Formulation Of Objective Function Research Articles

Traffic microsimulation for smart cities: Investigating the impact of objective function formulation on calibration efficiency

Traffic microsimulation for smart cities: Investigating the impact of objective function formulation on calibration efficiency

Sustainable and cost-effective optimal design of steel structures by minimizing cutting trim losses

Since the beginning of the structural optimization field, the optimal design was characterized by the least-weight configuration. In this sense, all the researchers agreed on adopting the minimum-weight optimization statement as the most promising approach to achieve an optimized employment of material. However, especially for steel structures, this approach completely fails the primary goal of encouraging standardization of pieces during the production phase. Except for rare cases, increasing diversity among structural elements leads to a dramatic increase in the financial cost as well as the environmental impact of the structure because of the material waste generated during the cutting procedure.In this paper, a real-coded Genetic Algorithm has been adopted and the well-known one-dimensional Bin Packing Problem has been implemented within the structural optimization process. The Objective Function formulation lies in a marked change of the paradigm in which the target function is represented by the amount of steel required by the factory instead of the structural cost (e.g. weight). The proposed approach is tested on different steel structures moving from 2D truss beams to 3D domes. Addressing the optimal stock of existing elements leads to a significant waste reduction of 40% in almost all the investigated case studies.

Optimal day-ahead active and reactive power management for microgrids with high penetration of renewables

In recent years, efforts have been made to increase the proportion of electricity demand met by Renewable Energy Sources (RESs). Distributed Energy Resources (DERs) play a crucial role in this frame, particularly in Microgrids (MGs) where DERs and clusters of loads are interconnected. This paper presents an Energy Management System (EMS) developed for a low-voltage MG installed in Italy, connecting Photovoltaic (PV) units, a Wind Turbine (WT), a Battery Energy Storage System (BESS), a Combined Heat and Power (CHP) unit and loads: the EMS aims to optimize the day-ahead scheduling of the MG, considering both economic and power quality criteria. The mathematical model incorporates the capability curves of the inverters connected to DERs and allows for curtailment of PV and WT units, with curtailment costs assessed using the Levelized Cost of Electricity (LCOE). Penalties for the absorption of reactive power from the external network are considered and evaluated in accordance with the current regulatory framework. Optimal Power Flow (OPF) equations are integrated into the EMS model, too. A preliminary analysis, carried out on a simplified MG, evaluates the impact of linearizing the DERs capability curves and OPF equations on the EMS’s outcomes. Finally, a sensitivity analysis evaluates the impact of different operational constraints and of different objective function formulations on the operation of the MG, discussing key energy and economic results.

Multi-objective sensor placement optimization in SHM systems with Kriging-based mode shape interpolation

Sensor location optimization plays a key role in the application and development of structural integrity monitoring methodologies, especially in large mechanical structures. Given the existence of an effective damage detection and identification procedure, the question of how many and where to place the acquisition points (sensors) so that the monitoring system operates at peak efficiency arises. In this study, an innovative methodology is proposed in order to maximize the quality of modal information and minimize the number of sensors in the SHM system. To maximize the quality of modal information, it considered the reconstruction of mode shapes using Kriging interpolation. The study was carried out on plate-type composite material structures for initial validation and later applied and validated on a main rotor blade of the AS-350 helicopter. The initial modal information (modal deformation) was obtained through the finite element method, and the multi-objective Lichtenberg algorithm was used in the complex optimization process. The proposed method presented in this work allows for the best possible distribution of a minimum and sufficient number of acquisition points in a structure in order to obtain more modal information for a better modal reconstruction from kriging interpolation of these minimum points. Numerical examples and test results show that the proposed method is robust and effective for distributing a reduced number of sensors in a structure and at the same time guaranteeing the quality of the information obtained, even in noisy situations. Numerical results considering both the simple and complex geometric cases show that the proposed combined FS-kriging method is effective in distributing a finite number of sensors on the structures and at the same time guaranteeing the quality of the modal information obtained. The results also indicate that the layout of sensors obtained by multi-objective optimization does not become trivial and symmetrical when a set of modes is considered in the objective function formulation. The proposed strategy is an advantage in modal testing as it is only necessary to acquire signals at a limited number of points, saving time and operating costs in vibration-based processes.

