Final Objective Function Value Research Articles

Multiscale topology optimization of structures by using isogeometrical level set approach

This study aims to optimize topology of structures at macro and micro scales, simultaneously, by using a level set method in an isogeometric analysis (IGA) framework. To achieve this, equilibrium and homogenization equations in the model are solved by IGA method. The level set functions are defined over a grid in parameter space of associating b-splines of the IGA model. Therefore, control net of the model and level set grid are separated and there is no need to refine the control net for having smooth boundaries. Sensitivity analyses for both scales are performed to calculate the velocity of boundary points and the level set functions are updated by solving reaction-diffusion equations. Finally, several 2D and 3D examples with different geometry and boundary conditions are provided to show performance and efficiency of the method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function. Also, by using IGA level set method, smooth boundaries are achieved in the final topology of micro and macro structures.

Optimal Reactive Power Compensation via D-STATCOMs in Electrical Distribution Systems by Applying the Generalized Normal Distribution Optimizer

This research deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) via the application of a master–slave optimization technique. The master stage determines the nodes where the D-STATCOMs must be located and their nominal rates by applying the generalized normal distribution optimizer (GNDO) with a discrete–continuous codification. In the slave stage, the successive approximations power flow method is implemented in order to establish the technical feasibility of the solution provided by the master stage, i.e., voltage regulation and device capabilities, among other features. The main goal of the proposed master–slave optimizer is to minimize the expected annual operating costs of the distribution grid, which includes the energy loss and investment costs of the D-STATCOMs. With the purpose of improving the effectiveness of reactive power compensation during the daily operation of the distribution grid, an optimal reactive power flow (ORPF) approach is used that considers the nodes where D-STATCOMs are located as inputs in order to obtain their daily expected dynamical behavior with regard to reactive power injection to obtain additional net profits. The GNDO approach and the power flow method are implemented in the MATLAB programming environment, and the ORPF approach is implemented in the GAMS software using a test feeder comprising 33 nodes with both radial and meshed configurations. A complete comparative analysis with the Salp Swarm Algorithm is presented in order to demonstrate the effectiveness of the proposed two-stage optimization approach in the fixed operation scenario regarding the final objective function values. In addition, different tests considering the possibility of hourly power injection using D-STATCOMs through the ORPF solution demonstrate that additional gains can be obtained in the expected annual operative costs of the grid.

Toward semi-automatic biologically effective dose treatment plan optimisation for Gamma Knife radiosurgery

Objective. Dose-rate effects in Gamma Knife radiosurgery treatments can lead to varying biologically effective dose (BED) levels for the same physical dose. The non-convex BED model depends on the delivery sequence and creates a non-trivial treatment planning problem. We investigate the feasibility of employing inverse planning methods to generate treatment plans exhibiting desirable BED characteristics using the per iso-centre beam-on times and delivery sequence. Approach. We implement two dedicated optimisation algorithms. One approach relies on mixed-integer linear programming (MILP) using a purposely developed convex underestimator for the BED to mitigate local minima issues at the cost of computational complexity. The second approach (local optimisation) is faster and potentially usable in a clinical setting but more prone to local minima issues. It sequentially executes the beam-on time (quasi-Newton method) and sequence optimisation (local search algorithm). We investigate the trade-off between time to convergence and solution quality by evaluating the resulting treatment plans’ objective function values and clinical parameters. We also study the treatment time dependence of the initial and optimised plans using BED95 (BED delivered to 95% of the target volume) values. Main results. When optimising the beam-on times and delivery sequence, the local optimisation approach converges several orders of magnitude faster than the MILP approach (minutes versus hours–days) while typically reaching within 1.2% (0.02–2.08%) of the final objective function value. The quality parameters of the resulting treatment plans show no meaningful difference between the local and MILP optimisation approaches. The presented optimisation approaches remove the treatment time dependence observed in the original treatment plans, and the chosen objectives successfully promote more conformal treatments. Significance. We demonstrate the feasibility of using an inverse planning approach within a reasonable time frame to ensure BED-based objectives are achieved across varying treatment times and highlight the prospect of further improvements in treatment plan quality.

