Quadratic Optimization Algorithm Research Articles

Efficient adaptive learning rate for convolutional neural network based on quadratic interpolation egret swarm optimization algorithm

Convolutional neural network (CNN) has recently become popular for addressing multi-domain image classification. However, most existing methods frequently suffer from poor performance, especially in performance and convergence for various datasets. Herein, we have proposed an algorithm for multi-domain image classification by introducing a novel adaptive learning rate rule to the conventional CNN. Specifically, we adopt the CNN to extract rich feature representations. Given that the hyperparameters of the learning rate have a positive effect on the prediction error, the Egret Swarm Optimization Algorithm (ESOA) is introduced to update the learning rate, which can jump out of local extrema during exploration. Therefore, combined with quadratic interpolation, the objective function can be approximated by a polynomial, thereby improving its prediction accuracy. To verify the robustness of the proposed algorithm, we conducted comprehensive experiments in five domain public datasets to fulfil the task of image classification. Meanwhile, the highest accuracy rate of 97.15 % was obtained on the test set. The performances of our method on 24 benchmark functions (CEC2017 and CEC2022) are compared with Particle Swarm Optimization (PSO), Genetic Algorithm(GA), Whale Optimization Algorithm(WOA), Catch Fish Optimization Algorithm(CFOA), GOOSE Algorithm(GO) and ESOA. In two benchmark sets, the performance metric values of our algorithm rank no. 1, especially in all unimodal functions in contrast with other baseline algorithms.

Advanced extraction of PV parameters’ models based on electric field impacts on semiconductor conductivity using QIO algorithm

This article presents a novel approach for parameters estimation of photovoltaic cells/modules using a recent optimization algorithm called quadratic interpolation optimization algorithm (QIOA). The proposed formula is dependent on variable voltage resistances (VVR) implementation of the series and shunt resistances. The variable resistances reduced from the effect of the electric field on the semiconductor conductivity should be included to get more accurate representation. Minimizing the mean root square error (MRSE) between the measured (I–V) dataset and the extracted (V–I) curve from the proposed electrical model is the main goal of the current optimization problem. The unknown parameters of the proposed PV models under the considered operating conditions are identified and optimally extracted using the proposed QIOA. Two distinct PV types are employed with normal and low radiation conditions. The VVR TDM is proposed for (R.T.C. France) silicon PV operating at normal radiation, and eleven unknown parameters are optimized. Additionally, twelve unknown parameters are optimized for a Q6-1380 multi-crystalline silicon (MCS) (area 7.7 cm2) operating under low radiation. The efficacy of the QIOA is demonstrated through comparison with four established optimizers: Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Salp Swarm Algorithm (SSA), and Sine Cosine Algorithm (SCA). The proposed QIO method achieves the lowest absolute current error values in both cases, highlighting its superiority and efficiency in extracting optimal parameters for both Single-Crystalline Silicon (SCS) and MCS cells under varying irradiance levels. Furthermore, simulation results emphasize the effectiveness of QIO compared to other algorithms in terms of convergence speed and robustness, making it a promising tool for accurate and efficient PV parameter estimation.

A memory interaction quadratic interpolation whale optimization algorithm based on reverse information correction for high-dimensional feature selection

Feature selection is a key technique for data dimensionality reduction, and there are many challenges in facing the exponential expansion phenomenon of high-dimensional decision space. In order to improve the quality of feature selection, we propose a memory interaction quadratic interpolation whale optimization algorithm based on reverse information correction (RQWOA). First, in order to improve the convergence capability of the Whale Optimization Algorithm (WOA) in high-dimensional space, we propose a quadratic interpolation mechanism with memory information interaction, improve the quality of the datum points used for quadratic interpolation through the proposed memory interaction mechanism, and accelerate the convergence speed and accuracy of the algorithm with the help of the quadratic interpolation on the algorithm exploitation capability. In addition, to address the invalid probability flip in the feature selection subset when mapping to the discrete space, we propose a reverse information correction mechanism to judge and correct each dimension in the feature subset by using the reverse complementary information provided by individuals with poor fitness values in the population, so as to better remove invalid or redundant features and improve the quality of feature selection. Finally, in the 15 high-dimensional feature datasets compared with the comparison methods, the accuracy of RQWOA is improved by 7.49 % on average, and the number of features is compressed by 80.42 % on average, which indicates that the RQWOA algorithm has stronger feature identification and redundancy removal capabilities and can better solve the feature selection problem.

