Nonlinear Programming Research Articles

Solving a class of two-stage stochastic nonlinear integer programs using value functions

Solving a class of two-stage stochastic nonlinear integer programs using value functions

Optimal planning and management of the energy–water–carbon nexus in hybrid AC/DC microgrids for sustainable development of remote communities

This paper presents a two-stage stochastic mixed-integer nonlinear programming model, which is linearized to a mixed-integer linear programming (MILP) form, for optimizing the energy–water–carbon (EWC) nexus in remote AC/DC microgrids aimed at sustainable community development. The model optimizes the selection, location, and operation of diesel generators, voltage source converters, photovoltaic systems, wind turbines, and battery energy storage systems while managing CO2 emissions. It accurately models the AC/DC microgrid’s operation, determining optimal voltages, currents, and converter states (inverter or rectifier). Uncertainties in power demand, water consumption, solar irradiation, and wind speed are modeled using stochastic scenarios generated via k-means clustering. The MILP model is implemented in GAMS and solved with the commercial solver CPLEX, ensuring global optimization. Results show that integrating distributed energy resources, compared to a case without these elements, reduces CO2 emissions of the diesel generators and the operational costs of the EWC nexus, highlighting the proposed approach’s environmental and economic benefits. These findings underline the importance of incorporating distributed energy resources in the sustainable development of microgrids.

Integrating machine learning model and computer-aided molecular design toward rational ionic liquid selection for separating fluorinated refrigerants

To reduce emissions and facilitate the reclamation of hydrofluorocarbons (HFCs), which are potent greenhouse gases, ionic liquid (ILs)-based absorption separation of HFCs from fluorinated refrigerant (FR) blends is considered as an effective approach. In this work, computer-aided ionic liquid design (CAILD) is carried out to rationally design ILs for separating FR blends, with the near-azeotropic R-32/R-125 system as an illustrative case study. Firstly, the machine learning algorithm, namely artificial neural network (ANN), is employed to develop a group contribution (GC) model for accurate prediction of FR-in-IL solubility. Then, a mixed-integer nonlinear programming (MINLP) problem is formulated and solved by integrating the ANN-GC model with two available GC models for predicting the melting point and viscosity of ILs. Consequently, the optimal three ILs including [C1C10Im][dca], [C1C11Im][dca], and [C1C12Im][dca] are identified. Finally, quantum chemistry calculations are conducted to disclose the separation mechanism from molecular perspective, further validating the reliability of the CAILD results.

Two modified conjugate gradient methods for unconstrained optimization

Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. Motivated by the construction of some modern CG methods, we propose two modified CG methods, named DHS* and DPRP*. Under the strong Wolfe line search (SWLS), the two presented methods are proven to be sufficient descent and globally convergent. Preliminary numerical results show that the DHS* and DPRP* methods are effective for the given test problems.

Optimization for Spectral and Power Characteristics of Bicolour LED Driver

LED-powered luminaires have the ability to offer cutting-edge features like temperature adjustment and color management. Color shift creates discomfort in human eyes. So it is essential to design a LED driver which will precisely control the color parameters of the LED driver. Precise control of color parameters like CRI, CCT, color intensity is very complex and challenging. This paper describes the nonlinear optimization methodology for the design of blended LED light sources. This paper presents the methodology that enables LED strings regarding various parameters, e.g. high color rendering index (CRI) and high luminous efficacy of a blended bi-color (namely red CCT-2500K and blue CCT-9000K) LED driving system. Due to the applied optimization, the obtained CRI is maintained 98.03%. The overall luminous intensity depends upon the combined luminous flux which depends upon the current control of both LED sources. These optimized LED currents ensure the desired CCT. The achieved luminous efficacy is 90% at two optimal peak wavelengths 601 nm and 426 nm respectively. Power loss is minimized by frequency optimization. At the same time power parameters i.e. low THD and high P. F. is also maintained. The nonlinear optimization is verified in Ltspice simulations and experimentally for two different luminaire strings.