Application of the Crow Search Algorithm to the Problem of the Parametric Estimation in Transformers Considering Voltage and Current Measures

The problem of the electrical characterization of single-phase transformers is addressed in this research through the application of the crow search algorithm (CSA). A nonlinear programming model to determine the series and parallel impedances of the transformer is formulated using the mean square error (MSE) between the voltages and currents measured and calculated as the objective function. The CSA is selected as a solution technique since it is efficient in dealing with complex nonlinear programming models using penalty factors to explore and exploit the solution space with minimum computational effort. Numerical results in three single-phase transformers with nominal sizes of 20 kVA, 45 kVA, 112.5 kVA, and 167 kVA demonstrate the efficiency of the proposed approach to define the transformer parameters when compared with the large-scale nonlinear solver fmincon in the MATLAB programming environment. Regarding the final objective function value, the CSA reaches objective functions lower than 2.75×10−11 for all the simulation cases, which confirms their effectiveness in minimizing the MSE between real (measured) and expected (calculated) voltage and current variables in the transformer.

Non-Smooth Regularization: Improvement to Learning Framework Through Extrapolation

Deep learning architectures employ various regularization terms to handle different types of priors. Non-smooth regularization terms have shown promising performance in the deep learning architectures and a learning framework has recently been proposed to train autoencoders with such regularization terms. While this framework efficiently manages the non-smooth term during training through proximal operators, it is limited to autoencoders and suffers from low convergence speed due to several optimization sub-problems that must be solved in a row. In this paper, we address these issues by extending the framework to general feed-forward neural networks and introducing variable extrapolation which can dramatically increase the convergence speed in each sub-problem. We show that the proposed update rules converge to a critical point of the objective function under mild conditions. To compare the resulting framework with the previously proposed one, we consider the problem of training sparse autoencoders and robustifying deep neural architectures against both targeted and untargeted attacks. Simulations show superior performance in both convergence speed and final objective function value.

A Novel Method for Source Tracking of Chemical Gas Leakage: Outlier Mutation Optimization Algorithm.

Chemical industrial parks, which act as critical infrastructures in many cities, need to be responsive to chemical gas leakage accidents. Once a chemical gas leakage accident occurs, risks of poisoning, fire, and explosion will follow. In order to meet the primary emergency response demands in chemical gas leakage accidents, source tracking technology of chemical gas leakage has been proposed and evolved. This paper proposes a novel method, Outlier Mutation Optimization (OMO) algorithm, aimed to quickly and accurately track the source of chemical gas leakage. The OMO algorithm introduces a random walk exploration mode and, based on Swarm Intelligence (SI), increases the probability of individual mutation. Compared with other optimization algorithms, the OMO algorithm has the advantages of a wider exploration range and more convergence modes. In the algorithm test session, a series of chemical gas leakage accident application examples with random parameters are first assumed based on the Gaussian plume model; next, the qualitative experiments and analysis of the OMO algorithm are conducted, based on the application example. The test results show that the OMO algorithm with default parameters has superior comprehensive performance, including the extremely high average calculation accuracy: the optimal value, which represents the error between the final objective function value obtained by the optimization algorithm and the ideal value, reaches 2.464e-15 when the number of sensors is 16; 2.356e-13 when the number of sensors is 9; and 5.694e-23 when the number of sensors is 4. There is a satisfactory calculation time: 12.743 s/50 times when the number of sensors is 16; 10.304 s/50 times when the number of sensors is 9; and 8.644 s/50 times when the number of sensors is 4. The analysis of the OMO algorithm’s characteristic parameters proves the flexibility and robustness of this method. In addition, compared with other algorithms, the OMO algorithm can obtain an excellent leakage source tracing result in the application examples of 16, 9 and 4 sensors, and the accuracy exceeds the direct search algorithm, evolutionary algorithm, and other swarm intelligence algorithms.

