Constrained Optimization Procedure Research Articles

Multi-objective optimization for perishable product dispatch in a FEFO system for a food bank single warehouse

One of the main challenges of food bank warehouses in developing countries is to determine how to allocate perishable products to beneficiary agencies with different expiry dates while ensuring food safety, meeting nutritional requirements, and minimizing the shortage. The contribution of this research is to introduce a new multi-objective, multi-product, and multi-period perishable food allocation problem based on a single warehouse management system for a First Expired-First Out (FEFO) policy. Moreover, it incorporates the temporal aspect, guaranteeing the dispatch of only those perishable products that meet the prescribed minimum quality standards. A weighted sum approach converts the multi-objective problem of minimizing a vector of objective functions into a scalar problem by constructing a weighted sum of all the objectives. The problem can then be solved using a standard constrained optimization procedure. The proposed mixed integer linear model is solved by using the CPLEX solver. The solution obtained from the multi-objective problem allows us to identify days and products experiencing shortages. In such cases, when there is insufficient available inventory, the total quantity of product to be dispatched is redistributed among beneficiaries according to a pre-established prioritization. These redistributions are formulated as integer programming problems using a score-based criterion and solved by an exact method based on dynamic programming. Computational results demonstrate the applicability of the novel model for perishable items to a real-world study case.

Modeling, testing, and optimization of novel lattice structures for enhanced mechanical performance

Cellular materials have drawn increasing interest in numerous applications due to their promising specific stiffness, strength and energy absorption capacity. In this work, a variety of rather novel lattice topologies pertinent to additive manufacturing are derived and examined. A number of these are derived by free-domain and constrained domain topology optimization procedures, while others are inspired by the triply periodic minimum surface (TPMS) sheet-based topologies. The topology optimization module utilized a single objective function of minimizing strain energy under linear elastic conditions. A total of fifteen different lattice topologies are investigated numerically, including both novel and conventional topologies (e.g. strut-based lattices) and their effective elastic properties are determined with respect to relative density through finite element analysis (FEA). Based on the preliminary FEA results, a number of these topologies are selected of which tessellated lattice structures are fabricated through laser powder bed fusion (LPBF) additive manufacturing technique out of Nylon thermoplastic material. The tessellated lattice structures are experimentally tested in compression and their mechanical performance, including uniaxial modulus, yield strength, and energy absorption capacity (EAC), is assessed. FEA simulations have been conducted using an elastic-plastic constitutive model for the Nylon base material. Both the experimental and numerical results reveal that the mechanical performance of the novel tube-based TPMS lattice P-100 and the combined loading (CL) topology derived through free-domain topology optimization surpasses all other topologies. P-100 uses a primitive TPMS with equal-length tubular connections in each direction, where the tubular length percentage compared to the primitive lattice size is 100%, while CL lattice topology is a free domain topology optimized under compressive loads on the centers of faces, edges, and vertices toward the center. The innovative lattice topologies proposed in the current study, particularly the P-100 and CL topologies, can become crucial in applications where it is necessary to improve the energy absorption capacity, such as sandwich panel cores, supports, and infills for 3D printed components.

Parallel-in-time optimization of induction motors

Parallel-in-time (PinT) methods were developed to accelerate time-domain solution of evolutionary problems using modern parallel computer architectures. In this paper we incorporate one of the efficient PinT approaches, in particular, the asynchronous truncated multigrid-reduction-in-time algorithm, into a bound constrained optimization procedure applied to an induction machine. Calculation of an optimal motor geometry with respect to its efficiency in the steady state is thus parallelized at each iteration of the optimization algorithm. As a result, a more efficient motor model is obtained about 11 times faster compared to optimization using the standard sequential time stepping.

A Human-in-the-Loop Segmented Mixed-Effects Modeling Method for Analyzing Wearables Data

Wearables are an important source of big data, as they provide real-time high-resolution data logs of health indicators of individuals. Higher-order associations between pairs of variables is common in wearables data. Representing higher-order association curves as piecewise linear segments in a regression model makes them more interpretable. However, existing methods for identifying the change points for segmented modeling either overfit or have low external validity for wearables data containing repeated measures. Therefore, we propose a human-in-the-loop method for segmented modeling of higher-order pairwise associations between variables in wearables data. Our method uses the smooth function estimated by a generalized additive mixed model to allow the analyst to annotate change point estimates for a segmented mixed-effects model, and thereafter employs Brent's constrained optimization procedure to fine-tune the manually provided estimates. We validate our method using three real-world wearables datasets. Our method not only outperforms state-of-the-art modeling methods in terms of prediction performance but also provides more interpretable results. Our study contributes to health data science in terms of developing a new method for interpretable modeling of wearables data. Our analysis uncovers interesting insights on higher-order associations for health researchers.

Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes

Repeatedly solving nonlinear partial differential equations with varying parameters is often an essential requirement to characterise the parametric dependences of dynamical systems. Reduced-order modelling (ROM) provides an economical way to construct low-dimensional parametric surrogates for rapid predictions of high-dimensional physical fields. This paper presents a physics-data combined machine learning (PDCML) method for non-intrusive parametric ROM in small-data regimes. Proper orthogonal decomposition (POD) is adopted for dimension reduction by deriving basis functions from a limited number of high-fidelity snapshots, and parametric ROM is thus transformed into establishing reliable mappings between the system parameters and the POD coefficients. To overcome labelled data scarcity, a physics-data combined ROM framework is developed to jointly integrate the physical principle and the small labelled data into feedforward neural networks (FNN) via a step-by-step training scheme. Specifically, a preliminary FNN model is firstly fitted via data-driven training, and then the governing physical rules are embedded into the loss function to improve the model interpolation and extrapolation performances through physics-guided training constrained by the labelled data. During the constrained optimisation procedure, dynamic weighting factors are used to adjust the physics-data proportion of the loss functions, aiming at continuously highlighting the physics loss as the primary optimisation objective and keeping the data loss as the constraint. This new PDCML method is tested on a series of nonlinear problems with different numbers of physical variables, and it is also compared with the data-driven ROM, the physics-guided ROM and the traditional projection-based ROM methods. The results demonstrate that the proposed method provides a cost-effective way for non-intrusive parametric ROM via machine learning, and it possesses good characteristics of high prediction accuracy, strong generalisation capability and small data requirement.

Causes-of-Death Specific Estimates from Synthetic Health Measure: A Methodological Framework.

Life expectancy at birth has attracted interest in various fields, as a health indicator that measures the quality of life. Its appeal relies on the ability to enclose and summarize all the factors affecting longevity. However, more granular information, provided by social indicators such as cause-of-death mortality rates, plays a crucial role in defining appropriate policies for governments to achieve well-being and sustainability goals. Unfortunately, their availability is not always guaranteed. Exploiting the relationship between life expectancy at birth and cause-of-death mortality rates, in this paper we propose an indirect model to produce estimates of death rates due to specific causes using the summary indicator of life expectancy at birth, thus the general levels of the observed mortality. By leveraging on a constrained optimization procedure, we ensure a robust framework where the cause-specific mortality rates are coherent to the aggregate mortality. The main advantage is that indirect estimations allow us to overcome the data availability problem: very often the cause-specific mortality data are incomplete, whereas data on the aggregate mortality are not. Using data from the Human Cause-of-Death Database, we show a numerical application of our model to two different countries, Russia and Spain, which have experienced a different evolution of life expectancy and different leading causes of death. In Spain, we detected the impact of several public health policies on the lowered levels of cancer deaths and related life expectancy increases. As regards the Russia, our results catch the effects of the anti-alcohol campaign of 1985–1988 on longevity changes.

Optimal Control Approach for the COVID-19 Pandemic in Bahia and Santa Catarina, Brazil

The COVID-19 pandemic is the most profound crisis of the twenty-first century. The SARS-CoV-2 virus was first registered in Brazil on March 2020, and its social and economic repercussions have been catastrophic. This paper investigates how to apply model predictive control (MPC) algorithms to plan appropriate social distancing policies that mitigate the pandemic effects. We consider MPC applications for the states of Bahia and Santa Catarina (Brazil), two regions of very different social and cultural demographics. We use Susceptible-Infected-Recovered-Deceased model to describe the pandemic dynamics in these two states, for which parameters are identified using a constrained optimization procedure. The control input to the process is a social isolation guideline passed to the population. Two MPC frameworks are developed and discussed: (a) a centralized approach, which coordinates a single predictive control policy for both states, and (b) a distributed strategy, for which a single MPC problem is solved for each state. We provide a series of simulation results in order to illustrate and compare the results obtained with both these MPC strategies. Discussions are drawn regarding the effectiveness of MPC to guide social distancing measures during pandemics and which approach (distributed, centralized) is more convenient, regarding different conditions.