Inferred attractiveness gravity-based models for estimating realized access at rural hospitals

Operating obstetric units in rural America is financially challenging in part due to low birth volume. Birth volume at a hospital decreases when birthers bypass it to go to a farther hospital. Beyond financial considerations, it is important from a healthcare equity perspective for hospitals to know whether certain subgroups of birthers avoid utilizing the hospital’s services. This can better inform resource allocation decisions targeting those subgroups. In this paper, we use a nonlinear programming optimization model, inferred attractiveness gravity-based model (GBM), to estimate realized access to obstetric care at hospitals in Montana. We compare three variations of GBM and benchmark our results to a regression-based conditional logit model. Results indicate that hospital attractiveness varies across the level of obstetric care provided and depends on the subgroup of birthers considered. While all GBMs produced smaller errors for hospitals with higher birth volumes, our novel variant was more accurate for low-volume hospitals. Bootstrapping analyses and resolving the models for population subgroups indicated large variations in hospital attractiveness. Research findings contribute to new knowledge about equity in access to obstetric care, the importance of considering population heterogeneity in GBMs, and the benefit of using hospital demand-based thresholds for GBMs in rural settings.

Approximate proximal methods for variational inequalities on Hadamard manifolds

ABSTRACT In this paper, we present an approximate proximal point method for addressing the variational inequality problem on Hadamard manifolds, and we analyse its convergence properties. The proposed algorithm exhibits inexactness in two aspects. Firstly, each proximal subproblem is approximated by utilizing the enlargement of the vector field under consideration, and subsequently, the next iteration is obtained by solving this subproblem while allowing for a suitable error tolerance. As an illustrative application, we develop an approximate proximal point method for nonlinear optimization problems on Hadamard manifolds.

Day-ahead dynamic operating envelopes using stochastic unbalanced optimal power flow

Driven by the energy transition, distribution networks are dealing with increasing uptake of distributed energy resources, including solar photovoltaic generation. Residential rooftop solar allows customers to minimize exposure to price increases in the market, which has led to high penetration of PV in regions with high amounts of solar hours such as Australia. Eventually, this leads to congestion in the network, either due to voltage rise, or due to overcurrent in lines or transformers. Distribution utilities are now moving on from static export limits for customers in congested networks, to dynamic limits that are based on the state of the network. It is considered thoughtful to give customers advance warning, e.g. day-ahead, of the moments and degrees of export limitation, despite uncertainty surrounding the future state of the network. Therefore, in this paper, we consider the application of general polynomial chaos expansion based stochastic unbalanced optimal power flow to the day-ahead determination of dynamic export limits. We perform a numerical study on a European style low voltage feeder and illustrate the impact of fairness principles on chance-constrained stochastic nonlinear optimization without the need of sampling, linearizing the power flow equations, or applying relaxations. Case studies show the necessity of considering unbalanced study of distribution system. It was observed that equality measures reduce the overall output of the system in an attempt to achieve equal relative injection, while alpha fairness with a higher value of alpha is a compromise between the efficiency and fairness in DOEs.

Designing employee benefits to optimize turnover: A prescriptive analytics approach

Employee turnover significantly impacts organizations, particularly those with substantial investments in training their workforce. To mitigate these effects, we propose a Prescriptive Human Resources Analytics approach that optimizes employee benefits to minimize total costs, focusing on turnover management The methodology models employee decision-making using a discrete choice model, with parameters estimated through maximum likelihood. We solve the resulting nonlinear optimization problem with a heuristic tailored to the problem’s complexity. We applied this methodology to a hospital case study, which was used to enhance the transportation system as an employee benefit, considering the associated turnover costs. The results demonstrate that our approach can reduce total costs, optimize the usage level of the designed benefits, and increase employee satisfaction. This research provides a robust framework for data-driven decision-making in HR, offering practical tools for improving employee retention strategies.

