Generalized Pattern Search Algorithm Research Articles

Quantum-Enhanced Generalized Pattern Search Optimization

While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in new behavior that could negatively impact the performance of the larger algorithm. The purpose of this work is to preserve the advantages of applying quantum search methods for generalized pattern search algorithms (GPSs) without violating the convergence criteria. It is well known that quantum search methods are able to reduce the expected number of oracle calls needed for finding the solution to a search problem from O(N) to O(N) However, the number of oracle calls needed to determine that no solution exists with certainty is exceedingly high and potentially infinite. In the case of GPS, this is a significant problem since overlooking a solution during an iteration will violate a needed assumption for convergence. Here, we overcome this problem by introducing the quantum improved point search (QIPS), a classical–quantum hybrid variant of the quantum search algorithm QSearch. QIPS retains the O(N) oracle query complexity of QSearch when a solution exists. However, it is able to determine when no solution exists, with certainty, using only O(N) oracle calls.

Optimization Of Hybrid Composite Laminates With Various Materials Using GA/GPSA Hybrid Algorithm for Maximum Dimensional Stability

In this study, it is aimed to obtain the highest dimensional stability against temperature changes in fiber-reinforced hybrid composite laminates considering eight different composite materials: Aramid/Epoxy, AS4/Epoxy, Boron/Epoxy, E-Glass/Epoxy, IM6/Epoxy, GY70/Epoxy, Kevlar49/Epoxy, and Spectra/Epoxy. The study focuses on finding the optimum continuous and traditional fiber angle orientations for the hybrid composite plates that would provide the lowest coefficients of thermal expansion. For this purpose, two different laminate sequences were investigated, each including two materials. A hybrid algorithm combining genetic algorithm and generalized pattern search algorithm was used in the optimization. A great number of hybrid design problems were solved repeatedly, and their results were compared both within themselves and to the optimum non-hybrid laminate results. Furthermore, the thermal durability of the selected optimum hybrid designs was evaluated by Tsai-Wu failure and Hashin-Rotem criteria. The results reveal that substantial increase in dimensional stability can be achieved by stacking sequence optimization of hybrid composite laminates with multiple material selection, and this hybrid design approach can offer the desired laminated composite structures for aerospace applications required to withstand extreme temperature changes.

Automated Equations of State Tuning Workflow Using Global Optimization and Physical Constraints

A computational model that can accurately describe the thermodynamics of a hydrocarbon system and its properties under various conditions is a prerequisite for running reservoir and pipeline simulations. Cubic Equations of State (EoS) are mathematical tools used to model the phase and volumetric behavior of reservoir fluids when compositional effects need to be considered. To anticipate uncertainty and enhance the quality of their predictions, EoS models must be adjusted to adequately match the available lab-measured PVT values. This task is challenging given that there are many potential tuning parameters, thus leading to various tuning results of questionable validity. In this paper, we present an automated EoS tuning workflow that employs a Generalized Pattern Search (GPS) optimizer for efficient tuning of a cubic EoS model. Specifically, we focus on the Peng–Robinson (PR) model, which is the oil and gas industry standard, to accurately capture the behavior of diverse multicomponent, complex hydrocarbon mixtures encountered in subsurface reservoirs. This approach surpasses the limitations of conventional gradient-based (GB) methods, which are susceptible to getting trapped in local optima. The proposed technique also allows physical constraints to be imposed on the optimization procedure. A gas condensate and an H2S-rich oil were used to demonstrate the effectiveness of the GPS algorithm in finding an optimized solution for high-dimensional search spaces, and its superiority over conventional gradient-based optimization was confirmed by automatically tracking globally optimal and physically sound solutions.

Multiobjective Optimization for Hurricane Retrofit to Improve Coastal Community Structural and Socioeconomic Resilience

With recent hurricanes causing devastating economic losses, structural damages, and societal impacts on coastal communities, residential building hurricane mitigation measures have gained increasing attention. However, retrofits are often costly and therefore beget inherent tradeoffs. In particular, the balancing of the postdisaster losses against upfront mitigation costs remains a constant challenge for community resilience planning. Existing mitigation optimization frameworks on the community scale have primarily focused on seismic hazards and typically have weak integration of the structural damages with the socioeconomic impacts. In the present study, finite element modeling of the residential buildings is applied to better incorporate the structural damages under combined wind and wave loadings. A multiobjective linear constrained optimization framework for improved residential building hurricane retrofit is developed to balance the structural damages, home displacements, morbidities, net direct economic losses, and initial mitigation expenditures under hurricane threats. For the present analysis, the mitigation actions of building elevation and improved construction practices are simulated. The framework is tested in a case study for an existing coastal community under 50-, 100- and 500-year hurricane events considering community-specific socioeconomic factors. The generalized pattern search algorithm is selected to determine the Pareto-optimal solutions. The results indicate large potential reductions in social, structural, and economic losses under optimized mitigation, but tradeoffs exist if the mitigation technique is found to be cost-ineffective, such as in the case of the improved construction practices. The findings highlight the importance of informed decision-making and home retrofits in improving community resilience.

