Nonlinear Constrained Optimization Research Articles

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.

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 CO[Formula: see text] 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 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.

A zeroing neural network model for form-finding problems: A nonlinear optimization approach

How to establish a simple and efficient nonlinear optimization problem form-finding model in noise environments is the main concern of this paper, thereby, a sequential quadratic programming form-finding (SQP) approach via a noise-tolerant zeroing neural network (NTZNN) is presented to solve the proposed problem. First, the rank of force density matrix is selected as optimization objective due to its crucial physical property. In addition, linear relations between the force density vectors and force density matrix are selected as the constraint conditions, which can ensure the tensegrity mechanism in a stable status. Furthermore, the simulations are shown that the presented SQP-NTZNN algorithm has superiority with anti-noise performance and computation efficiency, which by comparing the computational rate in the same noise environment with the novel form-finding algorithm. Eventually, the form-finding simulations under different initial conditions are formed to verify the importance of the constrained conditions, it can prove the high efficiency of the proposed nonlinear constrained optimization model which is transformed from the form-finding problem.

Superiorization of projection algorithms for linearly constrained inverse radiotherapy treatment planning.

We apply the superiorization methodology to the constrained intensity-modulated radiation therapy (IMRT) treatment planning problem. Superiorization combines a feasibility-seeking projection algorithm with objective function reduction: The underlying projection algorithm is perturbed with gradient descent steps to steer the algorithm towards a solution with a lower objective function value compared to one obtained solely through feasibility-seeking. Within the open-source inverse planning toolkit matRad, we implement a prototypical algorithmic framework for superiorization using the well-established Agmon, Motzkin, and Schoenberg (AMS) feasibility-seeking projection algorithm and common nonlinear dose optimization objective functions. Based on this prototype, we apply superiorization to intensity-modulated radiation therapy treatment planning and compare it with (i) bare feasibility-seeking (i.e., without any objective function) and (ii) nonlinear constrained optimization using first-order derivatives. For these comparisons, we use the TG119 water phantom, the head-and-neck and the prostate patient of the CORT dataset. Bare feasibility-seeking with AMS confirms previous studies, showing it can find solutions that are nearly equivalent to those found by the established piece-wise least-squares optimization approach. The superiorization prototype solved the linearly constrained planning problem with similar dosimetric performance to that of a general-purpose nonlinear constrained optimizer while showing smooth convergence in both constraint proximity and objective function reduction. Superiorization is a useful alternative to constrained optimization in radiotherapy inverse treatment planning. Future extensions with other approaches to feasibility-seeking, e.g., with dose-volume constraints and more sophisticated perturbations, may unlock its full potential for high performant inverse treatment planning.

Comparing optimization schemes for solving case studies with multiple heat exchangers using high-order pinch point temperature difference methods

Heat exchangers (HEs) are often modeled using pinch point temperature difference (ΔTpinch) methods when optimizing systems with HEs. However, even small inaccuracies in model predictions of HEs will introduce numerical noise that can cause optimization algorithms to fail. A recent study of single HEs suggests that high-order interpolation methods can compute ΔTpinch much faster than conventional methods. However, the performance of such methods when optimizing HE systems have not previously been tested.Heat pumps with 2 and 3 HEs, with and without an ejector are optimized using different schemes. Results from these case studies show that non-linear constrained gradient-based optimization algorithms are more than 5 times faster than particle swarm (PS), and that the conventional genetic algorithm (GA) should not be used. However, the main conclusion is that the case study optimizations are solved 5–10 times faster if ΔTpinch is calculated using hybrid high and low-order interpolation methods.

Adaptive Beamforming with Sidelobe Level Control for Multiband Sparse Linear Array

Multiband antenna arrays have the capability of effectively working in multiple frequency bands and thus significantly simplify the antenna system. To further reduce the system overhead, this paper discusses the joint design of antenna selection and adaptive beamforming for multiband antenna arrays, where the sidelobe level is also controlled so as to alleviate the effect of unknown sporadic interference. Based on the maximum signal-to-interference-plus-noise ratio (SINR) criterion and sidelobe level constraints, the proposed multiband sparse array design is formulated into a nonconvex constrained nonlinear optimization problem with an l0,2-mixed norm regularization. This problem ensures that the same antenna positions are selected at all operating frequencies while the beamformer weights of each frequency are optimized independently. By exploiting the semi-definite relaxation and the reweighted l1,∞-norm approximation, the problem is converted into a series of convex subproblems and is then effectively solved by the proposed iterative reweighted method. Numerical results show that the proposed multiband sparse array significantly reduces the sidelobe levels in all operating frequencies while maintaining the maximum SINR, so it provides superior performance of interference suppression.

Numerical fact-finding of different functions impact on the fuzzy preference programming optimality

The fuzzy analytic hierarchy process (FAHP) is a widely implemented approach for determining the weights of criteria and alternatives from pairwise comparison matrices. FAHP methodology uses triangular fuzzy as a tool for the decision-maker to arrange judgments expressed as the pairwise comparison matrix elements. FAHP is then modeled into a nonlinear constrained optimization problem to increase the decision maker’s satisfaction. However, in some cases, this model would yield multiple optimal solutions. Logarithmic fuzzy preference programming (LFPP) is offered to overcome this unfavorable situation. Nevertheless, LFPP includes a parameter in its model for which no specific method is available to determine. Meanwhile, the differences in parameter values will affect the solution. In the worst case, the weights obtained will be inaccurate. As a result, the decision taken based on the weights will be biased and unreliable. This issue is particularly important when it requires high accuracy. It includes the decisions on the portfolio investment, economic, human capital measurements, and shipping registry. Another crucial thing is that the use of the natural logarithm function in the LFPP method has the potential for an overflow effect at the computational stage when it is implemented to derive the weights. Therefore, in the application context, it is significant to improve the shortcomings of the LFPP method in terms of parameter involvement and the use of the logarithmic function. For this purpose, this paper proposes a non-parameter transcendental fuzzy preference programming (TFPP) model for deriving the optimal weights from fuzzy pairwise comparison matrices. The TFPP is obtained by investigating different functions’ effects on fuzzy preference programming (FPP). The proposed method has a more general form. One of the specific forms of the TFPP is chosen in a computational implementation. The numerical results confirm that the TFPP optimization model is reliable in obtaining the optimum global weights. The comparison with the LFPP method also shows that the TFPP is more efficient.