Mission Planning and Trajectory Optimization in UAV Swarm for Track Deception against Radar Network

In this article, a mission planning and trajectory optimization scheme in unmanned aerial vehicle (UAV) swarm for track deception against radar networks is proposed. The core of this scheme is to formulate the track deception problem as a model with the objective of simultaneously maximizing the number of phantom tracks while minimizing the total flight distance of the UAV swarm, subject to the constraints of UAV kinematic performance, phantom track rotation angles, and a homology test. It is shown that the formulated track deception problem is a mixed-integer programming, multivariable, and non-linear optimization model. By incorporating mission planning based on platform reuse and a particle swarm optimization (PSO) algorithm, a three-stage solution methodology is proposed to tackle the above problem. Through joint optimization for mission planning and flight trajectories of the UAV swarm, a low-speed UAV swarm is capable of generating a number of high-speed phantom tracks. Numerical results demonstrate that the proposed scheme enables a low-speed UAV swarm to generate as many high-speed phantom tracks as possible, effectively achieving track deception against radar network.

How Does Escherichia coli Allocate Proteome?

Microorganisms are shown to actively partition their intracellular resources, such as proteins, for growth optimization. Recent experiments have begun to reveal molecular components unpinning the partition; however, quantitatively, it remains unclear how individual parts orchestrate to yield precise resource allocation that is both robust and dynamic. Here, we developed a coarse-grained mathematical framework that centers on guanosine pentaphosphate (ppGpp)-mediated regulation and used it to systematically uncover the design principles of proteome allocation in Escherichia coli. Our results showed that the cellular ability of resource partition lies in an ultrasensitive, negative feedback-controlling topology with the ultrasensitivity arising from zero-order amino acid kinetics and the negative feedback from ppGpp-controlled ribosome synthesis. In addition, together with the time-scale separation between slow ribosome kinetics and fast turnovers of ppGpp and amino acids, the network topology confers the organism an optimization mechanism that mimics sliding mode control, a nonlinear optimization strategy that is widely used in man-made systems. We further showed that such a controlling mechanism is robust against parameter variations and molecular fluctuations and is also efficient for biomass production over time. This work elucidates the fundamental controlling mechanism of E. coli proteome allocation, thereby providing insights into quantitative microbial physiology as well as the design of synthetic gene networks.

Alignment of a 360° image with posed color images for locally accurate texturing of 3D mesh

With the popularity of 3D content like virtual tours, the challenges of 3D data registration have become increasingly significant. The registration of heterogeneous data obtained from 2D and 3D sensors is required to create photo-realistic 3D models. However, the alignment of 2D images with 3D models introduces a significant challenge due to their inherent differences. This article introduces a rigorous mathematical approach to align a 360° image with its corresponding 3D model generated from images with known camera poses followed by texture projection on the model. We use Scale-Invariant Feature Transform (SIFT) feature descriptors enhanced with a homography-based metric to establish correspondences between the faces of a cubemap and the posed images. To achieve optimal alignment, we use a non-linear least squares optimization technique with a custom objective function. Subsequently, the outcomes of the alignment process are evaluated through texturing using a customized raytracing algorithm. The resulting projections are compared against the original textures, with a comprehensive assessment of the alignment's fidelity and precision.

Coordinated active-reactive power optimization considering photovoltaic abandon based on second order cone programming in active distribution networks

On the basis of predecessors’ coordination optimization of active and reactive power in distribution network, For the necessity of the optimal operation in the distribution network, part of power generated from photovoltaic (PV) cannot be sold to users, and cannot enjoy subsidies. Similarly, the network loss in the power transmission will also bring a certain economic loss. This paper comprehensively considers the economic loss caused by the network loss and PV abandon of the distribution system, and establishes a model to minimize the economic loss. To solve this problem efficiently, the method of DistFlow equation and mixed integer second order cone programming (MISOCP) is used to solve the problem, in this method, the original mixed integer nonlinear programming non-convex problem is transformed into a convex problem, which makes the optimization problem easy to solve. The modified IEEE 33 and IEEE 69 distribution networks are tested by the above method. The optimized results are able to meet the target and have very small relaxation gaps, and the voltage level is also optimized. This coordinated optimization approach helps to optimize the economic operation for active distribution networks with PVs.

