Nonlinear Constrained Optimization Research Articles

Mechanism and Control Strategies for Current Sharing in Multi-Chip Parallel Automotive Power Modules

Multi-chip parallel power modules are highly favored in applications requiring high capacity and high switching frequency. However, the dynamic current imbalance between parallel chips caused by asymmetric layouts limits the available capacity. This paper presents a method to optimize dynamic current distribution by adjusting the lengths and connection points of bond wires. For the first time, a response surface model and nonlinear constraint optimization algorithm are introduced, along with parameter analysis based on finite element methods, to establish the response surface models for the parasitic inductance of bond wires and DBC (direct bonded copper). By leveraging the optimization goals for parasitic inductance and the analytical expressions of all response surfaces, the dynamic current sharing issue was transformed into a nonlinear constrained optimization problem. The solution to this optimization problem identified the optimal connection points for the bond wires, enhancing dynamic current sharing performance. Simulations and experiments were conducted, revealing that the optimized automotive-grade module exhibited a significant reduction in current differences between parallel branches, from 41.7% to 5.03% compared with the original design. This indicated that the proposed optimization scheme for adjusting bond wire connection points could significantly mitigate current disparities, thereby markedly improving current distribution uniformity.

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

Algorithm XXX: SOLNP+: A Derivative-Free Solver for Constrained Nonlinear Optimization

Batch-sizing and machinability data systems for milling operations: An optimal sustainable cost of quality approach

Nowadays, manufacturers make every effort to achieve a higher quality of their products at an attractive cost. With all the introduced legislation and incentives in the developed world to address global warming, machining shops in the West also strive to cut greenhouse emissions. This article offers an optimal approach to the micro Computer-Aided Process Planning (CAPP) problem to optimize the internal quality cost and buffering effect while keeping the environmental impact low. To optimize the machining parameters, the mathematical model is developed for different milling operations, face, side, and peripheral. cutting speed, feed rate, axial depth of cut, radial depth of cut, nose radius, and batch sizing while maximizing profit and meeting customer demand. A Mixed-Integer Nonlinear Programming (MINLP) model is formulated and solved using Classical Constrained Nonlinear Optimization (CCNO) and Genetic Algorithms (GAs). Surface roughness, used as a metric to evaluate the desired quality level of a finished machined part type, is modeled as a Gaussian random variable to model the surface roughness of the machined part utilizing a cumulative normal distribution. The ratio of rework and scrap is calculated in terms of the surface roughness of the machined part shifting away from the target and exceeding upper and lower specification limits. The internal failure cost model, addressing both scrap and rework, is developed based on Taguchi’s quadratic loss function. CCNO is employed to validate the results obtained by GAs, relaxing the lot-sizing integrality constraint and, thus, the convexity of the produced relaxed model. An iterative method employing a developed multi-regression model is used to solve for the expended power consumption (an inherent highly nonlinear environmental criterion of the developed model) within both GAs and CCNO. This study reveals that the machining parameters substantially impact the cost components of the objective function as well as the scrap and rework quantities. A stringent quality cost target can force the model to optimize the feed rate and nose radius to minimize the internal failure quality cost while improving the environmental impact, including direct and indirect power consumption and CO2 emissions considerations.

Trajectory Optimization to Enhance Observability for Bearing-Only Target Localization and Sensor Bias Calibration.

This study addresses the challenge of bearing-only target localization with sensor bias contamination. To enhance the system's observability, inspired by plant phototropism, we propose a control barrier function (CBF)-based method for UAV motion planning. The rank criterion provides only qualitative observability results. We employ the condition number for a quantitative analysis, identifying key influencing factors. After that, a multi-objective, nonlinear optimization problem for UAV trajectory planning is formulated and solved using the proposed Nonlinear Constrained Multi-Objective Gray Wolf Optimization Algorithm (NCMOGWOA). Simulations validate our approach, showing a threefold reduction in the condition number, significantly enhancing observability. The algorithm outperforms others in terms of localization accuracy and convergence, achieving the lowest Generational Distance (GD) (7.3442) and Inverted Generational Distance (IGD) (8.4577) metrics. Additionally, we explore the effects of the CBF attenuation rates and initial flight path angles.