A Nonlinear Optimization Design Algorithm for Nearly Linear-Phase 2D IIR Digital Filters

In this paper, a new optimization method for the design of nearly linear-phase two-dimensional infinite impulse (2D IIR) digital filters with a separable denominator is proposed. A design framework for 2D IIR digital filters is formulated as a nonlinear constrained optimization problem where the group delay deviation in the passband is minimized under prescribed soft magnitude constraints and hard stability requirements. To achieve this goal, sub-level sets of the group delay deviations are utilized to generate a sequence of filters, from which the one with the best performance is selected. The quality of the obtained filter is evaluated using three quality factors, namely, the passband magnitude quality factor Qh and the group delay deviation quality factor Qτ, while the third one is a new quality factor Qs that assesses the performance in the stopband relative to the minimum filter gain in the passband. The proposed framework is implemented using the interior-point (IP) method in a MATLAB environment, and the experimental results show that filters designed using the proposed method have good magnitude response and low group delay deviation. The performance of the resulting filters is compared with the results of other methods.

Optimized selection of fluid lubricant for cylindrical roller bearings under elastohydrodynamic lubrication

Roller bearings are widely used in machinery. Keeping the contact surfaces of bearings properly lubricated strongly mitigates wear effects, improving bearing fatigue life. Therefore, systematically selecting the lubricant fluid that satisfies bearing operation conditions allows the lubricating layer to be able to carry the applied load, the operating temperature, and the roughness on contact. The nonlinear constrained optimization method is used for lubricant selection, seeking to find the fluid that best fits the bearing operation conditions. Roller bearing lubrication is characteristically elastohydrodynamic (EHL); namely, the Hertz theory describes the load applied on the contacts of a cylindrical roller bearing, and the Stribeck condition classifies the tribological condition of the surfaces in contact. This work concludes that roughness and speed are the most important parameters to consider when choosing a fluid lubricant.

A sustainable two-echelon green supply chain coordination model under fuzziness incorporating carbon pricing policies.

Noxious effect on environmental due to carbon emissions is being addressed worldwide by governments through carbon pricing instruments. Two of prevalent instruments adopted by governments are simple carbon tax and cap-and-trade policy. Effectiveness of carbon pricing instruments towards achieving reduction in carbon emissions is a matter of study on one hand. Whereas, the planning of supply chain operations under imposition of such financial instruments is a challenge for small and medium scale business enterprises. Addressing this situation, the present study develops a supply chain model for coordinated planning of production and inventory replenishment schedules along with decision on economic amounts of expenditure for green resources. This decision model is formulated separately under the enforcement of each of two carbon pricing policies. The study focuses a manufacturer-retailer duo which works by adopting certain sustainability and conservation practices. Manufacturer reworks on rectifiable proportion of defective units, while retailer launches discounts-based sales of partially damaged units. The decision-making model developed in this study incorporates such activities. Furthermore, practical aspects like a slowdown in production due to unforeseeable disruptions and the effect of the quality of product and advertisement campaigns on demand rates are included in the proposed model. Under the purview of each carbon pricing policy, decision-making model is formulated as a nonlinear constrained optimization problem with objective towards profit maximization. A novel conception of fuzziness has been suggested for tackling imprecision in the assessment of certain parameters involved in the model. A numerical study on an appropriate case of a manufacturer-retailer duo system is presented. Empirical results of numerical study evince that a substantial reduction in carbon emission is achieved, even with an escalation in the profit through appropriate green expenditure. This trend is observed under the imposition of each of the carbon pricing policies, thereby substantiating an encouragement to supply chain partners for making expenditures on green resources. Thereby, the hypothesis of getting desired response on curbing emissions by incentivization through carbon pricing is satisfied in the studied case. Furthermore, a sensitivity analysis concludes the stability of formulated model against most of the parameters involved.

Health-considered energy management strategy for fuel cell hybrid electric vehicle based on improved soft actor critic algorithm adopted with Beta policy

Deep reinforcement learning-based energy management strategy (EMS) is essential for fuel cell hybrid electric vehicles to reduce hydrogen consumption, improve health performance and maintain charge. This is a complex nonlinear constrained optimization problem. In order to solve the problem of high bias caused by the inconsistency between the infinite support of stochastic policy and the bounded physics constraints of application scenarios, this paper proposes the Beta policy to improve standard soft actor critic (SAC) algorithm. This work takes hydrogen consumption, health degradation of both fuel cell system and power battery, and charge margin into consideration to design an EMS based on the improved SAC algorithm. Specifically, an appropriate tradeoff between money cost during driving and charge margin is firstly determined. Then, optimization performance differences between the Beta policy and the standard Gaussian policy are presented. Thirdly, ablation experiments of health constraints are conducted to show the validity of health management. Finally, comparison experiments indicate that, the proposed strategy has a 5.12% performance gap with dynamic programming-based EMS with respect to money cost, but is 4.72% better regarding to equivalent hydrogen consumption. Moreover, similar performances in validation cycle demonstrate good adaptability of the proposed EMS.