Constrained Optimization Techniques Research Articles

A model estimating the level of floral transition in olive trees exposed to warm periods during winter.

Rising winter temperatures jeopardize the fruit yield of trees that require a prolonged and sufficiently cold winter to flower. Predicting the exact risk to different crop varieties is the first step in mitigating the harmful effects of climate change. This work focused on olive (Olea europaea) - a traditional crop in the Mediterranean basin whose flowering depends on the sufficiency of cold periods and the lack of warm ones during the preceding winter. Yet, a satisfactory quantitative model forecasting its expected flowering under natural temperature conditions is still lacking. The effect of different temperature regimes on olive flowering level and flowering-gene expression was empirically tested. A modified 'dynamic model' describing the response of a putative flowering factor to the temperature signal was constructed. The crucial component of the model was an unstable intermediate, produced and degraded at temperature-dependent rates. The model accounts for both the number of cold and warm hours but also for their sequence. Empirical flowering and temperature data were applied to fit the model parameters, applying numerical constrained optimization techniques; the model outcomes were successfully validated. The model accurately predicted low-to-moderate flowering under winters with warm periods and properly accounted for the effects of warm periods during winter.

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field for fixed boundary equilibria

A simple and fast method to calculate the coil currents and the external poloidal flux and magnetic field consistent with a given internal magnetohydrodynamic (MHD) equilibrium and coil geometry is presented. The constrained optimization technique employed allows to fix the exact position of the X-points. The external poloidal flux and field are calculated using Green’s functions expressed in terms of elliptic integrals that are calculated using a fast and accurate routine. The calculation can be limited to the region between the plasma and the device wall. An example for a double null configuration is presented.

Constrained Bayesian optimization with a cardiovascular application

The present paper investigates constrained global optimization techniques for computationally expensive black box functions that are globally defined but subject to some a priori unknown taboo regions. This challenge typically arises in healthcare applications, where the goal is to maximize the efficacy of a drug while staying within critical safety limits imposed by an external medical regulator. Motivated by the additional challenge where the constrained global optimum lies along the constraint boundary, we comparatively assess the performance of established optimization methods coupled with different acquisition functions in terms of accuracy and efficiency on the physiological application aforementioned and several benchmark problems representative of the complexity of the physiological application. We find the best method based on an average score computed across all applications. We also propose an ensemble method combining results from individual methods, which vastly outperforms the best average method. Furthermore, our study provides a thorough qualitative analysis of the optimization results, emphasizing the challenges a user may encounter when applying Bayesian optimization on constrained optimization problems.

Optimal designs using generalized estimating equations in cluster randomized crossover and stepped wedge trials.

Cluster randomized crossover and stepped wedge cluster randomized trials are two types of longitudinal cluster randomized trials that leverage both the within- and between-cluster comparisons to estimate the treatment effect and are increasingly used in healthcare delivery and implementation science research. While the variance expressions of estimated treatment effect have been previously developed from the method of generalized estimating equations for analyzing cluster randomized crossover trials and stepped wedge cluster randomized trials, little guidance has been provided for optimal designs to ensure maximum efficiency. Here, an optimal design refers to the combination of optimal cluster-period size and optimal number of clusters that provide the smallest variance of the treatment effect estimator or maximum efficiency under a fixed total budget. In this work, we develop optimal designs for multiple-period cluster randomized crossover trials and stepped wedge cluster randomized trials with continuous outcomes, including both closed-cohort and repeated cross-sectional sampling schemes. Local optimal design algorithms are proposed when the correlation parameters in the working correlation structure are known. MaxiMin optimal design algorithms are proposed when the exact values are unavailable, but investigators may specify a range of correlation values. The closed-form formulae of local optimal design and MaxiMin optimal design are derived for multiple-period cluster randomized crossover trials, where the cluster-period size and number of clusters are decimal. The decimal estimates from closed-form formulae can then be used to investigate the performances of integer estimates from local optimal design and MaxiMin optimal design algorithms. One unique contribution from this work, compared to the previous optimal design research, is that we adopt constrained optimization techniques to obtain integer estimates under the MaxiMin optimal design. To assist practical implementation, we also develop four SAS macros to find local optimal designs and MaxiMin optimal designs.

