Gradient Search Algorithm Research Articles

A Recursive Optimization Approach for Buffer Allocation in Large Production Lines

Buffer allocation is a critical issue in the design stage of manufacturing systems, as buffer capacities may have a great impact on system performance. In this paper, we consider the problem of minimizing the total buffer capacity of a flow line to achieve a desired production rate. A recursive optimization approach is proposed to solve the problem in large production lines. Instead of optimizing a long line directly, the proposed approach decomposes it into two sub-lines, optimizes them recursively, and combines their solutions to find the optimal buffer distribution of the original line. Two different recursive algorithms are developed and their performance is demonstrated by comparing them with a gradient search algorithm. The numerical results show that the recursive algorithms are almost as accurate as the gradient algorithm, but much more efficient, especially for large production lines.

IMUPF-BIN: A new autonomous search method for radioactive sources

To solve the problem of mobile robots autonomously searching for unknown radioactive sources, this paper proposes an automatic source search strategy, abbreviated as IMUPF-BIN: the location of the radioactive source is estimated by improved unscented particle filtering (IMUPF) algorithm, and the search path is predicted and planned by bioinspired neural network (BIN) model. First, the search environment is expressed as an occupied grid map, and the BIN model is combined with the grid occupied map to obtain the environment information in the search process. Then, the unscented particle filter (UPF) which is used for source parameter estimation is improved by introducing the idea of linear optimization to improve the efficiency of particle usage and the diversity of particles. Further, the BIN model is introduced to reduce the influence of obstacles on the movement of the robot, thereby improving the search accuracy and efficiency of radioactive source. After the robot detects the radiation count value, the parameter information of the source is estimated through the IMUPF algorithm. By using the activity value of the BIN model and distributed model predictive control (DMPC) to plan the path, while continuously iterating the search process, the location of the radioactive source is finally determined. The simulation results show that in without obstacles environment, the localization accuracy of the IMUPF algorithm is improved by 85.6% and 52.8% compared to the standard particle filtering (PF) and UPF algorithm respectively, and the search time of the IMUPF-BIN algorithm is reduced by 75.9% compared to the gradient search (GS) algorithm. In obstacles environment, the localization accuracy of the IMUPF algorithm is improved by 80.8% and 35.9% compared to the PF and UPF algorithms respectively. In addition, the GS algorithm fails to search for the radioactive source due to the shield of obstacles, while the IMUPF-BIN algorithm can successfully search for radioactive source in a shorter search time.

Shunted piezoelectric patch adaptive vibration absorber set to maximise electric power absorption: A comparison between parallel and series RL-shunts

This paper presents a comparative study on two types of shunted piezoelectric patch adaptive vibration absorbers, which can be bonded in batches on thin-walled structures to control the broad-band resonant response of low order flexural modes. The self-contained control units are formed by a thin piezoelectric patch connected either to a series or to a parallel resistive-inductive (RL) network. The two components of the shunt are adapted online in such a way as to maximise the time-averaged electric power absorbed by the shunt, which corresponds to minimising the time-averaged total flexural response of the hosting structure. The study considers a practical demonstrator formed by a thin rectangular plate with five piezoelectric patches connected to digital RL-shunts, which is excited in bending by a stationary white noise point force. The aim of the paper is to contrast the tuning and vibration control properties of the series and parallel RL shunts. More specifically, the online implementation of a recursive two-paths tuning strategy along R-constant and L-constant paths with an extremum seeking gradient search algorithm is analysed first for the two types of shunts. Then, the vibration control performance produced by the two types of shunts is investigated for the case where they are tuned to control the resonant response of the first flexural mode of the plate.

Decision variable classification based multi-objective multifactorial memetic algorithm for multi-objective multi-task optimization problem

Multi-task multi-objective optimization problems need to consider the algorithm's convergence and the population's diversity. The information transfer of decision variables with different characteristics may harm the effect of knowledge reuse. This paper proposes a novel hybrid multi-objective multifactorial memetic algorithm to address this issue. The proposed variable classification method will classify decision variables into convergence-related and diversity-related decision variables. Only the same type of decision variables in the source and target tasks can transfer information to avoid negative transfer. Different evolutionary operators are adopted according to the characteristics of decision variables during individual recombination. In addition, the proposed algorithm hybridizes the immune algorithm as the global evolutionary operator and the evolutionary gradient search algorithm as the local search operator into the multifactorial framework to enhance the searching ability. Finally, the proposed algorithm is compared with the state-of-the-art multi-objective evolutionary multitasking algorithms. The results of the experiments show that the proposed algorithm can achieve promising performance on the classical and complex multi-task multi-objective benchmark test suites.

