Minimum Constraint Research Articles

Unsupervised Hyperspectral Band Selection With Multigraph Integrated Embedding and Robust Self-Contained Regression

Band selection is an effective means to alleviate the curse of dimensionality in hyperspectral data. Many methods select a compact and low redundant band subset, which is inadequate as it may degrade the classification performance. Instead, more emphasis shall be put on selecting representative bands. In this article, we propose a robust unsupervised band selection method to address this issue. Our method reveals bandwise representativeness based on the comprehensive interband neighborhood structure. It incorporates an interband neighborhood graph into a sparse self-contained regression model in order to provide a reasonable measure for bandwise representativeness. The derived coefficient matrix not only uncovers bandwise importance values but also is coherent to the generalized interband local neighborhood structure. For constructing the interband neighboring structural graph, an integrated multigraph model is employed to achieve better generalization performance. It combines the benefit of multiple graphs but is insusceptible to the defects of a single one. To enhance the reliability of this model, a joint trace minimum and nonnegative constraint is imposed on the coefficient matrix. Accordingly, a multigraph integrated embedding and robust self-contained regression model (MGRSR) is formulated. In addition, an iterative update algorithm is developed to solve the problem. Comparative experiments on three hyperspectral data sets illustrate that MGRSR is robust to various data and has superior performance compared with several state-of-the-art methods.

Sum-Rate Maximization of Wireless Powered Primary Users for Cooperative CRNs: NOMA or TDMA at Cognitive Users?

Recently, wireless powered cooperative cognitive radio networks (CRNs), which combine the technologies of radio frequency (RF) energy harvesting and CR, have drawn great attention. In such networks, energy cooperation between the cognitive users (CUs) and the wireless powered primary users (PUs) can be performed, where the CUs can charge the PUs wirelessly in exchange for the spectrum access. Specifically, energy cooperation and information transmission is executed in two phases, where the CUs transmit their data signals and the PUs harvest energy from these signals in the first phase, and the PUs transmit their data using the harvested energy in the second phase. In particular, we consider two multiple access schemes for the CUs, namely non-orthogonal multiple access (NOMA) and time-division multiple access (TDMA). For both NOMA and TDMA, the PU sum-rate maximization problems under the minimum CU sum-rate constraint are first simplified by exploring particular problem structure, then are transformed to convex problems, and finally are solved optimally. The PU sum-rates of the two schemes are compared theoretically as well as numerically. It is revealed that the circuit power consumption at the CUs, the required minimum CU sum-rate, and the PU energy harvesting sensitivity and saturation thresholds play key roles in the PU performance comparison of the two schemes.

A novel hybrid grey wolf optimization algorithm and artificial neural network technique for stochastic unit commitment problem with uncertainty of wind power

The unit commitment (UC) is highly complex to solve the increasing integrations of wind farm due to intermittent wind power fluctuation in nature. This paper presents a hybrid methodology to solve the stochastic unit commitment (SUC) problem depending on binary mixed integer generator combination with renewable energy sources (RESs). In this combination, ON/OFF tasks of the generators are likewise included to satisfy the load requirement as for the system constraints. The proposed hybrid methodology is the consolidation of grey wolf optimization algorithm (GWOA) and artificial neural network (ANN), hence it is called the hybrid GWOANN (HGWOANN) technique. Here, the GWOA algorithm is used to optimizing the best combination of thermal generators depending on uncertain wind power, minimum operating cost and system constraints – that is, thermal generators limits, start-up cost, ramp-up time, ramp-down time, etc. ANN is utilized to capture the uncertain wind power events, therefore the system ensures maximal application of wind power. The combination of HGWOANN technique guarantees the prominent use of sustainable power sources to diminish the thermal generators unit operating cost. The proposed technique is implemented in MATLAB/Simulink site and the efficiency is assessed with different existing methods. The comparative analysis demonstrates that the proposed HGWOANN approach is proficient to solve unit commitment problems and wind integration. Here, the HGWOANN method is compared with existing techniques such as PSO, BPSO, IGSA to assess the overall performance using various metrics viz. RMSE, MAPE, MBE under 50 and 100 count of trials. In the proposed approach, the range of RMSE achieves 9.26%, MAPE achieves 0.95%, MBE achieves 1% in 50 count of trials. Moreover, in 100 count of trials, the range of RMSE achieves 7.38%, MAPE achieves 1.91%, MBE achieves 2.87%.