A Real Time Bolometer Tomographic Reconstruction Algorithm in Nuclear Fusion Reactors

In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by means of a bolometer system that consists in a certain number of elements sensitive to the integral of the radiation along straight lines crossing the plasma. By placing the sensors in such a way to have families of crossing lines, sophisticated tomographic inversion algorithms allow to reconstruct the radiation tomography in the 2D poloidal cross-section of the plasma. In tokamaks, the number of projection cameras is often quite limited resulting in an inversion mathematic problem very ill conditioned so that, usually, it is solved by means of a grid-based, iterative constrained optimization procedure, whose convergence time is not suitable for the real time requirements. In this paper, to illustrate the method, an assumption not valid in general is made on the correlation among the grid elements, based on the statistical distribution of the radiation emissivity over a set of tomographic reconstructions, performed off-line. Then, a regularization procedure is carried out, which merge highly correlated grid elements providing a squared coefficients matrix with an enough low condition number. This matrix, which is inverted offline once for all, can be multiplied by the actual bolometer measures returning the tomographic reconstruction, with calculations suitable for real time application. The proposed algorithm is applied, in this paper, to a synthetic case study.

Prediction of Moment Using a Modified Discrete Vortex Method in Ground Effect

The aerodynamics around a wing is modified when it comes near the ground. This is generally referred to as ground effect. In this work, a discrete vortex method based model which can predict two-dimensional (2D) ground effect from its free flight data is proposed. The required data in free flight could be generated either from high fidelity CFD solver or experiments. In this method, strength of the vortex distribution as obtained from discrete vortex based method is modified using a constrained optimisation procedure to match the free flight aerodynamic data. This vortex distribution is further modified due the presence of the ground. The efficacy of present model is demonstrated for predicting the moment of multi element airfoils in ground effect. The predicted aerodynamic coefficient in ground effect compares well with high fidelity CFD data.

On the physically consistent characterisation of a system for FRF-based substructuring

Substructuring approaches have been extensively used since long time to predict the vibroacoustic behaviour of built-up mechanical systems. In the frequency domain, these methods build on the dynamic characterisation of the subsystems via frequency response functions at the coupling interfaces. Intensively used for subsystems connected by points, dynamic substructuring still constitutes an open area of research for systems comprising continuous interfaces. Within this framework, a method which allows to characterise subsystems connected along lines is presented. The approach is based on a discretisation of the continuous interfaces into a small set of points, where the information of the subsystems is condensed. For this purpose, an inverse approach is used, which allows to characterise the dynamics of the passive subsystem using data of the assembled system. A straightforward inversion, however, does not assure the physical consistency of the characterized subsystem. In other words, the subsystem extraction procedure must not only guarantee correct dynamic behaviour of the assembled system, but the obtained subsystem must also be reciprocal and passive. The central theme of this paper is the formulation of a constrained optimisation procedure for the enforcement of reciprocity and passivity on the inversely obtained subsystem characteristics. The method is validated on a structure made of two plates connected along a common edge through a beam.

Demystifying Lie Group Methods for Signal Processing: A Tutorial

Many problems in signal processing [e.g., filter bank design, independent component analysis (ICA), beamforming design, and neural network training] can be formulated as optimization over groups of transformations that depend continuously on real parameters (Lie groups). Such problems are usually tackled in two ways: using a constrained optimization procedure or using some parameterization to transform them into unconstrained problems.

Self-Oriented Empathy and Compassion Fatigue: The Serial Mediation of Dispositional Mindfulness and Counselor's Self-Efficacy.

This study aimed to explore the association between self-oriented empathy and compassion fatigue, and examine the potential mediating roles of dispositional mindfulness and the counselor’s self-efficacy. A total of 712 hotline psychological counselors were recruited from the Mental Health Service Platform at Central China Normal University, Ministry of Education during the outbreak of Corona Virus Disease 2019, then were asked to complete the questionnaires measuring self-oriented empathy, compassion fatigue, dispositional mindfulness, and counselor’s self-efficacy. Structural equation modeling was utilized to analyze the possible associations and explore potential mediations. In addition to reporting confidence intervals (CI), we employed a new method named model-based constrained optimization procedure to test hypotheses of indirect effects. Results showed that self-oriented empathy was positively associated with compassion fatigue. Dispositional mindfulness and counselor’s self-efficacy independently and serially mediated the associations between self-oriented empathy and compassion fatigue. The findings of this study confirmed and complemented the etiological and the multi-factor model of compassion fatigue. Moreover, the results indicate that it is useful and necessary to add some training for increasing counselor’s self-efficacy in mindfulness-based interventions in order to decrease compassion fatigue.