A Regularized Physics-Informed Neural Network to Support Data-Driven Nonlinear Constrained Optimization

A Regularized Physics-Informed Neural Network to Support Data-Driven Nonlinear Constrained Optimization

Life-cycle production optimization with nonlinear constraints using a least-squares support-vector regression proxy

When nonlinear constraints such as field liquid or water production rate, injection pressures, etc., as functions of time need to be honored in addition to linear ones, the life-cycle production optimization problem, a component of a closed loop reservoir management, becomes challenging and computationally expensive to perform using a high-fidelity reservoir simulator with the existing gradient-based methods using the adjoint or stochastic approximate gradient methods. Therefore, the objective of this study is to present computationally efficient methods for deterministic production optimization under nonlinear constraints using a kernel-based machine learning method where the cost function is the net present value (NPV). We use the least-squares support-vector regression (LSSVR) to approximate the NPV function. To achieve computational efficiency, we generate a set of output values of the NPV and nonlinear constraint functions, which are field liquid production rate (FLPR) and water production rate (FWPR) in this study, by running the high-fidelity simulator for a broad set of input design variables (well controls) and then using the collection of input/output data to train LSSVR proxy models to replace the high-fidelity simulator to compute NPV and nonlinear state constraint functions during iterations of sequential quadratic programming (SQP). To obtain improved (higher) estimated optimal NPV values, we use the existing so-called iterative sampling refinement (ISR) method to update the LSSVR proxy so that the updated proxy remains predictive toward promising regions of search space during the optimization. Direct and indirect ways of constructing LSSVR-based NPVs as well as different combinations of input data, including nonlinear state constraints and/or the bottomhole pressures (BHPs) and water injection rates, are tested as alternative feature spaces. The results obtained from our proposed LSSVR-based optimization methods are compared with those obtained from our in-house stochastic simplex approximate gradient (StoSAG)-based line-search SQP programming (LS-SQP-StoSAG) algorithm that uses directly a high-fidelity simulator to compute the gradients of the objective function and the nonlinear state functions with StoSAG for the Brugge reservoir model. The results show that nonlinear constrained optimization with the LSSVR ISR with SQP is computationally 3.25 fold more efficient than LS-SQP-StoSAG. In addition, the results show that constructing NPV indirectly using the field liquid and water rates for a waterflooding problem where inputs come from LSSVR proxies of the nonlinear state constraints requires significantly fewer training samples than the method constructing NPV directly from the NPVs computed from a high-fidelity simulator. LSSVR has advantages for its computational efficiency which is the main goal in our research, and robustness against overfitting especially for the cases where we have limited data. However, DNNs and random forest require large training size and require much more computational resources and longer training times. Also, Random Forests and Gradient Boosting Machines can be prone to overfitting and become computationally intensive.

A Novel Path-Following Method for Time-Varying Optimizations with Optimal Parametric Functions

We address a broad category of nonlinear constrained optimization problems. We then reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system to track the respective optimal solution. We then re-parameterize the dynamical system according to a linear combination of parametric functions. By applying the calculus of variations, we optimize these parametric functions to minimize the optimality distance. Consequently, we develop an iterative dynamic algorithm, termed as OP-TVO, to achieve efficient convergence to the solution. We compare the performance of the proposed algorithm with the prediction correction method (PCM) in terms of optimality and computational complexity. The results demonstrate that OP-TVO effectively competes with PCM for the given class of optimization problems, suggesting a promising alternative to PCM. This work also introduces a novel paradigm for solving parametric dynamic systems.

A new optimal strategy for energy minimization in wireless sensor networks

In recent years, evolutionary and metaheuristic algorithms have emerged as crucial tools for optimization in the field of artificial intelligence. These algorithms have the potential to revolutionize various aspects of our lives by leveraging the multidisciplinary nature of wireless sensor networks (WSNs). This study aims to introduce genetic and simulated annealing algorithms as effective solutions for enhancing WSN performance. Our contribution entails two main phases. Firstly, we establish mathematical models and formulate objectives as a nonlinear constrained optimization problem. Secondly, we develop two algorithmic solutions to address the formulated optimization problem. The obtained results from multiple simulations demonstrate the positive impact of the proposed strategies on improving network performance in terms of energy consumption.