Game Theoretic Approach for a Service Function Chain Routing in NFV With Coupled Constraints

In this brief, the service function chain (SFC) routing in network function virtualization (NFV) with server capacity limitation and user minimum target rate constraint is investigated simultaneously. After relaxing the constraints by the addition of extra cost terms, an extended NFV game incorporating the coupled constraints is formulated. By using semi-tensor product of matrices, we prove that the formulated game is a potential game which possesses at least one Nash equilibrium. We then present the equilibrium point algorithm for solving the SFC routes problem. The numerical simulation of two cases with constraints and without constraints illustrates the influence of coupled limitations on the SFC routing.

New interpretations of the ages and origins of the Hawkeye Granite Gneiss and Lyon Mountain Granite Gneiss, Adirondack Mountains, NY: Implications for the nature and timing of Mesoproterozoic plutonism, metamorphism, and deformation

The Hawkeye Granite Gneiss and Lyon Mountain Granite Gneiss are widespread Mesoproterozoic plutonic rocks that occur in the amphibolite- to granulite-facies Adirondack Highlands of northern New York, USA. The strongly deformed Hawkeye Granite Gneiss, previously dated by zircon multi-grain thermal ionization mass spectrometry (TIMS) U-Pb analyses at about 1100 Ma, was intruded by the weakly deformed Lyon Mountain Granite Gneiss. Previous sensitive high resolution ion microprobe (SHRIMP) analyses of Lyon Mountain Granite Gneiss zircon rims were considered to record the time of igneous emplacement at about 1.05 Ga, whereas the ages of zircon cores (~1.15 Ga) were interpreted as being inherited from nearby metaigneous country rocks. This interpretation has formed the basis of numerous models for the Mesoproterozoic structural and tectonic evolution of the Adirondacks Highlands. New U-Pb spot analyses (~15–20 µm diameter) by SHRIMP from four samples of Hawkeye Granite Gneiss and eight samples of Lyon Mountain Granite Gneiss challenge the historically accepted ages of the rocks. Using a combination of high-resolution CL imagery of oscillatory zoned cores and weakly zoned to unzoned rims, SHRIMP U-Pb geochronology, SHRIMP trace element geochemistry, and SEM petrography, we conclude that: (1) the Hawkeye Granite Gneiss was emplaced at about 1160–1155 Ma; (2) the vast majority of Lyon Mountain Granite Gneiss zircon cores yield ages of 1150–1145 Ma and are mainly primary, not inherited; and (3) the Hawkeye Granite Gneiss and Lyon Mountain Granite Gneiss zircon rims (~1080–1000 Ma) are metamorphic in origin, not igneous. Thus, both the Hawkeye Granite Gneiss and Lyon Mountain Granite Gneiss are considered herein to be late members of the mangerite-charnockite-granite (MCG) plutonic suite, emplaced during the waning stages of the Shawinigan orogeny. Zircon cores from two small plutons of largely undeformed fayalite granite of the Lyon Mountain Granite Gneiss are about 1142 Ma, providing a minimum age constraint for the termination of the Shawinigan. Zircon rim ages can be deconvoluted into multiple metamorphic events of the Ottawan and Rigolet tectonothermal events. These new interpretations have profound implications for structural, tectonic, and ore deposit models of the Adirondacks Highlands.

Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

A Cournot duopoly game is a two-firm market where the aim is to maximize profits. It is rational for every company to maximize its profits with minimal sales constraints. As a consequence, a model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. The CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. The current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. In the event of sales constraint and no sales constraint, the local stability conditions of the Cournot equilibrium are derived. The initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Two routes to chaos are analyzed by numerical simulation using 2D bifurcation diagram, one of which is period doubling bifurcation and the other is Neimark–Sacker bifurcation. Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms.