Allocation of Dynamic Operating Envelopes in Distribution Networks: Technical and Equitable Perspectives

A Dynamic Operating Envelope (DOE) specifies the available capacity to import/export power for Distributed Energy Resources (DERs) or connection points of a distribution network in a time interval without violating its physical and operational constraints. This paper proposes a two-stage, top-down approach to allocate DOEs in MV-LV (medium voltage-low voltage) integrated distribution networks. In the first stage, Distribution System State Estimation (DSSE) and Capacity Constrained State Optimisation (CCSO) techniques are employed to allocate DOEs at transformer connection points. Using network data from available metering infrastructure, DSSE estimates the current operational state of the network, whereas CCSO facilitates the DOE allocations at transformer connection points considering technical, soft-equitable and equitable perspectives. In the second stage, the allocated DOEs, containing available aggregate export/import power, are distributed among DERs of LV networks ensuring network integrity. Real-world data of an Australian MV-LV network is employed to demonstrate the effectiveness of proposed approach. Test results show that technical perspective can offer maximum allocated export/import power, whereas, minimum disparity of allocated power among different connection-points is attained for equitable perspective. Further, insightful performance studies of DOE and existing fixed export policies are conducted considering the condition of present as well as future power systems expecting substantial proliferations of renewables.

A comprehensive theoretical framework for sustainable network contracts: Contracting dimensions and Contract classification

Disruptions in the supply chains/networks result in both performance failures and a poor return on investment (ROI) of network assets. We propose that addressing this situation requires the governance of exchange relationships through contracts guided by sustainability principles. Specifically, we refer to these contracts in the supply and distribution context as “sustainable network contracts”, and the overall framework as the “sustainable contracting framework (SCF)/theory”. Despite the critical role of sustainable network contracts for all key stakeholders in the network, we identify a gap in the existing literature regarding the theory of sustainable network contracts. We bridge this gap by extending the extant dimensions of contracts, as described in Transaction Cost Economics and Relational Exchange Theory, to include sustainability dimensions - constituting the ‘what’ of theory building. To inform sustainable contracts, we propose and employ three factors: costs, benefits, and risks (CBR). We present the ‘how’ of the theory building, outlined in a five-step approach along with an analytical tool, to demonstrate the practical application of our framework. Additionally, we provide a rationale for adopting sustainable network contracts (the ‘why’ of the theory building). Our research methodology involves collecting interview-based data from senior executives (CXOs) (secondary and primary), collecting primary and secondary cost data (objective), integrating behavioral elements (subjective), and employing constrained optimization techniques to determine quantity allocation under various contract policies. Further, we map the proposed eight distinct contract types onto the CBR-space, thereby highlight the relevance of the contract types to real-world practices. This mapping considers network externalities, risks, and allows for a coordinated sustainable approach to contracting from the buyer's (retailer's) perspective. For managers, our framework would serve as an important tool that would inform the contract evaluation process, facilitate local versus global decision-making, safeguard network investments, and help align the interests of buyers and suppliers in each contracting cycle.

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.

Multiobjective-Based Constraint-Handling Technique for Evolutionary Constrained Multiobjective Optimization: A New Perspective