Optimizing AVR system performance via a novel cascaded RPIDD2-FOPI controller and QWGBO approach.

Maintaining stable voltage levels is essential for power systems' efficiency and reliability. Voltage fluctuations during load changes can lead to equipment damage and costly disruptions. Automatic voltage regulators (AVRs) are traditionally used to address this issue, regulating generator terminal voltage. Despite progress in control methodologies, challenges persist, including robustness and response time limitations. Therefore, this study introduces a novel approach to AVR control, aiming to enhance robustness and efficiency. A custom optimizer, the quadratic wavelet-enhanced gradient-based optimization (QWGBO) algorithm, is developed. QWGBO refines the gradient-based optimization (GBO) by introducing exploration and exploitation improvements. The algorithm integrates quadratic interpolation mutation and wavelet mutation strategy to enhance search efficiency. Extensive tests using benchmark functions demonstrate the QWGBO's effectiveness in optimization. Comparative assessments against existing optimization algorithms and recent techniques confirm QWGBO's superior performance. In AVR control, QWGBO is coupled with a cascaded real proportional-integral-derivative with second order derivative (RPIDD2) and fractional-order proportional-integral (FOPI) controller, aiming for precision, stability, and quick response. The algorithm's performance is verified through rigorous simulations, emphasizing its effectiveness in optimizing complex engineering problems. Comparative analyses highlight QWGBO's superiority over existing algorithms, positioning it as a promising solution for optimizing power system control and contributing to the advancement of robust and efficient power systems.

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].

An efficient primal-dual interior point algorithm for convex quadratic semidefinite optimization

An efficient primal-dual interior point algorithm for convex quadratic semidefinite optimization

A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians

A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear-equality-constrained optimization problems in which the objective function is defined by an expectation. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, wherein each search direction is computed as the sum of a normal step (toward linearized feasibility) and a tangential step (toward objective decrease in the null space of the constraint Jacobian). However, the proposed method is unique from others in the literature in that it both allows the use of stochastic objective gradient estimates and possesses convergence guarantees even in the setting in which the constraint Jacobians may be rank-deficient. The results of numerical experiments demonstrate that the algorithm offers superior performance when compared with popular alternatives. Funding: This material is based upon work supported by the U.S. National Science Foundation’s Division of Computing and Communication Foundations under award [CF-1740796], by the Office of Naval Research under award [N00014-21-1-2532], and by the National Science Foundation under award [2030859] to the Computing Research Association for the CIFellows Project.

Optimization of graphene/fibre reinforced cantilever skew laminates for maximum fundamental frequency via non-uniform distribution of reinforcements

Three-phase graphene/fibre-reinforced cantilever skew laminates are optimized with the design objective of maximizing the fundamental frequency. Four optimal design problems are formulated involving one, two, three, and four design variables: graphene content, fibre content, layer thicknesses, and the fibre orientations. Optimization is implemented using a Sequential Quadratic Programming optimization algorithm within finite element analysis. It is observed that optimizing the graphene and fibre contents across the thickness leads to increased fundamental frequency. A trend is observed for the frequency of skew laminates to increase but for their design efficiency to decrease compared to rectangular laminates.

A graphic structure based branch-and-bound algorithm for complex quadratic optimization and applications to magnitude least-square problem

A graphic structure based branch-and-bound algorithm for complex quadratic optimization and applications to magnitude least-square problem

Multiband Pattern Synthesis of Time-Modulated Conformal Array with Quadratic Convex Optimization Algorithm

Aiming at the multiband pattern synthesis problem of time-modulated conformal array antenna, a quadratic convex optimization algorithm is proposed for sum and difference beamforming with low sidelobe levels. This articles method synthesizes a difference beam with a low sidelobe level by generating nulls at the center frequency band and optimizing the switch-on duration time of array elements. And the sum beamforming and sidelobe suppression of the first-order sideband are realized by optimizing the switch-on instant time of the array elements. The proposed algorithm has excellent properties of sidelobe suppression and angular sweep. The simulation results of circular and satellite array antenna verify the effectiveness of the algorithm.

