Interior Point Optimization Research Articles

Measurement and Modeling of Self-Directed Channel (SDC) Memristors: An Extensive Study

This study systematically addresses the challenge of accurately modeling memristors, focusing on four distinct types doped with tungsten, tin, chromium, and carbon, fabricated by Knowm Inc. A comprehensive characterization is performed by subjecting the devices to sinusoidal excitations with varying frequencies and amplitudes, followed by data averaging and high-frequency filtering. The resulting measurements are fitted using three prominent memristor models: VTEAM, MMS, and Yakopcic. Additional bespoke modifications are assessed. These models, typically formulated as coupled algebraic differential equations integrating electrical quantities (voltage and current) with internal state variables governing device dynamics, are optimized using two robust approaches: (1) interior-point optimization with gradient-based search, and (2) Nelder–Mead gradient-free optimization, both with box constraints applied. A thorough comparison and discussion of the optimized model parameters ensue, accompanied by an examination of the sensitivity to diverse frequency and amplitude ranges. The findings inform conclusions and provide a foundation for future refinements, underscoring the importance of multi-model evaluation and advanced optimization strategies in precise memristor modeling. The presented methodology offers a valuable framework for elucidating optimal modeling paradigms tailored to specific memristor architectures and operating regimes, ultimately enhancing their integration in emerging neuromorphic and computational applications.

A hybrid algorithm based on Bayesian optimization and Interior Point OPTimizer for optimal operation of energy conversion systems

Optimization methods are essential to improve the operation of energy conversion systems including energy storage equipment and fluctuating renewable energy. Modern systems consist of many components, operating in a wide range of conditions and governed by nonlinear balance equations. Consequently, identifying their optimal operation (e.g. minimizing operational costs) requires solving challenging optimization problems, with the global optimum often hidden behind many local ones. In this work, we propose a hybrid method that advantageously combines Bayesian optimization (BO) and Interior Point OPTimizer (IPOPT). The BO is a global approach exploiting Gaussian process regression to build a surrogate model of the cost function to be optimized, while IPOPT is a local approach using quasi-Newton updates. The proposed BO-IPOPT combination allows leveraging the parameter space exploration of the BO with the quasi-Newton convergence of IPOPT once solution candidates are in the neighborhood of an optimum. Using a challenging constrained test function, we test BO-IPOPT in accuracy and computational efficiency. Finally, we showcase the proposed method in the optimal operation of a renewable steam generation system. The results show that BO-IPOPT combines high accuracy and computational efficiency, achieving up to 50% better objective function values at the same CPU time than other state-of-the-art methods.

Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach

Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.

Two-factor Rough Bergomi Model: American Call Option Pricing and Calibration by Interior Point Optimization Algorithm

Two-factor Rough Bergomi Model: American Call Option Pricing and Calibration by Interior Point Optimization Algorithm

Certifiably optimal rotation and pose estimation based on the Cayley map

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.

Interior-point policy optimization based multi-agent deep reinforcement learning method for secure home energy management under various uncertainties

Improving the efficiency of home energy management (HEM) is of great significance in reducing resource waste and prompting renewable energy consumption. With the development of advanced HEM systems and internet-of-things technology, more residents are willing to participate in the electricity market through a demand response mechanism, which can not only reduce the electricity bill but also stabilize the operation of the main grid through peak shaving and valley filling. However, the uncertainties from household appliance parameters, user behaviors, penetrated renewable energy, and electricity prices render the HEM problem a non-trivial task. Although previous deep reinforcement learning (DRL) methods have no requirement for system dynamics due to their model-free and data-driven merits, the unrestricted action space may violate the physical constraints of various devices, and few works have concentrated on this area before. To solve the above challenges, this paper proposes a novel interior-point policy optimization-based multi-agent DRL algorithm to optimize the home energy scheduling procedure while guaranteeing safety during its operation. Besides, a time-series prediction model based on a non-stationary Transformer neural network is proposed to predict the future trend of solar generation and electricity price, which can provide the agents with abundant information to make better decisions. The superior performance of our proposed predictive-control coupled method is demonstrated through extensive numerical experiments, which achieves more precise prediction results, near-zero constraint violations, and better trade-offs between cost and safety than several benchmark methods.

Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution

Parking difficulties have become a social issue that people have to solve. Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents. The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method (RF-LNMPC) in order to improve the overall path tracking accuracy in parking conditions. Firstly, A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively. Secondly, the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization, of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution. Thirdly, the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented. The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically. Finally, the proposed RF-LNMPC is implemented on a self-driving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions. The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.