Bad data correction in harmonic state estimation for power distribution systems: an approach based on generalised pattern search algorithm

This paper presents a novel methodology for bad data correction in harmonic state estimation for power distribution systems. An optimisation model is formulated considering an objective function to be minimised based on the weighted least squares. Inequality constraints are incorporated to the problem for those buses which are not monitored in real time by any dedicated meter, being their corresponding active and reactive powers considered between upper and lower bounds in order to provide supplementary information about the current system state. In this paper, a measurement calibration vector is introduced into the optimisation model, assuming that a correction factor is associated with the measurements gathered from the network. GPSA (Generalized Pattern Search Algorithm) is used to determine the optimal values of each calibration factor to provide correct state estimation results. A 69-bus test system is used for the computational simulations considering different case studies with multiple bad data to be identified and corrected proving the efficiency and viability of the proposed method. The main contribution of this work is the automatic detection of bad data, identification of the corrupted measurements and correction of the bad data ensuring that the system states are estimated with errors lower than 1%.

A Generalized Pattern Search Algorithm Methodology for solving an Under-Determined System of Equality Constraints to achieve Power System Observability using Synchrophasors

The impact of the generalized pattern search algorithm (GPSA) on power system complete observability utilizing synchrophasors is proposed in this work. This algorithmic technique is an inherent extension of phasor measurement unit (PMU) minimization in a derivative-free framework by evaluating a linear objective function under a set of equality constraints that is smaller than the decision variables in number. A comprehensive study about the utility of such a system of equality constraints under a quadratic objective has been given in our previous paper. The one issue studied in this paper is the impact of a linear cost function to detect optimality in a shorter number of iterations, whereas the cost is minimized. The GPSA evaluates a linear cost function through the iterations needed to satisfy feasibility and optimality criteria. The other issue is how to improve the performance of convergence towards optimality using a gradient-free mathematical algorithm. The GPSA detects an optimal solution in a fewer number of iterations than those spent by a recursive quadratic programming (RQP) algorithm. Numerical studies on standard benchmark power networks show significant improvement in the maximum observability over the existing measurement redundancy generated by the RQP optimization scheme already published in our former paper.

Data-Driven Optimization of Piezoelectric Energy Harvesters via Pattern Search Algorithm.

A data-driven optimization strategy based on a generalized pattern search (GPS) algorithm is proposed to automatically optimize piezoelectric energy harvesters (PEHs). As a direct search method, GPS can iteratively solve the derivative-free optimization problem. Taking the finite element method (FEM) as the solver and the GPS algorithm as the optimizer, the automatic interaction between the solver and optimizer ensures optimization with minimum human efforts, saving designers’ time and performing a more precise exploration in the parameter space to obtain better results. When employing it for the optimization of PEHs, the optimal length and thickness of PZT were 6.0 mm and 4.6 µm, respectively. Compared with reported high-output PEHs, this optimal structure showed an increase of 371% in output power, an improvement by 1000% in normalized power density, and a reduction of 254% in resonant frequency. Furthermore, Spearman’s rank correlation coefficient was calculated for evaluating the correlation among geometric parameters and output performance such as resonant frequency and output power, which provides a data-based perspective on the design and optimization of PEHs.

Calibration of energy simulation using optimization for buildings with dynamic shading systems

Physics-based energy simulation methods are widely used for the prediction of building energy consumption and daylighting in commercial buildings. Such simulations are performed to evaluate the design of new buildings or to predict the benefits of various retrofits to the building’s performance. However, there are uncertainties in the results from such simulations, with higher uncertainty if the model used is not validated empirically. This study focuses on the co-simulation of daylight and energy modeling to evaluate the energy performance impacts of dynamic shading. The Generalized Pattern Search algorithm is used to minimize the root mean square error between measured and simulated data to perform the calibration of the baseline energy model while adjusting the building envelope material properties. Next, the results using three different modeling methods for windows and shading devices in EnergyPlus were compared to measured data. The results show that the use of the simple layered model to represent the dynamic shading system performed better than other two models, when compared to the experimental data. They also indicate that part of the difference between the model results and experimental data originates from sky model calculations and ground reflectance inputs. From the results it is also observed that using different modeling methods for the window and shading device can impact the coincidental energy consumption results from cooling and lighting by up to 20%.