A symmetric splitting sequential quadratic optimization algorithm for two-block nonlinearly constrained nonconvex optimization

In this paper, a double-step-length symmetric splitting sequential quadratic optimization (DSL-SS-SQO) algorithm for solving two-block nonconvex optimization with nonlinear constraints is proposed. First, at each iteration, the idea of symmetric splitting is embedded into solving the quadratic optimization (QO) subproblem approximating the discussed problem. As a result, the QO subproblem is split into two small-scale QOs, which can generate two improved search directions for the two primal variables. Second, the augmented Lagrangian function is used as the merit function, and two step sizes are yielded by performing the Armijo line search along the two improved directions. Third, under mild conditions, the global convergence, strong convergence, iterative complexity, and Maratos effect of the DSL-SS-SQO algorithm are proven. Finally, some numerical results are reported, comparisons with the results obtained by the IPOPT solver are also provided, which preliminarily show that the proposed algorithm is promising.

Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization

Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization

A ridge estimation-sequence quadratic programming constraint optimization algorithm for data processing in multi-spectral thermometry

Multi-spectral thermometry plays an important role in the field of high temperature measurement. The data processing is the focus of multi-spectral thermometry, which usually requires an hypothetical emissivity model. The deviation between the hypothetical model and the true emissivity can inevitably affect the accuracy of the true temperature inversion. In order to eliminate the influence of hypothetical model on data processing results, a ridge estimation-sequence quadratic programming constraint optimization algorithm for data processing in multi-spectral thermometry is proposed. The algorithm can simultaneously calculate the true temperature and spectral emissivity of the target without hypothetical emissivity model in advance. The efficiency and superiority of proposed algorithm can be confirmed by the simulation results.

GPU-accelerated scalable solver with bit permutated cyclic-min algorithm for quadratic unconstrained binary optimization

A wide range of combinatorial optimization problems can be reduced to the Ising model, and equivalently the quadratic unconstrained binary optimization (QUBO) problem. Thus, in recent years, researchers have proposed to solve QUBO on FPGAs, GPUs, and special-purpose processors. The adaptive bulk search (ABS) is a previously-proposed framework for solving QUBO in parallel on multiple GPUs. In the ABS, a CPU host performs a GA-based global search while GPUs asynchronously perform many local searches in parallel. An original ABS adopts a simple local search algorithm called a cyclic-min algorithm, which does not use pseudo random numbers. However, the lack of randomness may cause a potential drawback of restricted bit-flipping operations in a local search. To avoid this drawback, this paper proposes a cyclic-min algorithm with randomly-generated multiple bit permutations, which enables a more effective local search with random number generation in CPUs (not in GPUs). Furthermore, this paper introduces a scalable implementation of the ABS with MPI and OpenMP. Our experimental results on TSUBAME3.0 show that the solution quality improves and the throughput linearly increases as the number of GPUs increases; with 256 GPUs, it evaluates 20.1×1012 solutions per second.

Optimization of a Permanent Magnet Synchronous Motor for e-Mobility Using Metamodels

Permanent magnet synchronous motors (PMSMs) with rectangular coils in hairpin windings exhibit improved fill factor and reduced end turn of the coils, which in turn improve the efficiency and power density of PMSMs, making them ideal for e-mobility applications. Herein, the shape of a PMSM was optimized for torque ripple reduction using metamodels to improve the noise and vibrational performance of the motor. The objective function of the optimal design aimed to minimize the torque ripple, and the average torque and efficiency were set as constraints. The notch width and depth and barrier length were selected as the design variables to satisfy the objective function and constraints. Using the optimal Latin hypercube design technique, 27 experimental points were selected, and a finite element analysis (FEA) was performed for each point. Furthermore, a function approximation was performed using six metamodels, and the best metamodel was selected using the root mean square error test. Moreover, the optimization was performed by combining the best metamodels for each variable with a sequential two-point diagonal quadratic approximation optimization algorithm. The torque ripple was improved by approximately 1.63% compared with the initial model, whereas the constraint values remained constant. Finally, an FEA was performed on the optimal point, and the FEA results matched with those of the optimal method.