When and where to step: Terrain-aware real-time footstep location and timing optimization for bipedal robots

Online footstep planning is essential for bipedal walking robots, allowing them to walk in the presence of disturbances and sensory noise. Most of the literature on the topic has focused on optimizing the footstep placement while keeping the step timing constant. In this work, we introduce a footstep planner capable of optimizing footstep placement and step time online. The proposed planner, consisting of an Interior Point Optimizer (IPOPT) and an optimizer based on Augmented Lagrangian (AL) method with analytical gradient descent, solves the full dynamics of the Linear Inverted Pendulum (LIP) model in real time to optimize for footstep location as well as step timing at the rate of 200 Hz. We show that such asynchronous real-time optimization with the AL method (ARTO-AL) provides the required robustness and speed for successful online footstep planning. Furthermore, ARTO-AL can be extended to plan footsteps in 3D, allowing terrain-aware footstep planning on uneven terrains. Compared to an algorithm with no footstep time adaptation, our proposed ARTO-AL demonstrates increased stability in simulated walking experiments as it can resist pushes on flat ground and on a 10° ramp up to 120 N and 100 N respectively. Videos22https://youtu.be/2pwDTEJzmjI. and open-source code33https://github.com/WangKeAlchemist/ARTO-AL/tree/master. are released.

Advancing Predictive Maintenance with PHM-ML Modeling: Optimal Covariate Weight Estimation and State Band Definition under Multi-Condition Scenarios

The proportional hazards model (PHM) is a vital statistical procedure for condition-based maintenance that integrates age and covariates monitoring to estimate asset health and predict failure risks. However, when dealing with multi-covariate scenarios, the PHM faces interpretability challenges when it lacks coherent criteria for defining each covariate’s influence degree on the hazard rate. Hence, we proposed a comprehensive machine learning (ML) formulation with Interior Point Optimizer and gradient boosting to maximize and converge the logarithmic likelihood for estimating covariate weights, and a K-means and Gaussian mixture model (GMM) for condition state bands. Using real industrial data, this paper evaluates both clustering techniques to determine their suitability regarding reliability, remaining useful life, and asset intervention decision rules. By developing models differing in the selected covariates, the results show that although K-means and GMM produce comparable policies, GMM stands out for its robustness in cluster definition and intuitive interpretation in generating the state bands. Ultimately, as the evaluated models suggest similar policies, the novel PHM-ML demonstrates the robustness of its covariate weight estimation process, thereby strengthening the guidance for predictive maintenance decisions.

Effect of coil and chamber structure on plasma radial uniformity in radio frequency inductively coupled plasma

Enhancing plasma uniformity can be achieved by modifying coil and chamber structures in radio frequency inductively coupled plasma (ICP) to meet the demand for large-area and uniformly distributed plasma in industrial manufacturing. This study utilized a two-dimensional self-consistent fluid model to investigate how different coil configurations and chamber aspect ratios affect the radial uniformity of plasma in radio frequency ICP. The findings indicate that optimizing the radial spacing of the coil enhances plasma uniformity but with a reduction in electron density. Furthermore, optimizing the coil within the ICP reactor, using the interior point method in the Interior Point Optimizer significantly enhances plasma uniformity, elevating it from 56% to 96% within the range of the model sizes. Additionally, when the chamber aspect ratio k changes from 2.8 to 4.7, the plasma distribution changes from a center-high to a saddle-shaped distribution. Moreover, the plasma uniformity becomes worse. Finally, adjusting process parameters, such as increasing source power and gas pressure, can enhance plasma uniformity. These findings contribute to optimizing the etching process by improving plasma radial uniformity.

Modern software capabilities for shape optimization of shells

The article is devoted to the shape optimization of shell structures in Comsol Multiphysics using three gradient-based methods: IPOPT (Interior Point OPTimizer), SNOPT (Sparse Nonlinear OPTimizer) and MMA or GCMMA (the Method of Moving Asymptotes). Two types of complex shapes, such as right helicoid and developable helicoid are taken for the computational experiment. The task is to investigate the initial design and optimization process of two helicoids. To obtain a more accurate result and an interesting design solution, the calculation is carried out using three physics-controlled mesh sizes: extra coarse, fine and extra fine with varying values of special optimization settings, such as maximum displacement (dmax) and filter radius (Rmin). The results obtained using the three methods allow to conclude that the mesh element size and studied parameters dmax and Rmin have a significant impact on the final optimization result.

