of the deviation in the refractive index were positive and decreased with temperature. In order to simultaneously investigate the dependence of the refractive index on concentration, temperature and wavelength, we correlated the experimental data with a two-term Cauchy equation. Furthermore, a comparative study of 11 refractive index mixing rules was performed to assess their prediction ability. More advanced mixing rules do not lead to any improvement in comparison with the simple linear mixing rule (Arago-Biot) for estimating refractive index and the concentration contrast factor of the mixture studied. The results are expected to be useful for tuning the properties of an ionic liquid by adding water or selecting the temperature or optical region.

Optimization of blending and production processes considering origin mines and metallurgical units using linear programming rules

ABSTRACT This paper discusses a model that can optimize plant operation by considering transportation cost and metallurgical assays. All boundary conditions were set using ore samples taken from different locations in the same mine. Transportation from the mine to milling plants, dumping areas, and leaching units is also analyzed. Transportation from the mill to the smelter depends on assay results to ensure market readiness. We hypothesize that the grade of the material varies according to its source because milling plants are built to process different types of ore. Mines and processing units may be far apart, and therefore, it is critical to optimize production. Previous studies have discussed mine production optimization but did not consider metallurgical plants. The proposed model merges all units of a production system to determine the optimal planning solution. Linear programming uses network formulations of planning problems to consider a combination of mining and metallurgy operations. This technology is useful for analyzing the combination of two major systems, and hence, the dual theory was used in formulating the problem. The final model was applied to minimize the costs of production and distribution. The study checked the optimality of the solution for accuracy and its use as an indicator for long-term planning.

Application of modified SeDeM expert diagram system for selection of direct compression excipient for liquisolid formulation of Neusilin® US2

In the present investigations, the SeDeM expert diagram system, modified to include two important compression properties, i.e. mean yield pressure, Py, and compactibility parameter, σtmax, was used to identify a diluent most suitable for the direct compression of a liquisolid formulation of Neusilin® US2 (50NEU). The mean incidence values of 50NEU demonstrated that it had poor flowability and compactibility, and was highly hygroscopic. Three commonly used directly compressible tablet diluents, viz. lactose monohydrate, microcrystalline cellulose, and dibasic calcium phosphate, selected based on their index of good compressibility (IGC) values were evaluated for their usefulness for direct compression of 50NEU. Mathematical equations based on the linear and power mixing rules were used to calculate the percentage of diluent required for direct compression. The powder blends prepared using lactose monohydrate resulted in fragile tablets, dibasic calcium phosphate exhibited poor compactibility, however, powder blends containing microcrystalline cellulose resulted in tablets with acceptable compactibility. This demonstrated the significance of a rational selection of excipients based on their SeDeM parameters rather than the IGC values. Additionally, the study results showed that the modified SeDeM expert system was superior to the conventional SeDeM system for the selection of diluent for direct compression.

Influence of grain size distribution on mechanical properties and HDI strengthening and work-hardening of gradient-structured materials

Gradient structures (GS) with various grain size distributions are successfully architectured in a commercial low-alloying steel by using the pre-torsion and thermal annealing routes, and the corresponding mechanical properties and hetero-deformation induced (HDI) strengthening and work-hardening are investigated. Results demonstrate that an optimal grain size distribution from ~5.0 ± 2.8 μm at the surface to 11.1 ± 4.5 μm at the center leads to the maximum HDI strengthening of ~325 MPa. The HDI work-hardening intensifies continuously with the decreased average grain size of the GS due to the formation of abundant geometrical necessary dislocations (GNDs) whose density decreases abnormally from the fine-grain surface to the coarse-grain core caused mainly by the interactions between the short-range GNDs and long-range GNDs. Thanks to the HDI strengthening and work-hardening, the yield strength increases with a reduction of uniform ductility approximately following the linear inverse rule, in stark contrast to the banana-shaped strength-ductility trade-off of monolithic materials, and an exceptional strength-ductility synergy is achieved.

Robust Optimization for Models with Uncertain Second-Order Cone and Semidefinite Programming Constraints

In this paper, we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem can then (approximately) be solved by using adjustable robust linear optimization techniques. For example, we show that if linear decision rules are used, then the final robust counterpart consists of SOC or SDP constraints, respectively, which have the same computational complexity as the nominal version of the original constraints. We propose an efficient method to obtain good lower bounds. Moreover, we extend our approach to other classes of robust optimization problems, such as nonlinear problems that contain wait-and-see variables, linear problems that contain bilinear uncertainty, and general conic constraints. Numerically, we apply our approach to reformulate the problem on finding the minimum volume circumscribing ellipsoid of a polytope and solve the resulting reformulation with linear and quadratic decision rules as well as Fourier-Motzkin elimination. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it with the state-of-the-art copositive approach. Moreover, we apply the proposed approach to a robust regression problem and a robust sensor network problem and use linear decision rules to solve the resulting adjustable robust linear optimization problems, which solve the problem to (near) optimality. Summary of Contribution: Computing robust solutions for nonlinear optimization problems with uncertain second-order cone and semidefinite programming constraints are of much interest in real-life applications, yet they are in general computationally intractable. This paper proposes a computationally tractable approximation for such problems. Extensive computational experiments on (i) computing the minimum volume circumscribing ellipsoid of a polytope, (ii) robust regressions, and (iii) robust sensor networks are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