Hull geometry optimisation of wave energy converters: On the choice of the optimisation algorithm and the geometry definition

It is key in the development of wave energy systems to aim at designing economically competitive solutions that enable maximal annual energy production. Previous studies identify the Wave Energy Converter (WEC) structure, i.e. the hull, to have one of the largest cost reduction potentials. Due to this potential, geometry optimisation of WECs has been previously considered, however, most of these studies have been limited by the simplicity of the employed geometrical shapes and the lack of accurate cost models. It is, therefore, important to include an adaptable geometry definition capable of generating diverse WEC shapes, and to account for other factors that can have an effect on costs. These considerations result in a more challenging optimisation problem, and a more complex objective function. The goal of this study is to address the challenge of finding a suitable and efficient optimisation method for WEC geometry design. In this paper, different geometry definitions, such as using simple shapes or B-spline surfaces, and different meta-heuristic optimisation algorithms, such as genetic algorithms or particle swarm optimisation are applied to this problem to find the most suitable choices. Results show an improvement in final objective function values of up to 224% when using an adaptable geometry definition and up to 11% when employing the most suitable optimisation algorithm compared to previous results. In conclusion, the choice of the different elements of the optimisation formulation have a large impact on the quality of the optimisation results and should be based on preliminary studies as presented here.

Modified particle swarm algorithm for the optimal water allocation of reservoir

Abstract At present, meta-heuristic algorithms are the most popular methods for the optimization of the operations of reservoirs. In order to avoid inappropriate solutions, i.e. spills occurring when the reservoir is not full, a modified method is proposed that can adjust the trajectories of the particles, using the particle swarm algorithm, according to the operation rule of the reservoir. The method was tested in a case study, and was compared to two commonly used methods for generating particle position vectors. These included the direct method, which uses water supply and water spills as the iteration variables, and the indirect method, which uses water storages (water levels) as the iteration variables. The results showed that the three methods could achieve similar solutions at the 75% probability of exceedance. There was no difference in the convergence speeds or the final objective function values of the three models. However, at the 50% probability of exceedance, the modified method produced results that followed the operation rule of the reservoir, whereas the other two methods could lead to inappropriate water spills. This new method may provide a reference for other meta-heuristic algorithms in models of the optimal operation of reservoirs.

Design approach and performance analysis of trap filter for three-phase PV grid integration systems using evolutionary search algorithms

The main objective of this article is to provide an efficient design approach of passive grid filters based on evolutionary search algorithms. The case study is conducted on a passive trap filter (one of modern high order passive filters that can provide better performance compared with first order scheme) to be incorporated with a three-phase grid-tied inverter fed from PV array and a battery bank, forming a typical PV grid integration system. The filter design approach is mainly based on particle swarm optimization technique (PSO) as one of the efficient evolutionary search algorithms meanwhile Genetic Algorithm (GA) has been utilized as well for comparison purposes. The developed PSO algorithm searches for the optimum numerical values of filter passive components that can optimize a customized objective function of multiple terms. Unlike single-term objective function, the adopted approach has the advantage of involving multiple items in the customized objective function, such as harmonic attenuation factor and the numerical values of passive filter elements to be minimized. Moreover, the evolutionary search-based design approach is characterized by offering several groups of solutions for the same optimization problem. Thus, the obtained solution is not unique. Consequently, the choice between those solutions depends on the system designers who can select the most convenient solution among several alternatives based on component availability in market, the overall cost of the filter and the desired upper limit of THD of grid currents. The obtained results of this study demonstrate also the capability of evolutionary search approach to get optimum values of filter components that achieve good harmonic attenuation and satisfy the related grid codes such as the IEEE standard 519. Compared with traditional filter design method, the obtained results indicate that the PSO technique achieves lower numerical values of filter parameters in the most of parameters, resulting in an overall reduction in the size and cost of the passive grid filter. In addition, the employed GA succeeded to provide satisfactory numerical values of trap filter as well. However, the PSO technique is better than GA in several terms such as lower final value of objective function and lower numerical values of filter elements and convergence to the optimal solution(s) irrespective the initial guess values.Matlab® has been employed as a simulation platform for PSO and GA algorithms. While the overall grid integration system has been modelled and studied using professional version of PSIM software®.