Controlling nodal displacement of pantographic structures using matrix condensation and interior-point optimization: A numerical and experimental study

This study presents an innovative approach for the precise control of nodal displacements in pantographic structures. The method is founded on the Matrix Condensation of Force Method, seamlessly integrated with an Interior Point Optimization algorithm. This combination offers a unique advantage by allowing users to manipulate displaced nodes within a defined coordination domain. Furthermore, this approach introduces the Interior Point Optimization algorithm as an indispensable tool to eliminate inactive turnbuckles and minimize overall actuation requirements. Traditional control methods typically demand a substantial number of turnbuckles and extensive actuation efforts to attain the desired nodal coordinates. The interconnected nature of node movements, wherein changes in one node affect others, adds complexity to determining the impact of bar length alterations on each node. To address this challenge, precisely control power of the Interior Point Optimization algorithm systematically explores numerous scenarios to identify solutions that minimize both actuation and turnbuckle usage. The current technique's effectiveness is validated through rigorous comparisons with established methods, experimental modeling, and rigorous testing using SAP 2000 software. Notably, the current approach yields remarkable results, requiring a staggering 60% less actuation and reducing the reliance on turnbuckles by up to 40% compared to previous methods. This innovation promises to significantly enhance the efficiency and cost-effectiveness of controlling pantographic structures, marking a substantial advancement in this field.

Dynamic Optimization for Petrophysical Property Estimation in Unsteady-State Coreflooding Using Pyomo

Summary This paper deals with a mathematical modeling and optimization-based approach for estimating relative permeability and capillary pressure from average water saturation data collected during unsteady-state waterflooding experiments. Assuming the Lomeland-Ebeltoft-Thomas (LET) model for the variation of the relative permeability with saturation, the appropriate governing equations, boundary, and initial conditions were solved within the Pyomo framework. Using interior point optimization (IPOPT) with a least-squares objective function, the six parameters of the LET model that ensure the history matching between the measured and calculated average saturation are determined. Additionally, we inferred the capillary pressure function and performed a Sobol sensitivity analysis on the LET model parameters. The results showcase the reliability and robustness of our proposed approach, as it estimates the crucial parameters driving the variation of oil-water flow relative permeability across several cases and effectively predicts the capillary pressure trend. The proposed approach can be seen as an alternative to experimental and numerical simulation-based techniques for predicting relative permeability and capillary pressure curves.

Online Preventive Control for Transmission Overload Relief Using Safe Reinforcement Learning With Enhanced Spatial-Temporal Awareness

The risk of transmission overload (TO) in power grids is increasing with the large-scale integration of intermittent renewable energy sources. An effective online preventive control schemes proves to be vital in safeguarding the security of power systems. In this paper, we formulate the online preventive control problem for TO alleviation as a constrained Markov decision process (CMDP), targeted to reduce the load rate of overloaded lines by implementing generation re-dispatch, transmission and busbar switching actions. The CMDP is solved with a state-of-the-art safe deep reinforcement learning method, based on the computationally efficient interior-point policy optimization (IPO), which facilitates desirable learning behavior towards constraint satisfaction and policy improvement simultaneously. The performance of IPO method is further improved with an enhanced perception of spatial-temporal correlations in power gird nodal and edge features, combining the strength of edge conditioned convolutional network and long short-term memory network, fostering more effective and robust preventive control policies to be devised. Case studies on a real-world system and a large-scale system validate the superior performance of the proposed method in TO alleviation, constraint handling, uncertainty adaptability and stability preservation, as well as its favorable computational performance, through benchmarking against both model-based and reinforcement learning-based baseline methods.

Extended Linear Regression and Interior Point Optimization for Identification of Model Parameters of Fixed Wing UAVs

Extended Linear Regression and Interior Point Optimization for Identification of Model Parameters of Fixed Wing UAVs

Optimal Power Flow for Unbalanced Three-Phase Microgrids Using an Interior Point Optimizer

Optimal power flow (OPF) analysis enables the in-depth study and examination of islanded microgrid design and operation. The development of the analysis framework, including modeling, formulating, and selecting effective OPF solvers, however, is a nontrivial task. As a result, this paper presents a tutorial on an OPF modeling framework, offering a mathematical model that can be readily implemented using established open-source software tools such as OpenDSS, Pyomo, and IPOPT. The framework is versatile, capable of representing single-phase and unbalanced three-phase islanded microgrids. Various inverter models, such as those of grid forming and following equipped with their operating characteristics, can be incorporated. The efficacy of the proposed framework is demonstrated in studying the OPF of single-phase and three-phase microgrids.