Onion (Allium cepa) Profit Maximization via Ensemble Learning-Based Framework for Efficient Nitrogen Fertilizer Use

Onion (Allium cepa) is a major field vegetable in South Korea and has been produced for a long time along with cabbage, radish, garlic, and dried peppers. However, as field vegetables, including onions, have recently been imported at low prices, the profitability of onion production in South Korea is beginning to be at risk. In order to maximize farmers’ profits through onion production, this study develops onion yield prediction models via an ensemble learning-based framework involving linear regression, polynomial regression, support vector regression, decision tree, ridge regression, and lasso regression. The use of nitrogen fertilizers is considered an independent variable in the development of the yield prediction model. This is because the use of nitrogen fertilizers accounts for the highest production cost (13.47%) after labor cost (41.21%) and seed cost (17.42%), and it also directly affects onions yields. For the model development, five research datasets on changes in onion yield according to changes in the use of existing nitrogen fertilizers were used. In addition, a non-linear optimization model was devised using onion yield prediction models for the profit maximization of onion production. As a result, the developed non-linear optimization model using polynomial regression enables an increase in profits from onion production by 67.28%.

Collaborative Optimization for Active Distribution Network with Soft Open Point and Energy Storage

Background: The increasing use of high-penetration distributed clean energy has led to voltage fluctuations in the distribution network that surpass safety limits and pose challenges to economic and low-carbon operation. Traditional voltage regulation devices are unable to meet the real-time high-precision voltage control needs when encountering frequent fluctuations due to physical limitations. The Soft Open Point (SOP) can provide continuous reactive power to achieve rapid voltage regulation. Objective: We propose a collaborative optimization approach that fully considers the regulatory capabilities of SOP and energy storage to eliminate voltage violations and reduce network losses. Methods: This study introduces an active distribution network reactive power voltage optimization approach that incorporates intelligent SOP and energy storage, combining conventional devices (such as on-load tap changers and capacitor banks) with contemporary devices (such as SOP, distributed generators, and energy storage) to establish synergy. A coordinated optimization model was developed, considering various operational constraints to minimize network losses and regulate the voltage of distribution network nodes. By using linearization and quadratic relaxation, the original non-convex mixed-integer non-linear optimization model was transformed into a Mixed-Integer Second-Order Cone Programming (MISOCP) model to meet the requirements of rapid voltage regulation. Results: A case study was conducted on the IEEE 33-node test system, showing that the proposed approach effectively reduces network losses and eliminates voltage violations. Conclusion: The feasibility and effectiveness of the proposed methodology have been validated, confirming its ability to ensure the safe and economic operation of active distribution networks.

Two-stage spatiotemporal cooperative reentry guidance strategy using transformer and improved beluga whale optimization

This research addresses the challenge of insufficient control margin caused by the coupling of multiple constraints in the cooperative precise reentry guidance of hypersonic vehicles. Drawing inspiration from the concept of spatiotemporal decoupling control, a rapid guidance strategy is developed to ensure precise handling of all constraints, including attack time, attack angle, and trajectory constraints. Initially, during the early phase of gliding flight, the adjustment of the heading angle is conceptualized as a single variable root-solving problem, in relation to the entrance width of the lateral azimuth error corridor. Subsequently, a lateral azimuth error corridor with adaptively narrowing entrance width, coupled with a Transformer network-based bank angle predictor, is incorporated to achieve precise fine-tuning of the heading angle under the soft constraint of velocity. In the later phase of gliding flight, the design of a cooperative guidance law under complex multiple constraints is transformed into a nonlinear rapid optimization problem of control commands. An enhanced beluga whale optimization suited to this guidance task is proposed. Finally, numerical simulations are carried out to validate the effectiveness of the proposed strategy under both nominal and uncertain conditions.