NMPC Through qLPV Embedding: A Tutorial Review of Different Approaches

Abstract Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. The qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant. Thereby, these strategies generate online programs with reduced numerical burden, much faster to solve than the Nonlinear Programs generated with regular NMPC. The general lines of these methods: (i) The qLPV embedding is formulated with state-dependent scheduling parameters; (ii) Recursive extrapolation procedures are used to estimate the values of these parameters along the prediction horizon; (iii) These estimates are used to compute linear predictions, which are incorporated by the constrained optimisation procedure. This paper details the overall concept of these novel NMPC techniques and reviews two different (efficient) implementation options. Realistic academic examples are provided to illustrate their performances.

Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure.

Mediation analysis is an important approach for investigating causal pathways. One approach used in mediation analysis is the test of an indirect effect, which seeks to measure how the effect of an independent variable impacts an outcome variable through 1 or more mediators. However, in many situations the proposed tests of indirect effects, including popular confidence interval-based methods, tend to produce poor Type I error rates when mediation does not occur and, more generally, only allow dichotomous decisions of "not significant" or "significant" with regards to the statistical conclusion. To remedy these issues, we propose a new method, a likelihood ratio test (LRT), that uses nonlinear constraints in what we term the model-based constrained optimization (MBCO) procedure. The MBCO procedure (a) offers a more robust Type I error rate than existing methods; (b) provides a p value, which serves as a continuous measure of compatibility of data with the hypothesized null model (not just a dichotomous reject or fail-to-reject decision rule); (c) allows simple and complex hypotheses about mediation (i.e., 1 or more mediators; different mediational pathways); and (d) allows the mediation model to use observed or latent variables. The MBCO procedure is based on a structural equation modeling framework (even if latent variables are not specified) with specialized fitting routines, namely with the use of nonlinear constraints. We advocate using the MBCO procedure to test hypotheses about an indirect effect in addition to reporting a confidence interval to capture uncertainty about the indirect effect because this combination transcends existing methods. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Tuning Fairness by Balancing Target Labels.

The issue of fairness in machine learning models has recently attracted a lot of attention as ensuring it will ensure continued confidence of the general public in the deployment of machine learning systems. We focus on mitigating the harm incurred by a biased machine learning system that offers better outputs (e.g., loans, job interviews) for certain groups than for others. We show that bias in the output can naturally be controlled in probabilistic models by introducing a latent target output. This formulation has several advantages: first, it is a unified framework for several notions of group fairness such as Demographic Parity and Equality of Opportunity; second, it is expressed as a marginalization instead of a constrained problem; and third, it allows the encoding of our knowledge of what unbiased outputs should be. Practically, the second allows us to avoid unstable constrained optimization procedures and to reuse off-the-shelf toolboxes. The latter translates to the ability to control the level of fairness by directly varying fairness target rates. In contrast, existing approaches rely on intermediate, arguably unintuitive, control parameters such as covariance thresholds.

Optimal artifact suppression in simultaneous electrocorticography stimulation and recording for bi-directional brain-computer interface applications

Objective. Electrocorticogram (ECoG)-based brain-computer interfaces (BCIs) are a promising platform for the restoration of motor and sensory functions to those with neurological deficits. Such bi-directional BCI operation necessitates simultaneous ECoG recording and stimulation, which is challenging given the presence of strong stimulation artifacts. This problem is exacerbated if the BCI’s analog front-end operates in an ultra-low power regime, which is a basic requirement for fully implantable medical devices. In this study, we developed a novel method for the suppression of stimulation artifacts before they reach the analog front-end. Approach. Using elementary biophysical considerations, we devised an artifact suppression method that employs a weak auxiliary stimulation delivered between the primary stimulator and the recording grid. The exact location and amplitude of this auxiliary stimulating dipole were then found through a constrained optimization procedure. The performance of our method was tested in both simulations and phantom brain tissue experiments. Main results. The solution found through the optimization procedure matched the optimal canceling dipole in both simulations and experiments. Artifact suppression as large as 28.7 dB and 22.9 dB were achieved in simulations and brain phantom experiments, respectively. Significance. We developed a simple constrained optimization-based method for finding the parameters of an auxiliary stimulating dipole that yields optimal artifact suppression. Our method suppresses stimulation artifacts before they reach the analog front-end and may prevent the front-end amplifiers from saturation. Additionally, it can be used along with other artifact mitigation techniques to further reduce stimulation artifacts.