Improved sampling strategies for ensemble-based optimization

We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s2) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s2) designs previously suggested in the literature.

Sensitivity Analysis and Calibration of an Integrated Hydrologic Model in an Irrigated Agricultural Basin With a Groundwater‐Dependent Ecosystem

AbstractWhile sensitivity analysis and calibration are common practice in integrated hydrologic modeling, little work has been done to understand how the design of the sensitivity analysis and calibration affects the simulation outcome in these often highly nonlinear models. This is especially true for irrigated agricultural basins with a strong connection between land use, groundwater, and surface water. Using a range rather than a single set of initial parameter values, multiple sensitivity analyses, calibrations, and linearity tests were performed using UCODE_2014 on the Scott Valley Integrated Hydrologic Model. Calibration results show that parameters related to crop demand and applied irrigation water are most sensitive. Influence statistics show that low streamflow observations provide the most information during model calibration, indicating preference should be given to these observations during model development, sensitivity analysis, and calibration. Importantly, due to the nonlinearity of the integrated model, significant differences are found in results when initial parameter values are sampled from within their respective expected ranges. Estimates for some parameters varied up to an order of magnitude between calibrations, while all produced similar final objective function values, groundwater elevations, and stream flow. Confidence intervals for individual sensitivity analyses and calibration runs only spanned a fraction of the ensemble estimated parameter range across multiple runs. Our work suggests that a calibration design with multiple sensitivity analyses and calibrations of integrated hydrologic models, each using one of several widely varying sets of initial values, provides a frugal approach to identify parameters across the global parameter space.

A hybrid optimization approach for efficient calibration of computationally intensive hydrological models

ABSTRACTThe calibration of hydrological models is formulated as a blackbox optimization problem where the only information available is the objective function value. Distributed hydrological models are generally computationally intensive, and their calibration may require several hours or days which can be an issue for many operational contexts. Different optimization algorithms have been developed over the years and exhibit different strengths when applied to the calibration of computationally intensive hydrological models. This paper shows how the dynamically dimensioned search (DDS) and the mesh adaptive direct search (MADS) algorithms can be combined to significantly reduce the computational time of calibrating distributed hydrological models while ensuring robustness and stability regarding the final objective function values. Five transitional features are described to adequately merge both algorithms. The hybrid approach is applied to the distributed and computationally intensive HYDROTEL model on three different river basins located in Québec (Canada).

Evaluation of rapidarc optimitation strategies using objetive function values

Introduction Eclipse treatment planning system includes various optimization strategies than can be employed to improve the quality of the ultimate treatment plan for RapidArc Purpose The purpose of this study is to analyze the new strategies included in the PRO3 optimization algorithm for three phantoms and to examine the results using the final objective function values. Materials and methods Three phantoms were created in Eclipse 10.0 with varying shapes and locations for the planning target volumes and organs at risk. These phantoms were taken from Oliver et al. described in Med Phys. (Vol. 11, No. 1, Winter 2010) A baseline optimization consisting in a single 358 o arc with collimator at 45 o was applied to all phantoms. Seven different strategies were evaluated and compared to the baseline strategy using the reporting objective function. Each strategy was compared against baselines using paired Student’s t-test. Results The strategies that resulted with a significant difference from the baseline were: add an 358 o arc with a collimator at 315 o (p Conclusion In our study, we conclude that the optimal collimator angle that minimized target function value is 45 o . From the seven different strategies, only three of them produced significant different final objective function values from baseline. These three strategies are: ad a new arc with orthogonal collimator angle from baseline, using the fit and shield option and fit the isocenter with arc geometry tool.