New multicellular marine macroalgae from the early Tonian of northwestern Canada

AbstractMolecular phylogenetic data suggest that photosynthetic eukaryotes first evolved in freshwater environments in the early Proterozoic and diversified into marine environments by the Tonian Period, but early algal evolution is poorly reflected in the fossil record. Here, we report newly discovered, millimeter- to centimeter-scale macrofossils from outer-shelf marine facies of the ca. 950–900 Ma (Re-Os minimum age constraint = 898 ± 68 Ma) Dolores Creek Formation in the Wernecke Mountains, northwestern Canada. These fossils, variably preserved by iron oxides and clay minerals, represent two size classes. The larger forms feature unbranching thalli with uniform cells, differentiated cell walls, longitudinal striations, and probable holdfasts, whereas the smaller specimens display branching but no other diagnostic features. While the smaller population remains unresolved phylogenetically and may represent cyanobacteria, we interpret the larger fossils as multicellular eukaryotic macroalgae with a plausible green algal affinity based on their large size and presence of rib-like wall ornamentation. Considered as such, the latter are among the few green algae and some of the largest macroscopic eukaryotes yet recognized in the early Neoproterozoic. Together with other Tonian fossils, the Dolores Creek fossils indicate that eukaryotic algae, including green algae, colonized marine environments by the early Neoproterozoic Era.

Energy-Efficient Resource Allocation for IRS-Assisted Multi-Antenna Uplink Systems

In this letter, we study the resource allocation for an intelligent reflecting surface (IRS)-assisted uplink system, where the base station is equipped with multiple antennas. We propose to jointly optimize the transmit power of the users, active beamforming at the base station, and passive beamforming at the IRS to maximize the overall system energy efficiency while maintaining users' minimum rate constraints. This problem belongs to a highly intractable non-convex bi-quadratic programming problem, for which an iterative solution based on block coordinate descent is proposed. Extensive simulations are conducted to demonstrate the effectiveness of the proposed scheme and the benefits of having more elements at the IRS.

A Zonal Displacement Approach via Grid Point Weighting in Building Generalization

When generalizing a group of objects, displacement is an essential operation to resolve the conflicts arising between them due to enlargement of their symbol sizes and reduction of available map space. Although there are many displacement methods, most of them are rather complicated. Therefore, more practical methods are still needed. In this article, a new building displacement approach is proposed. For this purpose, buildings are grouped and zones are created for them in the blocks via Voronoi tessellation and buffering. Linear patterns are then detected through buffer analyses and the respective zones are narrowed to be able to preserve these patterns. After all the buildings are displaced inside their zones, grid points are generated and then weighted through kernel density estimation and buffer analyses to find suitable locations. Accordingly, the buildings are displaced toward the computed locations iteratively. The proposed approach directly enforces minimum distance and positional accuracy constraints while several indirect mechanisms are used for preserving spatial patterns and relationships. For the quality evaluation of the displacement, the angle, length and shape comparison measures are introduced, computed based on the (Delaunay) triangles or the azimuth comparison measure of the connection lines, generated for the buildings. The quality evaluation criteria are yielded according to the visual assessment of the displacement quality and the quantitative analysis of the measures. The findings demonstrate that the proposed approach is quite effective and practical for zonal building displacement.

Optimal control and learning for cyber‐physical systems

Optimal control and learning for <scp>cyber‐physical</scp> systems

Hardness of Motion Planning with Obstacle Uncertainty in Two Dimensions

We consider the problem of motion planning in the presence of uncertain obstacles, modeled as polytopes with Gaussian-distributed faces (PGDFs). A number of practical algorithms exist for motion planning in the presence of known obstacles by constructing a graph in configuration space, then efficiently searching the graph to find a collision-free path. We show that such an exact algorithm is unlikely to be practical in the domain with uncertain obstacles. In particular, we show that safe 2D motion planning among PGDF obstacles is -hard with respect to the number of obstacles, and remains -hard after being restricted to a graph. Our reduction is based on a path encoding of MAXQHORNSAT and uses the risk of collision with an obstacle to encode variable assignments and literal satisfactions. This implies that, unlike in the known case, planning under uncertainty is hard, even when given a graph containing the solution. We further show by reduction from -SAT that both safe 3D motion planning among PGDF obstacles and the related minimum constraint removal problem remain -hard even when restricted to cases where each obstacle overlaps with at most a constant number of other obstacles.