Control allocation optimization for an over-actuated tandem tiltwing eVTOL aircraft considering aerodynamic interactions

This paper describes control allocation strategies for a tandem tiltwing electric vertical take-off and landing (eVTOL) aircraft with distributed propulsion. The control mappings are constructed as local surrogate models that relate the control effectors to the aircraft's aeropropulsive forces and moments across the full flight envelope, including interactional aerodynamics effects. Control allocation optimization problems are formulated based on force and moment commands for specific flight conditions. Specifically, a nonlinear programming formulation based on nonlinear control mapping is proposed for control allocation optimization, and the problem is solved using a sparse nonlinear optimizer. The solutions obtained from different formulations such as the minimization of force and moment residuals and the minimization of control effort are investigated. Furthermore, these solutions are compared with the solutions obtained using linear control mapping-based formulations. Results presented for the cases of forward flight, low speed flight & hover, and flight in the transition corridor suggest that considering aerodynamic interactions while formulating and solving the control allocation problem is necessary for higher levels of accuracy compared to linear approaches. One-propeller-out scenarios and moment and force generation cases are also investigated. Finally, control allocation for steady and accelerated operation in the transition corridor is discussed. The contribution of the methods and results in the paper is a nonlinear control allocation methodology for the entire flight envelope of an over-actuated tandem tiltwing eVTOL aircraft.

Artificial neural network-based control of powered knee exoskeletons for lifting tasks: design and experimental validation

Abstract This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.

Effect of DG penetration on hybrid relay coordination using user-defined dual-setting directional overcurrent relays and distance relays

ABSTRACT The efficient coordination of the distance and directional overcurrent relays (DOCRs) is jeopardized by the massive deployment of renewable distributed generation (DG) into electrical power networks. The two key aspects influencing the relay coordination are the bidirectional flow of current and increased short-circuit currents due to DG integration. This study investigates the consequences of variable DG penetration on the distance and dual-setting DOCRs (DS-DOCRs) coordination. As a result, common optimal relay settings have been obtained that can be utilized for variable DG penetration levels in modified IEEE-14 bus test system. For the distance relays (DRs), a fixed zone 1 and variable zone 2 operation have been considered. The proposed combined protection scheme is tested on a modified IEEE-14 bus test system using DS-DOCRs and DRs. The relay coordination problem is formulated as a constrained non-linear optimization problem and solved by genetic algorithm (GA) and gray wolf optimization (GWO). In this paper, DS-DOCRs with user-defined relay characteristics have demonstrated superior performance in line protection compared to conventional DOCRs with normal inverse (NI) characteristics. In addition, a comprehensive comparative analysis of optimization algorithms has been performed between GA and GWO algorithms.

AXIAL DEFORMATION OF SPINEBIO-TENSEGRITY MODELAT DIFFERENT DEPLOYABLE SCHEMES

The study presents the axial deformation of a spine bio-tensegrity model through a shape change strategy with different deployment schemes. The spine bio-tensegrity model mimics the total height, tapered form and natural curvature of a human spine. Three deployable schemes S1-S3 with a different combination of cables at alterable and fixed lengths (at the lower, middle and upper part of the model, respectively) were investigated to achieve a series of axial displacements at 200 mm, 400 mm and 600 mm in the z-direction. The shape change algorithm was developed to optimise the forced elongation of cables, incorporating an objective function designed for monitored nodes in the system to reach their prescribed targets during the optimisation process. Sequential quadratic programming was employed to solve a nonlinear optimisation problem in the shape change analysis involving inequality constraints. The efficiency of the deployable schemes was evaluated based on the deformed shapes, convergence curve and axial forces of the spine bio-tensegrity model. The finding shows in addition to axial deformation, the model in deployment scheme S1 preserves the slenderness characteristic of the spine. In contrast, the model exhibits excessive expansion in the thoracic region in schemes S2 and S3. Greater total computational steps in deployment scheme S3, followed by S2 and S1, reveal that the active cables set near the monitored nodes allow the model to sense and act faster to reach their targets. The study contributes to understanding the structural behaviour and deployment strategy for a structure mimicking a biological system.