Real-time inverse high-dose-rate brachytherapy planning with catheter optimization by compressed sensing-inspired optimization strategies

This paper demonstrates that optimization strategies derived from the field of compressed sensing (CS) improve computational performance in inverse treatment planning (ITP) for high-dose-rate (HDR) brachytherapy.Following an approach applied to low-dose-rate brachytherapy, we developed a reformulation of the ITP problem with the same mathematical structure as standard CS problems. Two greedy methods, derived from hard thresholding and subspace pursuit are presented and their performance is compared to state-of-the-art ITP solvers.Applied to clinical prostate brachytherapy plans speed-up by a factor of 56–350 compared to state-of-the-art methods. Based on a Wilcoxon signed rank-test the novel method statistically significantly decreases the final objective function value (p < 0.01). The optimization times were below one second and thus planing can be considered as real-time capable.The novel CS inspired strategy enables real-time ITP for HDR brachytherapy including catheter optimization. The generated plans are either clinically equivalent or show a better performance with respect to dosimetric measures.

MEDICAL STAFF SCHEDULING USING SIMULATED ANNEALING

Purpose: The efficiency of medical staff is a fundamental feature of healthcare facilities quality. Therefore the better implementation of their preferences into the scheduling problem might not only rise the work-life balance of doctors and nurses, but also may result into better patient care. This paper focuses on optimization of medical staff preferences considering the scheduling problem. Methodology/Approach: We propose a medical staff scheduling algorithm based on simulated annealing, a well-known method from statistical thermodynamics. We define hard constraints, which are linked to legal and working regulations, and minimize the violations of soft constraints, which are related to the quality of work, psychic, and work-life balance of staff. Findings: On a sample of 60 physicians and nurses from gynecology department we generated monthly schedules and optimized their preferences in terms of soft constraints. Our results indicate that the final value of objective function optimized by proposed algorithm is more than 18-times better in violations of soft constraints than initially generated random schedule that satisfied hard constraints. Research Limitation/implication: Even though the global optimality of final outcome is not guaranteed, desirable solutionwas obtained in reasonable time. Originality/Value of paper: We show that designed algorithm is able to successfully generate schedules regarding hard and soft constraints. Moreover, presented method is significantly faster than standard schedule generation and is able to effectively reschedule due to the local neighborhood search characteristics of simulated annealing.

First application of quantum annealing to IMRT beamlet intensity optimization

Optimization methods are critical to radiation therapy. A new technology, quantum annealing (QA), employs novel hardware and software techniques to address various discrete optimization problems in many fields. We report on the first application of quantum annealing to the process of beamlet intensity optimization for IMRT.We apply recently-developed hardware which natively exploits quantum mechanical effects for improved optimization. The new algorithm, called QA, is most similar to simulated annealing, but relies on natural processes to directly minimize a system’s free energy. A simple quantum system is slowly evolved into a classical system representing the objective function. If the evolution is sufficiently slow, there are probabilistic guarantees that a global minimum will be located.To apply QA to IMRT-type optimization, two prostate cases were considered. A reduced number of beamlets were employed, due to the current QA hardware limitations. The beamlet dose matrices were computed using CERR and an objective function was defined based on typical clinical constraints, including dose-volume objectives, which result in a complex non-convex search space. The objective function was discretized and the QA method was compared to two standard optimization methods, simulated annealing and Tabu search, run on a conventional computing cluster.Based on several runs, the average final objective function value achieved by the QA was 16.9 for the first patient, compared with 10.0 for Tabu and 6.7 for the simulated annealing (SA) method. For the second patient, the values were 70.7 for the QA, 120.0 for Tabu and 22.9 for the SA. The QA algorithm required 27–38% of the time required by the other two methods.In this first application of hardware-enabled QA to IMRT optimization, its performance is comparable to Tabu search, but less effective than the SA in terms of final objective function values. However, its speed was 3–4 times faster than the other two methods. This initial experiment suggests that more research into QA-based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes.