Data-Driven Chance-Constrained Optimal Gas-Power Flow Calculation: A Bayesian Nonparametric Approach

This paper proposes a data-driven chance-constrained optimal gas-power flow (OGPF) calculation method without any prior assumption on the distribution of uncertainties of wind power generation. The Gaussian mixture model is employed to fit the uncertainty distribution, where the Bayesian nonparametric Dirichlet process is adopted to tune the component number. To facilitate the online application of the proposed methods, an online-offline double-track distribution construction approach is established, where the frequency of training the relatively time-consuming Dirichlet process Gaussian mixture model can be reduced. On account of the quadratic gas consumption expression of gas-fired generators as well as the linear decision rule based uncertainty mitigation mechanism, the chance constraints would become quadratic ones with quadratic terms of uncertainties, which makes the proposed model more intractable. An equivalent linear separable counterpart is then provided for the quadratic chance constraints, after which the intractable chance constraints could be converted into traditional linear ones. The convex-concave procedure is used to crack the nonconvex Weymouth equation in the gas network and the auxiliary quadratic equalities. Simulation results on two test systems validate the effectiveness of the proposed methods.

A collective investment problem in a stochastic volatility environment: The impact of sharing rules

It is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors’ well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

Belief elicitation with multiple point predictions

We propose a simple, incentive compatible procedure based on binarized linear scoring rules to elicit beliefs about real-valued outcomes - multiple point predictions. Simultaneously eliciting multiple point predictions with linear incentives reveals the subjective probability distribution without pre-defined intervals or probabilistic statements. We show that the approach is theoretically as robust as existing methods, while adapting flexibly to different beliefs. In a laboratory experiment, we compare our procedure to the standard approach of eliciting discrete probabilities on pre-defined intervals. We find that elicitation with multiple point predictions is faster, perceived as less difficult and more consistent with a subsequent decision. We further find that multiple point predictions are more accurate if beliefs vary between participants. Finally, we provide experimental evidence that pre-defined intervals anchor reports.

Energy and reserve dispatch with distributionally robust joint chance constraints

We develop a two-stage stochastic program for energy and reserve dispatch of a joint power and gas system with a high penetration of renewables. Data-driven distributionally robust chance constraints ensure that there is no load shedding and renewable spillage with high probability. We solve this problem efficiently using conditional value-at-risk approximations and linear decision rules. Out-of-sample experiments show that this model dominates the corresponding stochastic program without chance constraints that models the effects of load shedding and renewable spillage explicitly.

A real-time optimal control strategy for multi-zone VAV air-conditioning systems adopting a multi-agent based distributed optimization method

Determining the proper trade-off among thermal comfort, Indoor Air Quality (IAQ) and energy use is important for optimal control of air-conditioning systems. The number of optimization variables increases as systems become increasingly complex, as with multi-zone VAV (Variable Air Volume) air-conditioning systems, leading to large-scale mathematics programming challenges and inconveniences in the implementation of conventional centralized optimization strategies. This paper therefore proposes a real-time optimal control strategy adopting a multi-agent based distributed optimization method for multi-zone VAV air-conditioning systems. The proposed strategy consists of three novel schemes. First, a temperature set-point reset scheme adopts a linear rule to correlate the resetting of the temperature set-points in individual zones to simplify the optimization problem while applying proper optimization in individual zones. Second, a multi-objective optimization scheme optimizes the fresh air ratio of the supply air and the temperature set-point in the critical zone by formulating the multi-objective optimization problem. Third, a multi-agent distributed optimization scheme is developed to solve the optimization problem in a distributed manner, facilitating the deployment of local control devices of limited capacity. A TRNSYS-MATLAB co-simulation testbed is constructed to test and validate the proposed strategy. Test results show that the strategy is effective in properly balancing thermal comfort, IAQ and energy use while largely reducing programming challenges. The distributed optimization method can provide almost the same optimal outputs as conventional centralized optimization methods.

Multistage robust mixed-integer optimization under endogenous uncertainty

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In the robust optimization context, however, it has rarely been considered. This work addresses multistage robust mixed-integer optimization with decision-dependent uncertainty sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect the uncertainty set. We derive a tractable reformulation of the problem by leveraging recent advances in the construction of nonlinear decision rules, and introduce discontinuous piecewise linear decision rules for continuous recourse. Computational experiments are performed to gain insights on the impact of endogenous uncertainty, the benefit of discrete recourse, and computational performance. Our results indicate that the level of conservatism in the solution can be significantly reduced if endogenous uncertainty and mixed-integer recourse are properly modeled.