Energy and spectral efficiency trade-off in OCDMA-PON assisted by non-linear programming methods

Two important metrics for performance evaluation in optical code division multiple access networks (OCDMA) are energy efficiency (EE) and spectral efficiency (SE). Both metrics are investigated in this work through the bi-objective optimization approach by analyzing the trade-off between SE and EE. We first formulate the SE–EE optimization as a bi-objective optimization (BOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the BOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted sum method. Nonlinear programming methods as sequential quadratic programming method (SQP) and majoration–minimization (MaMi) are applied to solve the BOO problem, with QoS guarantees for the OCDMA networks. Resource efficiency (RE) is able to explore the trade-off between EE and SE in OCDMA networks. The optimization methods were applied and their performance-complexity trade-offs are compared with the exhaustive search (ES) method. Numerical results were performed considering practical and realistic scenarios, including a wide range of nodes, while the solutions obtained by the methods are represented in the Pareto front.

Energy Efficient Subchannel and Power Allocation in Cooperative VLC Systems

This letter studies the energy efficiency (EE) optimization of cooperative visible light communication (VLC) systems while considering the inter-cell interference and the lineof-sight blockage problems. Specifically, the optimization problem of subchannel and power allocation to maximize EE under transmit power budgets and users' minimum rate constraints is considered. The formulated problem turns out to be a difficult nonlinear fractional program for which a low-complexity iterative solution based on fractional programming theory and the quadratic transform approach is proposed. Extensive simulations are conducted to show the efficacy of the proposed scheme over conventional approaches. In addition, the outage analysis and impacts of varying the transmit power and the subchannel bandwidth on the EE performance are investigated.

Uncertainty‐oriented double‐scale topology optimization with macroreliability limitation and micromanufacturing control

AbstractThis article proposes an uncertainty‐oriented double‐scale topology optimization method considering macroreliability limitation and micromanufacturing control. The procedure combines the homogenization method to solve the equivalent elastic property of the microstructure, the feature distance theory to evaluate reliability, a density projection for manufacturability control, and the solid isotropic material with penalization model to suppress intermediate density. To coupling the micro–macro scale, the equivalent elastic property of the cell microstructure is evaluated by the numerical homogenization method and then endowed to the macroelement for finite element analysis. Uncertainty factors existed in optimization parameters are evaluated by the interval convex set model. By utilizing the interval parameter vertex method and the feature distance theory, the reliability of displacement constraint in the optimization model is evaluated and constrained. In terms of length scale control, the microdensity design variables are projected by a threshold function to obtain a clear microstructure that satisfies the preset minimum length scale constraint. Finally, three numerical examples are presented to illustrate the effect of micromanufacturing control, as well as the necessity of considering parameter uncertainty.

Diagenetic and Epigenetic Mineralizing Events in the Kalahari Copperbelt, Botswana: Evidence from Re-Os Sulfide Dating and U-Th-Pb Xenotime Geochronology