Multiobjective-based constraint-handling techniques are popular in evolutionary constrained single-objective optimization. However, most of these techniques run into troubles when dealing with constrained multiobjective optimization problems (CMOPs). That is, they have difficulty optimizing too many objective functions, are ineffective in maintaining population diversity, or are challenged in establishing appropriate additional objective functions. As a remedy to these limitations, we propose a novel technique called NRC for handling CMOPs. The novelty of NRC lies in its three sorting procedures: nondominated sorting, reversed nondominated sorting, and constrained crowding distance sorting, which are performed in sequence to provide driving forces toward the Pareto front (PF) of a transformed unconstrained multiobjective optimization problem (treating the overall constraint violation as an additional objective function), the boundary front, and the constrained PF, respectively. With the combination of these three different forces, NRC can conveniently approach the desired PF from diverse search directions. The effectiveness of NRC is experimentally verified. Also, we incorporate NRC into a two-archive mechanism and develop a novel constrained multiobjective evolutionary algorithm, called NRC2. Comprehensive experiments on 49 benchmark CMOPs and 21 real-world ones demonstrate that NRC2 is significantly superior or comparable to six state-of-the-art constrained evolutionary multiobjective optimizers on most test instances.

A Two-Phase Constraint-Handling Technique for Constrained Optimization

A two-phase constraint-handling technique is integrated into the evolutionary algorithms to solve constrained optimization problems (called TPDE) in this article. In phase one, denoted as the exploration phase, an exterior penalty function method with the dynamic penalty coefficients is developed to compare any two candidate solutions, which aims to push the population into the feasible region. To reduce the computational burden, in phase two, denoted as the exploitation phase, an interior penalty function method with the dynamic penalty coefficients is developed, which enhances the search ability by using the information of constraints in feasible solutions. During the optimization process, differential evolution is adopted as the search algorithm to produce the offspring population. Experiment results on four benchmark test suites, namely, IEEE CEC 2006, IEEE CEC 2010, IEEE CEC 2017, and IEEE CEC 2020, indicate that TPDE is competitive with other popular algorithms.

Edge-Oriented Social Distance Monitoring System Based on MTCNN

Social distance monitoring (SDM) systems are vital in fighting the spread of the coronavirus (COVID-19). Existing SDM systems employ bounding box-method, which imposes inaccurate distance estimation due to the high variance in its output coordinates. To solve this problem, an SDM system based on multitask cascaded convolutional neural networks (MTCNN) is proposed. Instead of using bounding box coordinates, face detection and facial landmarks localization of MTCNN is used to provide fixed coordinates and increase the distance estimation accuracy of SDM. However, while the accuracy issue is solved by using MTCNN, the SDM system suffer from large computational requirements due to the cascaded networks added on top of the distance estimation process. To deal with this challenge, a constrained optimization technique is employed to each stage of MTCNN with the goal of reducing its hardware requirements while keeping the same reliability as the original implementation. Experimental results show that the SDM system based on the optimized MTCNN achieves higher accuracy performance with reduced computational requirements as compared to conventional SDM systems. This allows the proposed SDM system using optimized MTCNN to be deployed efficiently on edge devices.

Prediction of nature of hysteresis and hysteresis based extraction of viscoelastic material model parameters

As almost all materials exhibit viscoelastic behaviour, it is important to understand the material behaviour which would help in its application in different fields. The current research work firstly focuses on understanding the dissipating behaviour of any viscoelastic material through operator-based multi-element model from the experimental hysteresis subject to cyclic or periodic displacement loading. Genetic algorithm-based constrained optimization technique is used as an extraction technique by curve fitting. Further, the technique is used to predict the model parameters of a pig’s lumbar spinal motion segment subjected to periodic displacement loading. Following the derived model parameters, the effect of varying periodic loading on the calculated hysteresis is also compared.

On Employing a Constrained Nonlinear Optimizer to Constrained Economic Dispatch Problems

Recently, different metaheuristic techniques, their variants, and hybrid forms have been extensively used to solve economic load dispatch (ELD) problems with and without valve point loading (VPL) effects. Due to the randomization involved in these metaheuristic techniques, one has to perform extensive runs for each experiment to get an optimal solution. The process may sometimes become laborious and time-consuming to converge to an optimal solution. On the other hand, advanced calculus-based techniques, being deterministic, perform iteration systematically and come up with the same solution on each run of the experiment. Since ELD problems are constrained optimization problems, we are proposing the constrained (deterministic) optimization algorithm for their solutions. Various 13-unit, 38-unit, and 40-unit thermal test systems are considered. Valve point loading (VPL) effects are also considered in some cases. Computer-based numerical results depict that the constrained optimization algorithm shows evidence of being almost as competitive in a total fuel cost as the metaheuristic optimization techniques, especially for the less-constrained ELD problems but with far reduced computation time. This finding validates the application of the constrained optimization technique to solve the economic dispatch problem.