Heat transfer enhancement in microchannel heat sinks with dual split-cylinder and its intelligent algorithm based fast optimization

Microchannel heat sink (MCHS) with dual split-cylinder (initial model) is proposed in this work, to obtain better thermal performance (TP) and eliminate local heat transfer deterioration. Comparing with the MCHS with cylinder (prototype), the results indicate that the maximum relative increment of TP of initial model is 34.63%, obtained at Re = 200. And, the temperature uniformity is also improved at this case as well. However, this superiority is weakened as Re increases or decreases. Therefore, intelligent algorithm based fast optimization method, combing three dimensional geometry reconstruction, spatial discretization, and simulation, is further established and applied in the initial model. The generalized pattern search algorithm (GPS) is utilized to control the direct search of width (Swidth) and location (Slocation) of dual split-cylinder channel for optimum TP. In the optimization, the interval size of search is adjusted to improve optimization precision and avoid the duplication of search points. After optimization, the optimum Swidth for each Re differs, which is decreased with the increase of Re. While, for all Re, the optimum Slocation are decreased to the boundary of design variables range. Accordingly, comparing with initial model, the TP of optimized model is increased a lot at each Re. And, the largest TP = 3.10 is obtained at Re = 300. And that, the maximum relative increment of TP from prototype model to optimized model is obtained at Re = 250, which is 63.41%. Besides, the temperature uniformity of optimized model is also improved effectively, which is more obvious as Re increases.

Multi-fidelity algorithms for the horizontal alignment problem in road design

Multi-fidelity algorithms for solving the horizontal alignment problem in road design are considered. A multi-fidelity surrogate model is built and quantile regression is used to understand its accuracy at various fidelity levels. Two algorithms are compared: a generalized pattern search algorithm with adaptive precision control, and a trust-region algorithm for unconstrained problems with controlled error. To make a fair comparison, the parameters of each algorithm are tuned on five small roads using performance profiles. Then the algorithms are evaluated on 35 roads, ranging from small to very large roads. The results show that using multi-fidelity surrogates in optimization algorithms provide notable speed-up when compared to single-fidelity algorithms while preserving the quality of solutions (cost error ). On the longest roads, higher speed-up and better accuracy are observed.

Endmembers abundance estimators based on spectral shape similarity using genetic algorithm and generalized pattern search algorithm

We develop two endmembers abundance estimators based on a genetic algorithm (GA) and a generalized pattern search algorithm. This development aims to estimate more accurate abundances of endmembers in cases of brightness and shading noises, which is an issue in other endmember abundance estimation methods based on the least square method, such that the estimators depend on spectral shape similarity as a matching criterion between spectral signatures, because shape similarity methods are independent on the spectral reflectance amplitude and not sensitive to brightness noise effects on it. The strategy used for unmixing problem analysis is based on the popular linear spectral mixture model. GA is used as a heuristic optimization technique, and generalized pattern search is used as a direct search algorithm. Spectral angle mapper, spectral information divergence methods, and the combination of both of these are used as objective functions for optimization techniques. All experiments have been performed on the proposed estimators and the traditional fully constrained least squares method as a state-of-the-art method. Experiments have been applied on simulated multispectral and hyperspectral datasets with different noise conditions. In addition, a hyperspectral real dataset from a cuprite region (Las Vegas, Nevada, USA) was used for testing performance. The experimental results show that proposed estimators are better than fully contained least squares method across all experiments and especially in cases of noisy datasets.

Generalized optimization of cross-flow staggered tube banks using a subscale model

Finding a general optimum arrangement of the cross-flow staggered tube banks causes a significant decrease in using available energy resources due to their extensive use in industrial applications. This paper presents a numerical optimization study by generalized pattern search algorithm (GPSA) to investigate optimum longitudinal and transverse pitches of the staggered tube banks in turbulent flow regime. Symmetric and periodic boundary conditions are employed to simulate all the tube banks without considering the entire volume. Using these boundary conditions, the optimization process can be directly performed by simulating the flow and heat transfer through tube banks with a CFD code and the previous researchers' correlations are not employed in this process. The “goodness factor” which takes into consideration the effects of both heat transfer and pressure drop simultaneously in a proper order is used as the objective function. In the first part of the study, optimum pitches are calculated for specific inlet Reynolds and Prandtl numbers. Subsequently, the effect of both inlet Reynolds and Prandtl numbers are separately investigated on the optimum pitches in the turbulent regime. Results show that the optimum dimensionless longitudinal and transverse pitches of the staggered tube banks are independent of the inlet Reynolds and Prandtl numbers in the turbulent regime and equal to PL, opt ≅ 1 and PT, opt ≅ 1.3, respectively. As a result, a general compact arrangement for staggered tube banks is proposed that is applicable in practical applications due to its high efficiency and compactness.