A robust crow search algorithm based power system state estimation

The State Estimation (SE) computational procedure plays a crucial role in modern electric power system security control by monitoring and analyzing operational conditions and predicting any emergency. In order to estimate state variables, Power System State Estimation (PSSE) takes into account the magnitudes and phases of voltage on each bus. To address the state estimation challenges in power systems, in this paper, we propose a novel application of the Crow Search Algorithm (CSA) specifically tailored for the state estimation problem. We have assessed the introduced algorithm using the frameworks of both the IEEE 14-bus and IEEE 30-bus test systems. The first formulation is the Weighted Least Square (WLS) method, and the second is the Weighted Least Absolute Value (WLAV) method, both of which are objective function formulations. By comparing the results, it is clear that CSA-based SE is superior to the other metaheuristic algorithms considered, namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Artificial Bee Swarm Optimization (ABSO). As a point of comparison, we use the Newton–Raphson method for calculating load flow. It has been shown that the proposed CSA-based SE technique has better accuracy than the other two algorithms in all different test systems. With this study, the power system is operated more accurately and reliably by the operators operating the system.

Evolutionary Large-Scale Multiobjective Optimization: Benchmarks and Algorithms

Evolutionary large-scale multiobjective optimization (ELMO) has received increasing attention in recent years. This study has compared various existing optimizers for ELMO on different benchmarks, revealing that both benchmarks and algorithms for ELMO still need significant improvement. Thus, a new test suite and a new optimizer framework are proposed to further promote the research of ELMO. More realistic features are considered in the new benchmarks, such as mixed formulation of objective functions, mixed linkages in variables, and imbalanced contributions of variables to the objectives, which are challenging to the existing optimizers. To better tackle these benchmarks, a variable group-based learning strategy is embedded into the new optimizer framework for ELMO, which significantly improves the quality of reproduction in large-scale search space. The experimental results validate that the designed benchmarks can comprehensively evaluate the performance of existing optimizers for ELMO and the proposed optimizer shows distinct advantages in tackling these benchmarks.

Optimization of steel beams with external pretension, considering the environmental and financial impact

With the advancement technology for reinforced concrete structures, it becomes increasingly feasible to use this technology for steel structures. The objective of this work is to present the formulation of the optimization problem of steel beams with external pretension with straight or polygonal tracing cables, considering the environmental and economic impacts. For the objective function formulation, the minimization of CO2 emission and cost in the design of the structure were considered. As constraints were established the states limits imposed by ABNT NBR 8800:2008. The program was developed within the MATLAB Platform (MATLAB®. Guia do usuário R2016a (2016) The Math Works Inc) and the optimization problem solution was obtained through the native genetic algorithms method. Routine validation was performed using examples found in the literature and an analysis of the predominant collapse modes was performed. The results indicate that monosymmetric profiles have gains when it comes to reducing CO2 emissions and cost when compared to doubly symmetrical profiles, in addition it was observed that straight cables generate better values of CO2 emission and cost when compared to polygonal cables.

Economic optimization and predictive control for nonlinear systems using Lyapunov based nonlinear cost function design

Optimal control of physical processes depends on the formulation of objective functions and contemplation of appropriate predictive control. In this article, we propose a new framework, to blend the concepts of the Lyapunov-based economic model predictive control (Ly-EMPC) scheme with the novel cost-efficient profit function design. Furthermore, Lyapunov’s stability criteria is employed to verify the existence of duality and optimality for the designed economic stage costs. This method differs from the existing EMPC techniques by implementing Lagrange multipliers in the rotated cost function as a measure of stability. The closed-loop performance using the regularized Ly-EMPC is validated against a standard tracking objective-based nonlinear MPC for three benchmark examples through an econometrics gauge factor. Interestingly, in contrast to tracking NMPC, the proposed Ly-EMPC scheme excels in economic performance, while the formation of nonlinear economic stage cost is conceptually simpler, novel, and practically profitable.