Abstract The ages of sedimentation and copper-silver mineralization in the late Meso- to Neoproterozoic Kalahari Copperbelt in Botswana, an economically significant copper province, have previously been poorly constrained within an ~600 m.y. period that spans the Neoproterozoic from the assembly and breakup of Rodinia to the assembly of Gondwana. Rhenium-osmium geochronology of molybdenite and copper sulfide minerals and U-Th-Pb laser ablation split-stream inductively coupled plasma-mass spectrometry (LASS ICP-MS) analysis of xenotime grains are utilized to provide absolute and relative age data on the host rocks and mineralizing events within the Ghanzi Ridge region of the Kalahari Copperbelt. The data reveal a prolonged history of events, which is partially comparable with depositional and mineralizing events in the neighboring Central African Copperbelt. Abundant disseminated molybdenite is located within a shale layer near the base of the Proterozoic D’Kar Formation at the Northeast Mango Two deposit. Unusual molybdenite textures suggest organic matter may have been a precursor. Two molybdenite separates from a small calcite-molybdenite stringer in a wall-rock fragment that is enclosed within an epigenetic quartz-calcite-chalcopyrite vein with ill-defined and mismatched margins yielded Re-Os ages of 981 ± 3 and 981 ± 7 Ma. These ages indicate an early hydrothermal mineralizing event in the basin. A xenotime inclusion intergrown with molybdenite and chalcopyrite within the epigenetic vein yielded a younger U-Th-Pb age of 538 ± 8 Ma, suggesting two mineralizing events are preserved in a complex 6-cm-wide vein. Based on vein texture and alteration, the ages represent an ~981 Ma calcite-molybdenite mineralization event overprinted by an ~538 Ma quartz-chalcopyrite-molybdenite mineralization event, perhaps during reopening of the vein. Re-Os and U-Th-Pb geochronology were utilized at the Zone 6 deposit on minerals associated with a hydrothermal quartz-calcite-chalcocite-idaite-bornite vein. Several authigenic xenotime grains that occur along the margin of the vein yielded three concordant U-Th-Pb ages that indicate xenotime growth at ~950 to 925 Ma while other xenotime grains in a similar position yielded mostly discordant data, suggesting disturbance of the isotopic system in the xenotime grains. A coprecipitated chalcocite-idaite mixture within the hydrothermal vein produced an Re-Os age of 549.0 ± 11.2 Ma. Re-Os analysis obtained from a coprecipitated molybdenite-bornite mixture at the Northeast Fold deposit yielded an age of 515.9 ± 2 Ma. Together, the earliest Neoproterozoic Re-Os molybdenite and U-Th-Pb xenotime ages provide both a minimum depositional age constraint for the lowermost D’Kar Formation and clear evidence that diagenetic hydrothermal mineralizing events took place within the Ghanzi basin. The timing of this mineralizing event corresponds with a poorly documented regional thermal event that affected the northern margin of the Kalahari craton during the final stages of the assembly of Rodinia at ~980 Ma. The lower to middle Ghanzi Group of the Kalahari Copperbelt is at least 100 m.y. older than the host rocks within the neighboring Central African Copperbelt, which are associated with the breakup of Rodinia. The latest Neoproterozoic to Cambrian Re-Os and U-Th-Pb ages indicate that hydrothermal copper-silver mineralizing events occurred during the Pan-African (~600–480 Ma) fold-thrust evolution of the Ghanzi-Chobe zone and were broadly synchronous with widespread epigenetic hydrothermal copper-cobalt mineralizing events in the adjacent Central African Copperbelt.

Supply chain coordination with competing suppliers under price-sensitive stochastic demand

In this paper, we investigate a supply chain where two competing suppliers sell substitutable products through a common retailer who faces price-dependent stochastic demand. The retailer jointly decides the order quantity and the retail price for each product. Unlike most existing research assuming customer homogeneity, we divide the customers into two types: i) the price-sensitive type and ii) the brand-loyalty type, and investigate the issues of supply chain coordination. Our results show that neither buy-back contracts nor the buy-back related hybrid contracts (i.e., the hybrid buy-back and revenue-sharing contract and the hybrid buy-back and sales rebate contract) can achieve the coordination of such a supply chain. Furthermore, under buy-back contracts for the decentralized supply chain, we analyze the retailer's optimal retail price and order quantity when each supplier imposes a minimum order-quantity constraint. Our result shows that there exists a unique optimal decision for the retailer under some mild restrictions.

Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers

We present a topology optimization approach for the design of fluid-to-fluid heat exchangers which rests on an explicit meshed discretization of the phases at stake, at every iteration of the optimization process. The considered physical situations involve a weak coupling between the Navier–Stokes equations for the velocity and the pressure in the fluid, and the convection–diffusion equation for the temperature field. The proposed framework combines several recent techniques from the field of shape and topology optimization, and notably a level-set based mesh evolution algorithm for tracking shapes and their deformations, an efficient optimization algorithm for constrained shape optimization problems, and a numerical method to handle a wide variety of geometric constraints such as thickness constraints and non-penetration constraints. Our strategy is applied to the optimization of various types of heat exchangers. At first, we consider a simplified 2D cross-flow model where the optimized boundary is the section of the hot fluid phase flowing in the transverse direction, which is naturally composed of multiple holes. A minimum thickness constraint is imposed on the cross-section so as to account for manufacturing and maximum pressure drop constraints. In a second part, we optimize the design of 2D and 3D heat exchangers composed of two types of fluid channels (hot and cold), which are separated by a solid body. A non-mixing constraint between the fluid components containing the hot and cold phases is enforced by prescribing a minimum distance between them. Numerical results are presented on a variety of test cases, demonstrating the efficiency of our approach in generating new, realistic, and unconventional heat exchanger designs.

A Model of the Discount Rule and the Nonlinear Pricing Strategy in the Electronic Commerce Market

In the electronic commerce market, the minimum order quantity or the minimum order value constraints are present.A minimum quantity of the commodity bundle or the minimum purchase value are to be ordered to get the commodity with or without discounts offers that is selected to buy.This acts as a source of nonlinear pricing if the discount rule is set strategically.The present paper gives a theoretical idea of a nonlinear pricing strategy when the minimum order constraints are present with a discount rate.A theoretical understanding has been explained here, where the buyer would buy more than the requirements if the discount rules are set strategically along with the minimum order constraints.

Boosting Graph Embedding on a Single GPU

Graphs are ubiquitous, and they can model unique characteristics and complex relations of real-life systems. Although using machine learning (ML) on graphs is promising, their raw representation is not suitable for ML algorithms. Graph embedding represents each node of a graph as a d-dimensional vector which is more suitable for ML tasks. However, the embedding process is expensive, and CPU-based tools do not scale to real-world graphs. In this work, we present GOSH, a GPU-based tool for embedding large-scale graphs with minimum hardware constraints. GOSH employs a novel graph coarsening algorithm to enhance the impact of updates and minimize the work for embedding. It also incorporates a decomposition schema that enables any arbitrarily large graph to be embedded with a single GPU. As a result, GOSH sets a new state-of-the-art in link prediction both in accuracy and speed, and delivers high-quality embeddings for node classification at a fraction of the time compared to the state-of-the-art. For instance, it can embed a graph with over 65 million vertices and 1.8 billion edges in less than 30 minutes on a single GPU.

Non-Orthogonal Multiple Access in Distributed Antenna Systems for Max-Min Fairness and Max-Sum-Rate

The distributed antenna systems (DAS) and non-orthogonal multiple access (NOMA) are the key technologies to boost the data rate of the cellular system in terms of small cell and multiple access, respectively. To meet the high data rate requirements for 5G and beyond, we suggest a framework of using NOMA in DAS. In the proposed scheme, RRUs which are geographically distributed in the cell serve the cell-edge users within their own coverage. Meanwhile, the macro BS, which covers the entire cell region with relatively high transmit power, supports both the cell-center and the cell-edge users with identical resources by using NOMA. Compared to the conventional DAS where the macro BS and the RRU serve the cell-center and the cell-edge users, respectively, the proposed framework also boosts the data rate of the cell-center user by improving the reliability of successive interference cancellation (SIC) at the cell-center user. In the proposed framework, this paper also proposes the optimal power allocation rules maximizing the user fairness in two different cases of instantaneous channel gain information (CGI) and channel distribution information (CDI) known at the transmitter. Also, the power allocation methods maximizing the sum-rate with a minimum rate constraint and the weighted sum-rate are presented in the case of CGI known at the transmitter. Simulation results show that the proposed framework of using NOMA in DAS can boost data rates more in a variety of system environments compared to the conventional NOMA or DAS.