On the optimization of the support vector machine regression hyperparameters setting for gas sensors array applications

Support Vector Machine Regression (SVR) has been shown to be more accurate compared to other machine learning techniques that are commonly used for chemical sensors arrays applications. However, the performance of SVR depends strongly on the selection of its hyperparameters. Most of time, researchers in this field rely on trivial grid search methods to find suitable values of SVR hyperparameters by minimizing the cross-validation prediction error. This method is not a practical solution because of the large domain of possible parameter values, which is further exacerbated by the lack of prior knowledge on the data. In this article, we investigate the optimization of SVR hyperparameters by combining the SVR algorithm with a simple algorithm for SVR parameters selection. We begin by studying the influence of each hyperparameter on SVR performance. We then propose the Generalized Pattern Search algorithm (GPS) as a faster alternative to determine these hyperparameters. Finally, we demonstrate that the proposed GPS algorithm, with its simplicity and robustness, gives similar results compared to more complicated alternatives, such as Genetic Algorithms, Simulating Annealing, Bayesian Optimization or Particle Swarm Optimization.

On the estimation and optimization capabilities of the fatigue life prediction models in composite laminates

In this study, the estimation and optimization capabilities of the multiaxial fatigue life prediction models, namely, Failure Tensor Polynomial in Fatigue, Fawaz–Ellyin, Sims–Brogdon and Shokrieh–Taheri are investigated comparatively. Fatigue life predictions are obtained for multidirectional graphite/epoxy, glass/epoxy, carbon/epoxy and carbon/PEEK composite laminate data taken from the literature. The prediction study shows that the models can predict the fatigue behavior of the multidirectional laminates at different degrees of proximity. In the optimization, a hybrid algorithm combining particle swarm algorithm and generalized pattern search algorithm is used to search the optimum stacking sequence designs of the laminated composites for maximum fatigue life. The hybrid algorithm shows superior performance in terms of computational time and finding improved global optima compared to the best results presented in the literature. After the capability of the models and the reliability of the algorithm are revealed, several lay-up design problems involving different cyclic loading scenarios are solved. The results indicate that the reliability of the optimization may considerably change according to the used model even if the model may yield reasonable prediction results.

Optimising the thermal environment and the ampacity of underground power cables using the gravitational search algorithm

This study takes into consideration a problem that commonly occurs at the design stage of underground cable lines and that relates to the manner of determining the optimal values for dimensions of cable trench and bedding, interaxial spacings between power cables in flat formation and cable ampacities. The problem is formulated as a non-linear optimisation problem with constraints. The gravitational search algorithm, simulated annealing algorithm and generalised pattern search algorithm are used to solve the problem. The optimal solutions are obtained based on the following three optimisation criteria: (i) minimisation of the total installation costs, i.e. the total costs for producing the cable trench, laying the bedding material, laying the backfill material and installing the cables, (ii) maximisation of the cable ampacity and (iii) a simultaneous application of the minimisation of the total installation costs and the maximisation of the cable ampacity. The constraints on design and control variables are introduced through penalty factors by means of which the objective function is expanded. The procedure is conducted taking into account the effect of drying out of the soil surrounding the cables.

Optimum design of fatigue-resistant composite laminates using hybrid algorithm

In this study, a fatigue life prediction model termed as Failure Tensor Polynomial in Fatigue (FTPF) is applied to the optimum stacking sequence design of laminated composites under various in-plane cyclic loadings to obtain maximum fatigue life. The validity of the model is investigated with an experimental correlation using the data available in the literature. The correlation study indicates the reliability of FTPF, and its applicability to different composite materials and multidirectional laminates. In the optimization, a hybrid algorithm combining genetic algorithm and generalized pattern search algorithm is used. It is found by test problems that the hybrid algorithm shows superior performance in finding global optima compared to the so far best results in the literature. After the verifications, a number of problems including different design cases are solved, and the optimum designs constituted of discrete fiber angles which give the maximum possible fatigue lives are proposed to discuss. A comparison study is also performed with selected design cases to demonstrate potential advantages of using non-conventional fiber angles in design.