An efficient self‐healing network through quadratic probing optimization mechanism

SummaryIn recent years, mobile networks have been widely used in wide range of applications. Complexity is one of the major issues in mobile networks. The best way to administer the complexity of recent mobile networks is self‐organizing networks. Whenever a fault occurs in the network or in a node, it must be identified and at the same time, healed from within for smooth operation. In this paper, self‐healing is achieved by using a quadratic probing optimization algorithm. This algorithm has a time complexity using O (log n). A self‐healing algorithm is proposed here that uses self‐healing mechanisms to detect, identify, and respond to node breaks.

A chaotic strategy-based quadratic Opposition-Based Learning adaptive variable-speed whale optimization algorithm

In this paper, a chaotic strategy-based quadratic opposition-based learning adaptive variable-speed whale optimization algorithm is proposed. The improved algorithm is used to solve the problems that the whale optimization algorithm’s convergence accuracy and convergence speed are insufficient. Firstly, the proposed algorithm is initialized by a method based on chaotic maps and quadratic opposition-based learning strategy to obtain a population with better ergodicity. Secondly, by introducing an adaptive variable speed adjustment factor, each search link unites to form a negative feedback regulation network, thereby effectively balancing the algorithm’s exploration ability and exploitation ability. Finally, 20 benchmark test functions and 3 complex constrained engineering optimization problems were used to conduct extensive tests on the improved algorithm. The results show that the improved algorithm has better performance than others in terms of convergence speed and convergence accuracy in a majority of cases, and can effectively jump out of the local optimum.

Design and experiment of multi-mode steering system of agricultural machinery for hilly and mountainous area

In order to improve the steering flexibility of agricultural machinery in hilly and mountainous areas, a multi-mode steering system with front wheel steering, rear wheel steering, and four-wheel steering has been developed. The hydraulic steering system based on load sensitivity principle and proportion-integration-differentiation (PID) controlling algorithm was designed, which overcomes the negative impact of external load changes on flow control accuracy. The mechanical-hydraulic-controlling coupling model established in the AMESim and the sequential quadratic combinatorial optimization algorithm (SQCOA) was adopted to obtain the optimal combination of PID parameters. The simulation results demonstrate that the parameters such as pressure, speed, displacement of hydraulic cylinders, etc. in different steering modes meet the design requirements. To examine and verify the system performance, the test platform was researched and developed for conducting steering radius and displacement measurement. The experimental data illustrated that the front and rear hydraulic cylinders have good synchronization accuracy in four-wheel steering mode, and the fast switch of steering mode can be realized. The maximum error rate of is steering radius 4.21% and 3.77%, respectively, in two-wheel steering and four-wheel steering modes. The research methods and conclusions can provide a theoretical basis and reference for the other steering system development.

DEFT-FUNNEL: an open-source global optimization solver for constrained grey-box and black-box problems

The fast-growing need for grey-box and black-box optimization methods for constrained global optimization problems in fields such as medicine, chemistry, engineering and artificial intelligence, has led to the development of new efficient algorithms for finding the best possible solution. In this work, we present DEFT-FUNNEL, an open-source global optimization algorithm for general constrained grey-box and black-box problems that belongs to the class of trust-region sequential quadratic optimization algorithms. Polynomial interpolation models are used as surrogates for the black-box functions and a clustering-based multistart strategy is applied for searching for the global minima. Numerical experiments show that DEFT-FUNNEL compares favorably with state-of-the-art methods on two sets of benchmark problems: one set containing problems where every function is a black box and another set with problems where some of the functions and their derivatives are known to the solver. The code as well as the test sets used for experiments are available at the Github repository http://github.com/phrsampaio/deft-funnel.

A decision space algorithm for multiobjective convex quadratic integer optimization

We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks for efficient points by fixing subsets of variables to integer values and by using lower bounds in the form of hyperplanes in the image space derived from the continuous relaxations of the restricted objective functions. We show that the algorithm stops after finitely many fixings of variables with detecting both the full efficient and the nondominated set of multiobjective strictly convex quadratic integer problems. A major advantage of the approach is that the expensive calculations are done in a preprocessing phase so that the nodes in the branch-and-bound tree can be enumerated fast. We show numerical experiments on biobjective instances and on instances with three and four objectives.