A fully finite-element based model-space algorithm for three-dimensional inversion of magnetotelluric data

SUMMARY We present a fully finite-element based inversion methodology for imaging 3-D magnetotelluric impedance data on unstructured meshes. The inverse problem is formulated using a minimum-structure Gauss–Newton type optimization scheme that minimizes an objective function with respect to the model perturbation. By introducing a rigorous regularization scheme, we derived a Ritz-type variational formulation of the model objective function and designed a face-based finite-element basis function to discretize the model gradient across tetrahedron’s inter-element boundaries. The forward modelling engine of our optimization scheme is based on a finite-element solution of the E-field Helmholtz equation that is enforced for the magnetotelluric simulation problem using the appropriate edge-based basis functions and 3D boundary conditions. The optimization algorithm developed here utilizes a message passing interface scheme and uses a direct solver to factorize and store both the regularization matrix and the forward modelling coefficient matrix on the processes working in parallel. Having to do this only once within each Gauss–Newton optimization cycle facilitates both the calculation of the dot product of the model regularization terms with the evolving model perturbation, and computing implicitly the sensitivity-vector products. We validated the methodology and the correctness of the developed algorithm for two test examples (COMMEMI 3Ds) from the literature. Also, by comparing the performance between classes of iterative solvers we demonstrated the superior performance of generalized minimum residual solver in reducing the residual norm of the iterative solver during model updates. Using the algorithm in a geologically realistic scenario, we imaged the anticipated geometry of the Lalor volcanogenic massive sulphide deposit in Canada. The feasibility of the imaging methodology is further evaluated with the survey data, for which, again the algorithm converged to the anticipated model solution reproducing the lithostratigraphic sequence of the ore deposit.

Manifold embedded joint geometrical and statistical alignment for visual domain adaptation

Supervised learning algorithms like KNN assume that the training and the testing data come from the same source, and hence, have the same distribution. However, in real life, such instances are rare. Domain adaptation (DA) aims to model a classifier that is invariant to the different features of the training data. Domain invariant features are utilized to reduce distribution differences, ensuring an iterative improvement on the predicted target labels. Existing DA approaches either perform manifold subspace learning or align cross-domain distributions. At the same time, there exists a couple of imperative limitations: (1) degenerated feature transformation, wherein the seemingly domain invariant features are distorted during transformation (2) formulation of a robust objective function that must consider critical objectives in a unified framework to minimize deviations geometrically and statistically. To the best of our knowledge, none of the existing DA approaches address these two limitations simultaneously. Therefore, we propose a novel domain adaptation framework, called Manifold Embedded Joint Geometrical and Statistical Alignment (MEJGSA) for visual domain adaptation to address these limitations. MEJGSA first learns manifold features, and then formulates a robust objective function to reduce divergence between domains geometrically and statistically. We also consider more reliable classifiers to generate pseudo-labels to preserve objective functions such as conditional distributions and target domain discriminant information. Extensive experiments on two widely used cross-domain adaptation datasets demonstrate that MEJGSA exhibits significant improvements in classification accuracy as compared to cutting-edge shallow and deep DA approaches. The MATLAB code for our proposed method will be publicly available at 11https://github.com/rakesh1000/MEJGSA.

Gradient Descent-Based Objective Function Reformulation for Finite Control Set Model Predictive Current Control With Extended Horizon

This article proposes a novel objective function formulation based on gradient descent (GD) for finite control set predictive current control (FCS-PCC) with extended horizon. FCS-PCC has become increasingly attractive for electrical drive applications owing to its short settling time, lower switching frequency, capability to handle multiple conflicting targets, and feasible inclusion of constraints. However, it still suffers from high-torque ripple and poor current quality at the steady state. To tackle the aforementioned issue, a GD-based objective function reformulation is employed in the FCS-PCC with extended horizon. First, the optimization problem underlying FCS-PCC is formulated as a constrained quadratic programming problem with proved convexity from a geometric perspective. Based on the above, the tracking error of the control objective is minimized more efficiently by searching along the direction of GD. Consequently, the objective function is reconstructed as the deviation between the normalized GD and derivative, combined with the extension of feasible set. The abovementioned procedures are iteratively learned in every prediction horizon. The effectiveness of the proposed algorithm is verified on a 2.2-kW induction machine platform with a prediction horizon of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> = 3. It is confirmed that the proposed algorithm outperforms the conventional and multistep FCS-PCC in steady state and transient state.