Monarch butterfly optimization-based genetic algorithm operators for nonlinear constrained optimization and design of engineering problems

Abstract This paper aims to present a hybrid method to solve nonlinear constrained optimization problems and engineering design problems (EDPs). The hybrid method is a combination of monarch butterfly optimization (MBO) with the cross-over and mutation operators of the genetic algorithm (GA). It is called a hybrid monarch butterfly optimization with genetic algorithm operators (MBO-GAO). Combining MBO and GA operators is meant to overcome the drawbacks of both algorithms while merging their advantages. The self-adaptive cross-over and the real-valued mutation are the GA operators that are used in MBO-GAO. These operators are merged in a distinctive way within MBO processes to improve the variety of solutions in the later stages of the search process, speed up the convergence process, keep the search from getting stuck in local optima, and achieve a balance between the tendencies of exploration and exploitation. In addition, the greedy approach is presented in both the migration operator and the butterfly adjusting operator, which can only accept offspring of the monarch butterfly groups who are fitter than their parents. Finally, popular test problems, including a set of 19 benchmark problems, are used to test the proposed hybrid algorithm, MBO-GAO. The findings obtained provide evidence supporting the higher performance of MBO-GAO compared with other search techniques. Additionally, the performance of the MBO-GAO is examined for several EDPs. The computational results show that the MBO-GAO method exhibits competitiveness and superiority over other optimization algorithms employed for the resolution of EDPs.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

Semi-Active Groundhook Control of Offshore Tension Leg Platforms Using Tuned Mass Damper With Optimized Parameters and Magneto-Rheological Damper Under Multiple Hazards

Abstract The purpose of the current study is to recommend an offshore tension leg platform (TLP) semi-active control system to lessen vibrations caused by various risks, such as the wind load and regular and irregular waves. State-of-the-art indicates that there has not been much study on semi-active management of offshore TLPs exposed to numerous hazards while taking into account system nonlinearities and employing a control method that is resilient to uncertainty. An augmented velocity–displacement-based groundhook (AVDB-GH) semi-active control scheme using magneto-rheological (MR) dampers, which is an improvement over the displacement-based groundhook (DB-GH) control algorithm, is proposed. The proposed controller uses a semi-active tuned mass damper (SATMD) consisting of a passive tuned mass damper (TMD) and two semi-active MR dampers as the control devices. Constrained nonlinear optimization is used to determine the SATMD's optimized parameters in order to produce the best control performance. A significant reduction in surge response of TLP is observed both in the time domain and the frequency domain. Compared to the SATMD using the usual DB-GH algorithm, the suggested control strategy more successfully decreases the key response variables—deck displacement, power spectral density, and acceleration. The effectiveness of the controller is better for regular waves than for irregular waves and wind forces. Because the performance of the controller is unaffected by changes in the mass and stiffness of the TLP, the controller can be regarded as robust.

Combined emission economic dispatch using quantum-inspired particle swarm optimization and its variants

The ever-increasing electricity demand, its dependency on fossil fuels, and the consequent environmental degradation are major concerns of this era. The worldwide domination of fossil fuels in bulk electricity generation is rapidly increasing the emissions of CO2 and other environmentally dangerous gases that are contributing to climate change. The economic and emission dispatch are two important problems in thermal power generation whose combination produces a complex highly constrained nonlinear optimization problem known as combined economic and emission dispatch. The optimization of combined economic and emission dispatch aims to allocate the generation of committed units to minimize fuel cost and emissions, simultaneously while honoring all equality and inequality constraints. Therefore, in this article, we investigate a solution of the combined economic and emission dispatch problem using quantum particle swarm optimization and its two modified versions, that is, enhanced quantum particle swarm optimization and quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor. The enhanced quantum particle swarm optimization algorithm achieves particles’ diversification at early stages and shows good performance in local search at later stages. The quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor boosts search performance of quantum particle swarm optimization and attains better global optimality. The suggested methods are employed to achieve solution for the combined economic and emission dispatch in four distinct systems, encompassing two scenarios with 6 units each, one with a 10-unit configuration, and another with an 11-unit setup. A comparative analysis with methodologies documented in existing literature reveals that the proposed approach outperforms others, demonstrating superior computational performance and robust efficiency.