A novel MPPT design using generalized pattern search for partial shading

This paper proposes a new Maximum Power Point Tracking (MPPT) technique for photovoltaic (PV) systems especially under Partial Shading (PS). This technique is based on Generalized Pattern Search (GPS) optimization algorithm. The proposed technique adopts the GPS algorithm owing to the reason that its major features like simple implementation, derivative free nature, fast convergence and high accuracy are ideally suited to deal with PS conditions. Furthermore, these features of GPS can well resolve the limitations and drawbacks of previous MPPT techniques, such as fluctuation, low efficiency, high complexity and slow convergence. For comparison, our proposed MPPT algorithm, the Particle Swarm Optimization (PSO) algorithm and the Perturb and Observe (P&O) algorithm have been implemented in MATLAB/Simulink. The comparison results demonstrate that the proposed MPPT technique can efficiently detect the global maximum (GM) in a fewer number of voltage samples, which is nearly 4 times less than the number of voltage samples required by PSO. Moreover, the steady state efficiency of the proposed MPPT is 99.8%, which is higher than the other MPPT techniques. Therefore, the proposed technique distinguishes itself from other MPPT techniques due to its superior quality in terms of convergence speed, dynamic and steady state efficiencies and low complexity.

Anisotropic oxidation prediction using optimized weight loss behavior of bismaleimide composites

High-temperature polymer matrix composites are susceptible to thermo-oxidation, which accelerates their degradation and reduces the service life. This work presents the viability of using experimental weight loss for modeling the spatial distribution of oxidation when the oxidized polymer matrix is not discernible due to cracking. The oxidized layer thickness and weight loss were predicted at a microscale level by implementing a volumetric integral in finite element analysis and scaled to a macroscale level by respective area ratios. Weight loss was shown to have a spatial distribution following the three-zone model. The proportionality parameter was optimized by fitting the scaled finite element predictions to the experimental results using artificial neural networks and a generalized pattern search algorithm. Aging experiments have been conducted at the operating temperature range of BMIs, 176.67 °C (350 °F) and 200 °C (392 °F). Optical dark field images were acquired to monitor longitudinal and transverse oxidation. Microscale simulations were conducted using representative volume elements utilizing COMSOL Multiphysics. A novel characteristic index for describing the completely oxidized matrix was the weight loss per unit volume that equals 0.44 mg/µm3 as shown by spatial distribution simulations. The orthotropic diffusivity resulted in a higher degree of anisotropy in the oxidized thickness compared to the weight loss %. At the representative volume element scale, the oxidized layer thickness simulations showed a higher degree of non-linearity at higher temperatures stemming from the cracking effect.

Windowed All Phase Biorthogonal Transform and Its Application in JPEG-Like Image Compression

This paper proposes new concepts of the windowed all phase biorthogonal transform (WAPBT), which is inspired by the all phase biorthogonal transform (APBT). In the light of windowed all phase digital filter theory, windowed all phase biorthogonal transforms is proposed. The matrices of WAPBT based on DFT, WHT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT, and the image compression scheme proposed in this paper is called WAPBT-based JPEG (WAPBT-JPEG). With optimal window sequence of WAPBT for image compression obtained by using generalized pattern search algorithm (GPSA), the peak signal to noise ratio (PSNR) and visual quality of the reconstructed images using the WAPBT-JPEG is outgoing DCT-based JPEG (DCT-JPEG) and APBT-based JPEG (APBT- JPEG) approximately at all bit rates. What is more, by comparison with DCT-JPEG, the advantage of proposed scheme is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation is easier. Index Terms—Windowed all phase biorthogonal transform (WAPBT), image compression, discrete cosine transform (DCT), JPEG algorithm, generalized pattern search algorithm (GPSA), windowed all phase digital filter (APDF)

The economics of timber and bioenergy production and carbon storage in Scots pine stands

We optimize timber and bioenergy production combined with carbon storage in Scots pine (Pinus sylvestris L.) stands, using an ecological-economic model. Forest growth is specified with a highly detailed process-based growth specification, and optimization is based on an efficient generalized pattern search algorithm. The optimized variables are rotation length, initial stand density, and the number, intensity, timing, and type of thinnings. The carbon pool includes all aboveground biomass (including dead trees) and timber products. The analysis includes the comparison of different carbon subsidy systems. The results are presented for the most relevant site types and thermal zones in Finland. Carbon storage increases the optimal rotation length, number of thinnings, and initial density at all forest sites. Carbon storage effects on stand density and harvests are strongest at poor sites. Timber output increases with carbon price. High natural mortality in our results implies notable carbon storage in dead trees and a positive contribution to biodiversity. The stand-level analysis is extended to a cost-efficient national-level carbon storage plan.