A New Parameterization Method for Large-Scale Reservoir History

A novel and simple parameterization method using an ensemble of unconditional model realizations is applied to decrease the dimension of the misfit objective function in large-scale history matching problems. The major advantage of this parameterization method is that the singular value decomposition (SVD) calculation is completely avoided, which saves time and cost for huge matrix decomposition and the eigenvectors computations in parameterization process. After objective function transforms from a higher dimension to a lower dimension by parameterization, a Monte Carlo approach is introduced to evaluate the gradient information in the lower domain. Unlike the adjoint-gradient algorithms, the gradient in our method is estimated by Monte Carlo stochastic method, which can be easily coupled with different numerical simulator and avoid complicated adjoint code. When the estimated gradient information is obtained, any gradient-based algorithm can be implemented for optimizing the objective function. The Monte Carlo algorithm combined with the parameterization method is applied to Brugge reservoir field. The result shows that our present method gives a good estimation of reservoir properties and decreases the geological uncertainty without SVD but with a lower final objective function value, which provides a more efficient and useful way for history matching in large scale field.

Data mining for decision making in engineering optimal design

Often in modeling the engineering optimization design problems, the value of objective function(s) is not clearly defined in terms of design variables. Instead it is obtained by some numerical analysis such as finite element structural analysis, fluid mechanics analysis, and thermodynamic analyses. Yet, the numerical analyses are considerably time consuming to obtain the final value of objective function(s). For the reason of reducing the number of analyses as few as possible, our methodology works as a supporting tool to the metamodels. The research in meta-modeling for multi-objective optimization are relatively young and there is still much research capacity to further explore. Here is shown that visualizing the problem on the basis of the randomly sampled geometrical big-data of computer aided design (CAD) and computer aided engineering (CAE) simulation results, combined with utilizing classification tool of data mining could be effective as a supporting system to the available meta-modeling approaches. To evaluate the effectiveness of the proposed method, a case study in 3D wing optimal design is proposed. Discussion focusing on how effective the proposed methodology could be in further practical engineering design problems is presented.

SU‐F‐BRD‐13: Quantum Annealing Applied to IMRT Beamlet Intensity Optimization

Purpose:We report on the first application of quantum annealing (QA) to the process of beamlet intensity optimization for IMRT. QA is a new technology, which employs novel hardware and software techniques to address various discrete optimization problems in many fields.Methods:We apply the D‐Wave Inc. proprietary hardware, which natively exploits quantum mechanical effects for improved optimization. The new QA algorithm, running on this hardware, is most similar to simulated annealing, but relies on natural processes to directly minimize the free energy of a system. A simple quantum system is slowly evolved into a classical system, representing the objective function. To apply QA to IMRT‐type optimization, two prostate cases were considered. A reduced number of beamlets were employed, due to the current QA hardware limitation of ∼500 binary variables. The beamlet dose matrices were computed using CERR, and an objective function was defined based on typical clinical constraints, including dose‐volume objectives. The objective function was discretized, and the QA method was compared to two standard optimization Methods: simulated annealing and Tabu search, run on a conventional computing cluster.Results:Based on several runs, the average final objective function value achieved by the QA was 16.9 for the first patient, compared with 10.0 for Tabu and 6.7 for the SA. For the second patient, the values were 70.7 for the QA, 120.0 for Tabu, and 22.9 for the SA. The QA algorithm required 27–38% of the time required by the other two methods.Conclusion:In terms of objective function value, the QA performance was similar to Tabu but less effective than the SA. However, its speed was 3–4 times faster than the other two methods. This initial experiment suggests that QA‐based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes.

On estimability of parsimonious term structure models: an experiment with the Nelson–Siegel specification

This study addresses operational issues in estimation of parsimonious term structure models. When using price errors, objective function in term structure estimation is a nonlinear function of the model parameters. This necessarily entails using numerical optimization techniques for estimation, which brings to fore the issue of (sensitivity of final results to) the choice of initialization of the optimization routine. This study assesses the sensitivity of the final objective function value and the final parameter vector to the choice of the ‘initial guess’ during the estimation of the popular Nelson–Siegel model. It turns out that there exist regions in the shape of the objective function where a slight change in (seemingly reasonable) initial vector takes one far from optimum. Choice of the (range of) ‘best’ starting vector turns out to be an empirical matter. Grid search is recommended. One must first get to a subset of initial values that results in the objective function value near a minimum and then assess the sensitivity of the final parameter vector to those relevant (subset of) initial values. The study illustrates the process using a typical trading day's data.