Optimal floating offshore wind farms for Mediterranean islands

Offshore wind will play an important role in achieving the Green Deal's goals of green transition and renewable energy generation. The European Union (EU) has launched an initiative to support a clean energy transition towards sustainable and renewable energy production in the EU islands. In fact, the Mediterranean islands obtain most of their energy supply from imported fossil fuels, making electricity costs generally very high due to their remote location. In this paper, we compare the optimal offshore wind farm layout, type and number of wind turbines for four selected sites next to Mediterranean islands. Each layout is evaluated in terms of levelised cost of energy, taking into account aerodynamic wake and transmission losses in the productivity estimation and a detailed cost model. Aerodynamic losses are modelled using a Jensen kinematic wake model and an area overlapping model to consider partial wake shadowing between wind turbines, while transmission losses are estimated as Ohmic losses of the inter-array and export transmission cables. Compared to the state-of-the-art PyWake code, the in-house MATLAB wake model demonstrated higher computational efficiency and is integrated into an efficient optimisation algorithm consisting of several iterations of the Interior-point optimisation algorithm. Results show that offshore wind turbines can provide renewable energy at a competitive price, especially at the most energetic site with an LCOE about 80 €/MWh. The normalised optimal LCOE and capacity factor as a function of the number of wind turbines are not significantly influenced by the chosen location and reach a maximum difference of 2–3 %, showing that they mainly depend on the type of wind turbine. The lowest optimal LCOE depending on the number of wind turbines is reduced by about 10 % and 25 % by the higher rated wind turbine.

Tolerance Synthesis of Delta-like Parallel Robots Using a Nonlinear Optimisation Method

Robotic systems require high accuracy in manipulating objects. Positioning errors are influenced by geometric tolerances and various sources. This paper introduces a new technique based on the interior-point algorithm optimisation method to allocate tolerances to the geometric parameters of a robot. This method consists of three steps. First, a method for modelling the kinematic problem as well as the geometric errors must be used. The Denavit–Hartenberg rule is the most suitable method for this modelling case. Then, a mathematical model for tolerance allocation is developed and used as a nonlinear multivariable optimisation problem. Finally, the “interior-point” algorithm is used to solve this optimisation problem. The accuracy and efficiency of the proposed method, in determining the tolerance allocations for a Delta parallel robot, is illustrated via calculation and simulation results. The values of the dimensional tolerances found are optimal. As a result, these values always keep the accuracy less than or equal to the imposed value.

Optimal Control of Anti-Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver

This paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation and inhibition factors is proposed. To achieve continuous and low-dose therapy, the related problem is simulated by an optimal regulator problem mathematically. By combining steepest descent, conjugate gradient, and Armijo techniques, a novel hybrid indirect iterative solver is designed. For accuracy and execution speed, the current solver is compared with an interior-point optimizer and sequential quadratic Hamiltonian methods. Cancer therapy under two different treatment strategies and 24 various versions of the general dynamical system is considered numerically. A comprehensive analysis of the corresponding outcomes is presented. Numerical results and related diagrams are provided.

Safe Deep Reinforcement Learning for Microgrid Energy Management in Distribution Networks With Leveraged Spatial–Temporal Perception

Microgrids (MG) have recently attracted great interest as an effective solution to the challenging problem of distributed energy resources’ management in distribution networks. In this context, despite deep reinforcement learning (DRL) constitutes a well-suited model-free and data-driven methodological framework, its application to MG energy management is still challenging, driven by their limitations on environment status perception and constraint satisfaction. In this paper, the MG energy management problem is formalized as a Constrained Markov Decision Process, and is solved with the state-of-the-art interior-point policy optimization (IPO) method. In contrast to conventional DRL approaches, IPO facilitates efficient learning in multi-dimensional, continuous state and action spaces, while promising satisfaction of complex network constraints of the distribution network. The generalization capability of IPO is further enhanced through the extraction of spatial-temporal correlation features from original MG operating status, combining the strength of edge conditioned convolutional network and long short-term memory network. Case studies based on an IEEE 15-bus and 123-bus test feeders with real-world data demonstrate the superior performance of the proposed method in improving MG cost effectiveness, safeguarding the secure operation of the network and uncertainty adaptability, through performance benchmarking against model-based and DRL-based baseline methods. Finally, case studies also analyze the computational and scalability performance of proposed and baseline methods.