Novel parameter extraction for Single, Double, and three diodes photovoltaic models based on robust adaptive arithmetic optimization algorithm and adaptive damping method of Berndt-Hall-Hall-Hausman

Experimental data-oriented parameter extraction helps in giving an accurate assessment to forecast the output current of the photovoltaic cells. This may be very beneficial in the modeling, optimization, partial shading, and assessment of the PV systems both practically and conceptually. Attributed to the reason that hybrid techniques incorporate the advantages of two or more algorithms, they outperform stochastic methods in solving the given complex multi-dimensional and multi-model optimization problems. Many authors have proposed hybrid methods to improve precision, steadiness, and overall efficiency. However, most of the algorithms concentrate on the methodology in the literature, and little attention has been paid to the objective function formulation, leading to a theoretical void in this area of research. In this work, we present a robust adaptive Arithmetic Optimization Algorithm based on the adaptive damping Berndt-hall-hall-Hausman (RaAOAAdBHHH) approach to efficacity determine the parameters of the single, double, and three diode PV model. The experimental results demonstrate that the proposed RaAOAAdBHHH approach successfully minimizes error to zero with rapid convergence, as determined by different statistical criteria and compared to experimental data.

The combined social engineering particle swarm optimization for real-world engineering problems: A case study of model-based structural health monitoring

Structural health monitoring (SHM) is a substantial research direction in structural engineering being scrutinized in recent years due to its significance in ensuring structural safety and reliability. The SHM using evolutionary computation has gained wide significance thanks to its computational capability and robust performance. By bearing in mind the necessity of efficient search mechanisms, a new algorithm merging the recent social engineering optimizer (SEO) and the particle swarm algorithm (PSO) is proposed in this work. The new algorithm, called the social engineering particle swarm optimization algorithm (SEPSO), combines the PSO population-based elitist-solution mechanism and the SEO two-solution attacker–defender paradigm to establish an effective global–local algorithm for solving complex engineering optimization problems. The SEPSO is developed, benchmarked, and compared with some state-of-the art algorithms using available test functions in the literature. Furthermore, the SEPSO is applied on selected mechanical design problems from the CEC2020 real-world constraint optimization competition in addition to comparison with the best-performed algorithms for benchmarking purpose. The SEPSO algorithm exhibits outstanding results when solving the benchmark functions and the real-world constraint optimization problems. Moreover, aiming to solve the complex problem of the SHM inverse problem, the SEPSO is employed. The SHM framework is presented and applied on the American Society of Civil Engineering (ASCE) frame structure based on an efficient fusion of objective function formulation. Several damage cases are tested using partial and noise-contaminated data. The proposed approach shows notable detectability and severity evaluation regardless the modal data malfunctions. Meanwhile, the proposed SEPSO can serve as an effective global–local search algorithm for solving real-world engineering problems.

Inverse Problem in Stochastic Approach to Modelling of Microstructural Parameters in Metallic Materials during Processing

The need for a reliable prediction of the distribution of microstructural parameters in metallic materials during processing was the motivation for this work. The model describing the evolution of dislocation populations, which considers the stochastic aspects of occurring phenomena, was formulated. The validation of the presented model requires the application of proper parameters corresponding to the considered materials. These parameters have to be identified through the inverse analysis, which, on the other hand, uses optimization methods and requires the formulation of the appropriate objective function. In our case, where the model involves the stochastic parameters, it is a crucial task. Therefore, a specific form of the objective function for the inverse analysis was developed using a measure based on histograms. The elaborated original stochastic approach to modeling the phenomena occurring during the thermomechanical treatment of metals was validated on commercially pure copper and selected multiphase steel.

Variable Selection with Multiply-Imputed Datasets: Choosing Between Stacked and Grouped Methods

Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This article considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as “stacked” and “grouped” objective functions. Building on existing work, we (i) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (ii) incorporate adaptive shrinkage penalties, (iii) compare these methods through simulation, and (iv) develop an R package miselect. Simulations demonstrate that the “stacked” approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. Supplementary materials for this article are available online.

Deterministic Robust Planning and Probabilistic Techno‐Economic Assessment of a Sector Coupled Community Energy System

AbstractThis paper proposes a systematic approach to examine the techno‐economical impact of a renewable based prosumer centric hybrid energy system (HES) connected to the local distribution grid. Systematic approach includes deterministic and probabilistic framework for optimal planning, scheduling, management, and assessment of HES. During the initiation stage, major components of the HES are identified as solar, Li‐ion batteries and biomass to enable cross‐sectoral participation whereas electric vehicle (EV) charging to promote smart electric‐mobility. Through stage‐wise data collection, processing, and training, hourly solar‐radiation historical data is classified into three seasons through kernelized space‐vector approach. Similarly, probabilistic assessment of EV arrival rate and charging requests are estimated through historical charging data. Based on initial system architecture, deterministic approach includes objective function formulation and its optimal solution through aggrandized class topper optimization (ACTO), particle swarm optimization (PSO), and JAYA algorithm. The objective function is realized through upper‐level economic problem and lower‐level technical sub‐problems. Analyzing the convergence characteristics, the optimal system dynamics and capacity estimated using ACTO is considered as the best with a minimum cost of energy of Rs. 4.235 per kWh. Finally, the probabilistic assessment is carried out through three levels of uncertainty to examine the system cost variations in each scenario.