A hybrid capuchin search algorithm with gradient search algorithm for economic dispatch problem

A hybrid capuchin search algorithm with gradient search algorithm for economic dispatch problem

ACA: Automatic search strategy for radioactive source

Nowadays, mobile robots have been used to search for uncontrolled radioactive source in indoor environments to avoid radiation exposure for technicians. However, in the indoor environments, especially in the presence of obstacles, how to make the robots with limited sensing capabilities automatically search for the radioactive source remains a major challenge. Also, the source search efficiency of robots needs to be further improved to meet practical scenarios such as limited exploration time. This paper proposes an automatic source search strategy, abbreviated as ACA: the location of source is estimated by a convolutional neural network (CNN), and the path is planned by the A-star algorithm. First, the search area is represented as an occupancy grid map. Then, the radiation dose distribution of the radioactive source in the occupancy grid map is obtained by Monte Carlo (MC) method simulation, and multiple sets of radiation data are collected through the eight neighborhood self-avoiding random walk (ENSAW) algorithm as the radiation data set. Further, the radiation data set is fed into the designed CNN architecture to train the network model in advance. When the searcher enters the search area where the radioactive source exists, the location of source is estimated by the network model and the search path is planned by the A-star algorithm, and this process is iterated continuously until the searcher reaches the location of radioactive source. The experimental results show that the average number of radiometric measurements and the average number of moving steps of the ACA algorithm are only 2.1% and 33.2% of those of the gradient search (GS) algorithm in the indoor environment without obstacles. In the indoor environment shielded by concrete walls, the GS algorithm fails to search for the source, while the ACA algorithm successfully searches for the source with fewer moving steps and sparse radiometric data.

An Optimization-based Adaptive Sliding Mode Control for an Inverted Pendulum

The work proposes an optimization-based robust adaptive gain sliding mode control technique to handle bounded behavior of uncertainties/perturbations without having the exact knowledge of the bound a priori. The constant of the sliding surface follows dynamical adaptive nature using three optimization techniques, i.e. Harmony Search Algorithm, Bacterial Foraging Optimization Algorithm and Gradient Search Algorithm to extenuate the extent of chattering. The gain of the switching control law, which is a part of the sliding mode control design, is calculated using the gain adaption technique. Lyapunov Stability Criterion is applied to assure the stability of the closed-loop system with adaptable gain and the optimized value of the sliding constant. An inverted Pendulum system has been taken to validate the proposition both in the simulation environment and the hardware platform.

Energy-efficient full-duplex D2D for SWIPT-empowered underlay cellular networks using a deep neural network

Close-packed small-cell networks enables a device-to-device (D2D) user equipment (DUE) to harvest energy from an ambient source, which increases the energy efficiency of the devices. Conceptually, full-duplex (FD) communications can double spectral efficiency compared to traditional half-duplex (HD) communications. However, the use of FD mode increases self-interference, which impacts spectral capacity and energy efficiency. In this paper, we study the performance of full-duplex D2D underlay cellular networks, where D2D devices decipher information and harvest energy simultaneously using SWIPT technology. Specifically, we build an optimization model to maximize the energy efficiency of the system, and obtain global- and sub-optimal solutions from the exhaustive search (ES) algorithm and the gradient search (GS) with barrier algorithm, respectively. In addition, we design deep neural networks (DNN) algorithm for the optimization model and evaluate the performance of the proposed DNN algorithm compared to the ES and GS algorithms. From the results, we confirm that the FD mode outperforms the HD mode in terms of energy efficiency and sum-rate and the proposed DNN algorithm can achieve near-global-optimal solution.

Piezoelectric patch vibration control unit connected to a self-tuning RL-shunt set to maximise electric power absorption

This paper presents a modular vibration control unit formed by a piezoelectric patch connected to a self-tuning RL-shunt, which can be bonded on thin structures to reduce the resonant response of a specific target low-order flexural mode due to a stationary stochastic excitation. The resistive and inductive components of the shunt are tuned online with an extremum seeking gradient search algorithm in such a way as to maximise the time-averaged electric power absorbed by the shunt from the resonant response of the target flexural mode of the structure. The tuning is thus implemented locally in the unit without the need of additional sensors to monitor the vibration of the structure. The paper presents both simulation and experimental results for a thin rectangular panel model structure, which is excited by a broadband stationary stochastic force and is equipped with five piezoelectric patches connected to the proposed self-tuning RL-shunts. To start with, the study shows that the resistance and inductance necessary to minimise the time-averaged resonant response of the target flexural mode closely match the values that would maximise the time-averaged electric power absorption by the shunt from the resonant response of the target flexural mode. Also, it shows that these two cost functions describe mirrored bell-surfaces with constant-inductance and constant-resistance principal axes. Hence, it proposes an independent inductance and resistance tuning sequence, which is based on an extremum seeking gradient search algorithm along the two principal directions of the electric power cost function. Finally, the online convergence to the optimal RL values of the proposed tuning algorithm is verified experimentally using a digital shunt.