The design and optimisation of tokamak poloidal field systems in the BLUEPRINT framework

Abstract As part of our aim to develop a reactor design framework, we present here our approach to the optimisation of plasma equilibria and tokamak poloidal field systems. A 2-D, free boundary, ideal magneto-hydrodynamic plasma equilibrium solver is described. We use it within the BLUEPRINT reactor design framework to design plasma equilibria and poloidal field coilsets for future fusion reactors in an integrated way. Plasma shape parameters (R0, A, δ, κ) and integral parameters (Ip, βp, li) are controlled for. Constrained optimisation procedures for the positions and currents of the poloidal field coils are presented; these account for current, field, force, and positional constraints on the coils. A pulse length constraint is incorporated in the optimisation procedure in the case of pulsed reactors. We demonstrate our approach on three different reactor concepts: single-null, double-null and negative triangularity tokamaks.

Multi-frequency fusion algorithm for detection of defects under fasteners with EC-GMR probe data

Rotating eddy current (EC) excitation with giant magnetoresistive (GMR) sensor pick up (EC-GMR) has proved to be a promising technique for detection of defects under fasteners in multi-layer riveted structures. Challenges in this application include arbitrary orientation of cracks, influence of dominant signal from steel fasteners and need for rapid inspection of parts. This paper presents a novel data fusion algorithm for suppressing signals from steel fastener and enhancing defect indications in multi-frequency EC-GMR measurements. The algorithm fuses transformed versions of EC-GMR probe data using a multi-dimensional constrained optimization procedure based on Sequential Least Square Programming (SLSQP). The optimal transformation parameters are determined by minimizing the field residue at a reference fastener site with no defects. Performance of the proposed algorithm is evaluated on experimental measurements acquired using EC-GMR sensor on a riveted lap-joint with steel fasteners and second layer EDM notches. Initial results demonstrate that bottom layer defects of different sizes and orientations can be successfully detected with this approach.

Experimental and computational investigation on dynamic fracture toughness (J1d) behavior of multi-pass SMA armor steel weldments

Dynamic fracture toughness (J1d) behavior of shield metal arc (SMA) welding of armor grade Armox 500 T steels prepared with low hydrogen ferritic steel (LHF) and austenitic stainless (ASS) steel consumables have been evaluated and compared. Three different techniques have been described and implemented to evaluate the dynamic fracture toughness (J1d) of investigated materials. Further, the results have been compared with Elastic plastic fracture mechanics (EPFM) approach. An investigation has also been performed regarding the influence of microstructures (for LHF and ASS weldments fusion zone) effect on dynamic fracture toughness (J1d) and fracture characteristic. Finally, a constrained optimization procedure of minimizing the mean absolute percent error (MAPE) has been used to determining the Johnson Cook (JC) hardening and Damage model for Armox 500 T to simulate the impact and damage behavior. Results revealed that, Dynamic fracture toughness (J1d) of weldment-2 (prepared by ASS consumables and consisted duplex microstructure) is 20% and 10% more than weldments-1 (prepared by LHF consumables and consisted acicular ferrite structure) and counterpart base metal (Armox 500 T). The MAPE and standard deviation between FEA and experimental results are less than 10% with a good value of regression coefficient (R) which shown the excellent prediction capability of developed model.

Formulation of min-max model predictive control as a box-constrained robust least squares estimation problem

The purpose of this paper is to propose a new approach to the Min-Max Model Predictive Control (MMMPC) of Linear Time-Invariant Discrete-time Polytopic (LTIDP) systems. The purpose is to simplify the treatment of complex issues like stability and feasibility analysis of robust MPC as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two Degrees Of Freedom (2DOF) control scheme where the output r(k) of the feedforward Input Estimator (IE) is used as input forcing a stable closed-loop system Σf. Σf is the feedback connection of an LTIDP plant Σp with an LTI dynamic controller Σg. The task of Σg is to guarantee the quadratic stability of Σf, as well as the fulfillment of hard constraints on some physical variables of Σf for any input r(k) satisfying an ”a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on-line minimization of a worst case finite-horizon quadratic cost functional and is applied to Σf according to the usual receding horizon strategy. Rather than resorting to an ”ad hoc” software, the numerical complexity issue is here addressed reducing the number of both decision variables and constraints involved in the on-line constrained optimization procedure. This is obtained modeling r(k) as a B-spline function, which is known to be a universal approximator which also admits a parsimonious parametric representation. This allows us to reformulate the minimization of the worst case cost functional as a box-constrained Robust Least Squares (RLS) estimation problem which can be efficiently solved using Second Order Cone Programming (SOCP).