Optimum design of tuned mass damper with pinched hysteresis under nonstationary stochastic seismic ground motion

The optimum design of a recent tuned mass damper with pinched hysteresis (TMD-PH) for seismic protection of structures is here investigated. The considered device consists of mixed NiTiNOL-steel wire ropes undergoing combined tension-flexure cycles. Previous studies demonstrated that concurrent interwire friction and phase transformation of the shape memory material exhibited by these composite wire ropes generate a peculiar pinched hysteretic behavior, which can be well described by means of a modified Bouc–Wen model. A stochastic-based optimum design methodology is here proposed for such TMD-PH, which is tailored to determine the best design parameters for the seismic protection of general structural systems. The seismic ground motion is modeled as a filtered nonstationary random process whereas the inherent pinched hysteresis of the device is dealt with via the stochastic linearization technique. The expressions of the linearization coefficients are obtained ad hoc and the optimum design of the TMD-PH is formulated as box-constrained single-objective optimization problem. Three objective function formulations are considered to reflect alternative design philosophies, namely, displacement-, acceleration- and energy-based design strategies. Unlike most literature studies addressing the optimum design of vibration absorbers via finite difference-based numerical schemes or non-gradient-based metaheuristic methods, the search for the optimal parameters of the TMD-PH is here performed by means of an iterative semi-analytical gradient-based numerical technique in which the derivatives for the covariance matrix of the system response are calculated analytically. A comprehensive numerical campaign is finally presented. First, a parametric study is carried out to evaluate the effects of the protected system characteristics and those of the seismic ground motion duration on the optimal parameters and performance of the device under consideration. The performance of the TMD-PH optimized according to the proposed methodology is also assessed in the context of a practical case study which makes use of synthetic and natural seismic ground motion records.

BlockTrust-RPL: distributed blockchain based authentication and trust validation for secure objective function formulation in RPL-IoT

BlockTrust-RPL: distributed blockchain based authentication and trust validation for secure objective function formulation in RPL-IoT

A Review of Model Predictive Controls Applied to Advanced Driver-Assistance Systems

Advanced Driver-Assistance Systems (ADASs) are currently gaining particular attention in the automotive field, as enablers for vehicle energy consumption, safety, and comfort enhancement. Compelling evidence is in fact provided by the variety of related studies that are to be found in the literature. Moreover, considering the actual technology readiness, larger opportunities might stem from the combination of ADASs and vehicle connectivity. Nevertheless, the definition of a suitable control system is not often trivial, especially when dealing with multiple-objective problems and dynamics complexity. In this scenario, even though diverse strategies are possible (e.g., Equivalent Consumption Minimization Strategy, Rule-based strategy, etc.), the Model Predictive Control (MPC) turned out to be among the most effective ones in fulfilling the aforementioned tasks. Hence, the proposed study is meant to produce a comprehensive review of MPCs applied to scenarios where ADASs are exploited and aims at providing the guidelines to select the appropriate strategy. More precisely, particular attention is paid to the prediction phase, the objective function formulation and the constraints. Subsequently, the interest is shifted to the combination of ADASs and vehicle connectivity to assess for how such information is handled by the MPC. The main results from the literature are presented and discussed, along with the integration of MPC in the optimal management of higher level connection and automation. Current gaps and challenges are addressed to, so as to possibly provide hints on future developments.

Fast estimation for robust supervised classification with mixture models

Label noise is known to negatively impact the performance of classification algorithms. In this paper, we develop a model robust to label noise that uses both labelled and unlabelled samples. In particular, we propose a novel algorithm to optimize the model parameters that scales efficiently w.r.t. the number of training samples. Our contribution relies on a consensus formulation of the original objective function that is highly parallelizable. The optimization is performed with the Alternating Direction Method of Multipliers framework. Experimental results on synthetic datasets show an improvement of several orders of magnitude in terms of processing time, with no loss in terms of accuracy. Our method appears also tailored to handle real data with significant label noise.