Improved nonlinear model predictive control with inequality constraints using particle filtering for nonlinear and highly coupled dynamical systems

Abstract Motion planning and controller design are challenging tasks for highly coupled and nonlinear dynamical systems such as autonomous vehicles and robotic applications. Nonlinear model predictive control (NMPC) is an emerging technique in which sampling-based methods are used to synthesize the control and trajectories for complex systems. In this study, we have developed the sampling-based motion planning algorithm with NMPC through Bayesian estimation to solve the online nonlinear constrained optimization problem. In the literature, different filtration techniques have been applied to extract knowledge of states in the presence of noise. Due to the detrimental effects of linearization, the Kalman filter with NMPC only achieves modest effectiveness. Moving horizon estimation (MHE), on the other hand, frequently relies on simplifying assumptions and lacks an effective recursive construction. Additionally, it adds another optimization challenge to the regulation problem that has to be solved online. To address this problem, particle filtering is implemented for Bayesian filtering in nonlinear and highly coupled dynamical systems. It is a sequential Monte Carlo method that involves representing the posterior distribution of the state of the system using a set of weighted particles that are propagated through time using a recursive algorithm. For nonlinear and strongly coupled dynamical systems, the novel sampling-based NMPC technique is effective and simple to use. The efficiency of the suggested method has been assessed using simulated studies.

Wind Power Bidding Based on an Ensemble Differential Evolution Algorithm with a Problem-Specific Constraint-Handling Technique

The intermittent nature of wind power generation induces great challenges for power bidding in the electricity market. The deployment of battery energy storage can improve flexibility for power bidding. This paper investigates an optimal power bidding strategy for a wind–storage hybrid power plant in the day-ahead electricity market. To handle the challenges of the uncertainties of wind power generation and electricity prices, the optimal bidding problem is formulated as a risk-aware scenario-based stochastic programming, in which a number of scenarios are generated using a copula-based approach to represent the uncertainties. These scenarios consider the temporal correlation of wind power generation and electricity prices between consecutive time intervals. In the stochastic programming, a more practical but nonlinear battery operation cost function is considered, which leads to a nonlinear constrained optimization problem. To solve the nonlinear constrained optimization problem, an ensemble differential evolution (EDE) algorithm is proposed, which makes use of the merits of an ensemble of mutant operators to generate mutant vectors. Moreover, a problem-specific constraint-handling technique is developed. To validate the effectiveness of the proposed EDE algorithm, it is compared with state-of-the-art DE-based algorithms for constrained optimization problems, including a constrained composite DE (C2oDE) algorithm and a novel DE (NDE) algorithm. The experimental results demonstrate that the EDE algorithm is much more reliable and much faster in finding a better bidding strategy against benchmarking algorithms. More precisely, the average values of the success rate are 0.893, 0.667, and 0.96 for C2oDE, NDE, and EDE, respectively. Compared to C2oDE and NDE, the average value of the mean number of function evaluations to succeed with EDE is reduced by 76% and 59%, respectively.

A Novel Fuzzy Best-Worst Multicriteria Decision-Making Method Based on the Dual Interval Algorithm for Environmental Decision Support Systems

Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty.

A machine learning-based stochastic optimal energy management framework for a renewable energy-assisted isolated microgrid system

ABSTRACT This paper proposes a cost-based stochastic optimal energy management framework for a renewable energy-assisted isolated microgrid system. These microgrids encourage the integration of multiple distributed energy sources, including the penetration of renewable energy. For this purpose, the optimal day-ahead dispatch of the connected energy resources is obtained for an economically viable system by solving a nonlinear constrained optimization problem. The renewable energy and the load demand data forecasting are accomplished using the Gaussian process regression learning model in the MATLAB/SIMULINK® environment for obtaining the day-ahead dispatch. The optimal problem is solved through sequential quadratic programming and a hybrid function approach incorporating particle swarm optimization for a comprehensive techno-economical analysis. A comparative assessment of the results is accomplished to obtain a more feasible and economical system operation corresponding to different time horizons and other critical factors such as fast iterations, computational accuracy, solution feasibility, convergence rate, etc.

Rate-independent gradient-enhanced crystal plasticity theory — Robust algorithmic formulations based on incremental energy minimization

Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated by means of the micromorphic approach. The elaborated algorithmic formulations rely on the underlying variational structure of (associative) crystal plasticity. To be more precise and in line with so-called variational constitutive updates or incremental energy minimization principles, an incrementally defined energy derived from the underlying time-continuous constitutive model represents the starting point of the novel numerically robust algorithmic formulations. This incrementally defined potential allows to compute all variables jointly as minimizers of this energy. While such discrete variational constitutive updates are not new in general, they are considered here in order to employ powerful techniques from non-linear constrained optimization theory in order to compute robustly the aforementioned minimizers. The analyzed prototype models are based on (1) nonlinear complementarity problem (NCP) functions as well as on (2) the augmented Lagrangian formulation. Numerical experiments show the numerical robustness of the resulting algorithmic formulations. Furthermore, it is shown that the novel algorithmic ideas can also be integrated into classic, non-variational, return-mapping schemes.