Constrained control allocation for dynamic ship positioning using deep neural network

Dynamic positioning (DP) is one of the key technologies towards ship autonomy. Ships in DP mode use thruster devices to maintain position and perform low-speed maneuvering. The motion controller issues force requests according to the measured ship state and motion objectives. These requests must be translated into individual thruster commands. Due to constraints in the thrusters, such as inertia and limited angles of operation, state-of-the-art control allocation methods apply constrained optimization techniques. Although such methods readily capture the handling of constraints, they may require significant computational resources in searching for optimized commands in real time. Here we show that a neural network may be applied to offer an effective evaluation of the mapping between motion controller requests and executable thruster commands. An Autoencoder-like neural network is trained with data generated using knowledge about the configuration of the thrusters. Custom loss functions shape the weights of the network, such that the overall motion objectives and thruster constraints are met. Then, the network is applied to perform low-speed maneuvering and stationkeeping in a simulator. Comparison relative to a state-of-the-art variable angle, constrained control allocator indicate similar dynamic performance with reduced peak power consumption.

Efficient Parallel Optimization for Approximating CAD Curves Featuring Super-convergence

We present an efficient, parallel, constrained optimization technique for approximating CAD curves with super-convergent rates. The optimization function is a disparity measure in terms of a piece-wise polynomial approximation and a curve re-parametrization. The constrained problem solves the disparity functional fixing the mesh element interfaces. We have numerical evidence that when the solver attains a minimum, the constrained disparity preserves the original super-convergence: 2p order for planar curves and ⌊32(p−1)⌋+2 for 3D curves, p being the mesh polynomial degree. Our optimization scheme consists of a globalized Newton method with a nonmonotone line search, and a log barrier function preventing element inversion in the curve re-parametrization. Moreover, we introduce a Julia interface to the EGADS geometry kernel and a parallel optimization algorithm. We test the potential of our curve mesh generation tool on a computer cluster using several aircraft CAD models. We conclude that the solver is well-suited for parallel computing, producing super-convergent approximations to CAD curves.

Constrained optimization assists deviated wellbore trajectory selection from families of quadratic and cubic Bezier curves

The ease of calculation of families of cubic and quadratic Bezier curves using just one or two control variables makes them well-suited for identifying smooth, deviated wellbore trajectories using easy-to-implement, constrained optimization techniques. Most wellbore trajectory optimization methods currently applied during the wellbore planning stages aim to minimize measured depth (MD) while constraining dog-leg severity (DLS) and/or torque and drag to select drillable, smooth wellbores. This study identifies the benefits of conducting MD optimization of Bezier curves using multiple constraints related to different characteristics of DLS and absolute changes in tool-face angle (ΔTFA). Whereas DLS is a major influence on wellbore tortuosity on the multi-meter scale, ΔTFA influences wellbore roughness on a finer scale and in a different way than DLS. As rotary-steerable bottom-hole assemblages are now the standard for drilling the multiple horizontal wells required for tight gas and oil reservoirs, minimizing the magnitude of TFA changes can speed up drilling and reduce borehole roughness. This study identifies the benefits of applying a sequence of up to four constraints (maximum DLS combined with average DLS and/or average or maximum ΔTFA) to minimize MD while achieving the smoothest possible wellbore trajectory from a family of cubic Bezier curves, configured to drill from a vertical starting location to a horizontal finishing location offset in 3D space. On the other hand, families of quadratic Bezier curves drilling some relatively simple trajectories between two points located on a two-dimensional plane can be effectively optimized for MD and smoothness using solely a maximum DLS constraint.

Magnetic particle tracking: A semi-algebraic solution

Magnetic Particle Tracking (MPT) is a relatively new non-invasive measurement technique which is often used to study dense granular flow. Its basic principle relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength at a suitable distance from the tracer. By assumption of a magnetic dipole and the use of minimization techniques, both location and orientation of the tracer can be determined. MPT is therefore uniquely suited for the study of non-spherical particles. The performance of the localization is largely dependent on the signal-to-noise ratio and very often relies on nonlinear optimization techniques, as the definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. In this paper, we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach is in the speed and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques.

Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems

This paper presents a new approach for reduction of commensurate fractional-order single-input-single-output systems. The minimization in the frequency response error of the reduced order model (ROM) relative to the original system is carried out in the F-plane. A constrained optimization technique is introduced to satisfy the angle criteria for F-domain stability of the proposed ROM. Significant improvements in both the time- and frequency-responses over the recently published literature are illustrated using several numerical examples.

New Robust Regression Method for Outliers and Heavy Sparse Noise Detection via Affine Transformation for Head Pose Estimation and Image Reconstruction in Highly Complex and Correlated Data: Applications in Signal Processing

In this work, we propose a novel method for head pose estimation and face recovery, particularly to solve the potential impacts of noises in signal processing to get an efficient and effective model that is more resilient with annoying effects through adding affine transformation with the low-rank robust subspace regression. Consequently, the corrupted images can be correctly recovered by affine transformations to render more best regression outcomes. Thereby, we need to search so as to get optimal parameters which can be regarded as convex constrained optimization techniques. Afterward, the alternating direction method for multipliers (ADMM) approach is considered and a new set of updated equations is well established so as to update the optimization parameters and affine transformations iteratively in a round-robin manner. Additionally, the convergence of these new updating equations is well scrutinized as well. Thus, the experimental simulations reveal that the proposed method outperforms the state-of-the-art works for head pose estimation and face recovery on some public databases.

Toward Reliable Controller Placements in Software-Defined Network Using Constrained Multi-Objective Optimization Technique

Software Defined Networking (SDN) makes it easy to control and manage the network due to a centralized control plane. However, this centralization also limits the scalability of SDN. To address this scalability issue, multiple controllers are deployed in the SDN. Placing multiple controllers poses several challenges, one of which is to find optimum locations for the placement of multiple controllers. The existing approaches for controller placement in a multiple-controller SDN environment overlook many aspects, like the path reliability for switch-to-controller and controller-to-controller communication, and the use of an efficient machine-learning algorithm. To address these issues, this paper proposes a novel approach, named as CMOPHA, that uses NSGA-II (a multi-objective optimization MOO algorithm) to compute the optimum placement of controllers based on the parameters of maximum switch-to-controller path reliability, and minimum value of switch-to-controller hop count, maximum controller-to-controller reliability, load-balancing among the controllers and a minimum number of controllers. We conduct simulations using real network traces. Based on the results, we show that CMOPHA improves the network performance in terms of end-to-end delay, hop count, computation time, and network availability compared to the existing state-of-the-art approach.

A Fast Optimization Method for High-Speed Link Inverse Design With SVR-AS Algorithm

A fast constrained design optimization technique is introduced for the inverse design of high-speed links. The proposed method makes use of the support-vector-regression-based active subspace (SVR-AS) method to generate a lower dimensional space of active variables as a linear weighted combination of the higher dimensional design space to help simplify the optimization problem. This newly developed technique successfully transforms the complex nonlinear constraint optimization problem into a linear constraint minimization problem and provides a directly solvable function for the optimal results associated with each active variable. Furthermore, the proposed optimization algorithm can be utilized for the optimization problem with equality and inequality constraints, which contain one- and multidimensional active variables generated from the SVR-AS method. Studies of two high-speed links with channel design parameters for nonreturn-to-zero pulse and IBIS-AMI equalization settings for four-level pulse amplitude modulation, respectively, are utilized to verify the efficiency of the method. The sensitivity analysis ability of the SVR-AS method is also presented for both the one- and multidimensional active variable cases.