Mathematical Camera Array Optimization for Face 3D Modeling Application.

Camera network design is a challenging task for many applications in photogrammetry, biomedical engineering, robotics, and industrial metrology, among other fields. Many driving factors are found in the camera network design including the camera specifications, object of interest, and type of application. One of the interesting applications is 3D face modeling and recognition which involves recognizing an individual based on facial attributes derived from the constructed 3D model. Developers and researchers still face difficulty in reaching the required high level of accuracy and reliability needed for image-based 3D face models. This is caused among many factors by the hardware limitations and imperfection of the cameras and the lack of proficiency in designing the ideal camera-system configuration. Accordingly, for precise measurements, we still need engineering-based techniques to ascertain the specific level of deliverables quality. In this paper, an optimal geometric design methodology of the camera network is presented by investigating different multi-camera system configurations composed of four up to eight cameras. A mathematical nonlinear constrained optimization technique is applied to solve the problem and each camera system configuration is tested for a facial 3D model where a quality assessment is applied to conclude the best configuration. The optimal configuration is found to be a 7-camera array, comprising a pentagon shape enclosing two additional cameras, offering high accuracy. For those who prioritize point density, a 9-camera array with a pentagon and quadrilateral arrangement in the X-Z plane is a viable choice. However, a 5-camera array offers a balance between accuracy and the number of cameras.

ToRoS: A Topology Optimization Approach for Designing Robotic Skins

Soft robotics offers unique advantages in manipulating fragile or deformable objects, human-robot interaction, and exploring inaccessible terrain. However, designing soft robots that produce large, targeted deformations is challenging. In this paper, we propose a new methodology for designing soft robots that combines optimization-based design with a simple and cost-efficient manufacturing process. Our approach is centered around the concept of robotic skins---thin fabrics with 3D-printed reinforcement patterns that augment and control plain silicone actuators. By decoupling shape control and actuation, our approach enables a simpler and cost-efficient manufacturing process. Unlike previous methods that rely on empirical design heuristics for generating desired deformations, our approach automatically discovers complex reinforcement patterns without any need for domain knowledge or human intervention. This is achieved by casting reinforcement design as a nonlinear constrained optimization problem and using a novel, three-field topology optimization approach tailored to fabrics with 3D-printed reinforcements. We demonstrate the potential of our approach by designing soft robotic actuators capable of various motions such as bending, contraction, twist, and combinations thereof. We also demonstrate applications of our robotic skins to robotic grasping with a soft three-finger gripper and locomotion tasks for a soft quadrupedal robot.

Developing inverse motion planning technique for autonomous vehicles using integral nonlinear constraints

The study considers issues of elaborating and validating a technique of autonomous vehicle motion planning based on sequential trajectory and speed optimization. This method includes components such as representing sought-for functions by finite elements (FE), vehicle kinematic model, sequential quadratic programming for nonlinear constrained optimization, and Gaussian N-point quadrature integration. The primary novelty consists of using the inverse approach for obtaining vehicle trajectory and speed. The curvature and speed are represented by integrated polynomials to reduce the number of unknowns. For this, piecewise functions with two and three degrees of freedom (DOF) are implemented through FE nodal parameters. The technique ensures higher differentiability compared to the needed in the geometric and kinematic equations. Thus, the generated reference curves are characterized by simple and unambiguous forms. The latter fits best the control accuracy and efficiency during the motion tracking phase. Another advantage is replacing the nodal linear equality constraints with integral nonlinear ones. This ensures the non-violation of boundary limits within each FE and not only in nodes. The optimization technique implies that the spatial and time variables must be found separately and staged. The trajectory search is accomplished in the restricted allowable zone composed by superposing an area inside the external and internal boundaries, based on keeping safe distances, excluding areas for moving obstacles. Thus, this study compares two models that use two and three nodal DOF on optimization quality, stability, and rapidity in real-time applications. The simulation example shows numerous graph results of geometric and kinematic parameters with smoothed curves up to the highest derivatives. Finally, the conclusions are made on the efficiency and quality of prognosis, outlining the similarities and differences between the two applied models.