Nonlinear optimization algorithm using monotonically increasing quantization resolution

AbstractWe propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed‐point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round‐off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round‐off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization‐based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

Extremum seeking online tuning of a piezoelectric vibration absorber based on the maximisation of the shunt electric power absorption

This paper is focussed on the extremum seeking online tuning of a shunted piezoelectric vibration absorber for the broadband control of the resonant response of a mechanical system subject to a stationary stochastic excitation. Two shunt circuits are considered, which are formed by a resistor and an inductor connected either in series or in parallel. The two components are tuned in such a way as to maximise the time-averaged electric power absorbed by the shunt, that is the time-averaged electric power dissipated by the shunt resistor. The paper shows that the proposed tuning approach leads to the same optimal resistive-inductive components of the shunt that would minimise the time-averaged vibration response of the mechanical system. Also, it demonstrates that the electric power objective function is characterised by a bell-type non-convex surface with a single maximum. Furthermore, it shows that the cost function has two principal directions characterised by constant-resistance and constant-inductance respectively. Accordingly, a two-paths tuning sequence is proposed, where the shunt inductance and resistance are tuned sequentially with an extremum seeking gradient search algorithm, which efficiently finds the optimal values by working along the two principal directions.

Градієнтна оптимізація двопараметричної віконної функції Найквіста для зменшення позасмугогово випромінювання в OFDM системі

The relationship between Nyquist pulses in the time domain and Nyquist window functions used in orthogonal frequency division multiplexing (OFDM) technology has been investigated. One of the ways to approximate the transition region of Nyquist window functions using piecewise linear functions has been analyzed. This method allowed increasing the number of degrees of signal freedom through the introduction of two additional parameters. The spectral density of the selected two-parameter Nyquist window function has been determined. Optimization of the synthesized signal by the criterion of minimum energy in the first side lobes of its spectral density has been performed. To solve the optimization problem, the gradient descent method with minimization of the function at each stage of the iteration by the golden section method is chosen. In the MATLAB programming environment, program has been created that works according to the selected optimization algorithm. With the maximum allowable relative error ε =10–3, the number of iterations of the gradient search method is 2 iterations. It is established that at the optimal values of the signal parameters the amount of energy concentrated in the first three side lobes of its spectral density is 12.6 dB less than for the rectangular window function. The graphs for the synthesized window function with optimal parameters in time and frequency domain are given in this paper. The use of the two-parameter Nyquist window function with reduced level of spectral density of the side lobes allows reducing the level of out-of-band radiation of the OFDM signal and increasing the resistance of the system with many subcarriers to frequency offsets caused by the mutual movement of the transmitter and receiver. It should be noted that the chosen gradient search algorithm is universal and can be used to optimize the Nyquist window functions by different criteria and regardless of the number of signal parameters.

Effective Online Order Acceptance Policies for Omnichannel Fulfillment

Problem definition: Omnichannel retailing has led to the use of traditional stores as fulfillment centers for online orders. Omnichannel fulfillment problems have two components: (1) accepting a certain number of online orders prior to seeing store demands and (2) satisfying (or filling) some of these accepted online demands as efficiently as possible with any leftover inventory after store demands have been met. Hence, there is a fundamental trade-off between store cancellations of accepted online orders and potentially increased profits because of more acceptances of online orders. We study this joint problem of online order acceptance and fulfillment (including cancellations) to minimize total costs, including shipping charges and cancellation penalties in single-period and limited multiperiod settings. Academic/practical relevance: Despite the growing importance of omnichannel fulfillment via online orders, our work provides the first study incorporating cancellation penalties along with fulfillment costs. Methodology: We build a two-stage stochastic model. In the first stage, the retailer sets a policy specifying which online orders it will accept. The second stage represents the process of fulfilling online orders after the uncertain quantities of in-store purchases are revealed. We analyze threshold policies that accept online orders as long as the inventories are above a global threshold, a local threshold per region, or a hybrid. Results: For a single period, total costs are unimodal as a function of the global threshold and unimodal as a function of a single local threshold holding all other local thresholds at constant values, motivating a gradient search algorithm. Reformulating as an appropriate linear program with network flow structure, we estimate the derivative (using infinitesimal perturbation analysis) of the total cost as a function of the thresholds. We validate the performance of the threshold policies empirically using data from a high-end North American retailer. Our two-location experiments demonstrate that local thresholds perform better than global thresholds in a wide variety of settings. Conversely, in a narrow region with negatively correlated online demand between locations and very low shipping costs, global threshold outperforms local thresholds. A hybrid policy only marginally improves on the better of the two. In multiple periods, we study one- and two-location models and provide insights into effective solution methods for the general case. Managerial implications: Our methods provide effective algorithms to manage fulfillment costs for online orders, demonstrating a significant reduction over policies that treat each location separately and reflecting the significant advantage of incorporating shipping in computing thresholds. Numerical studies provide insights as to why local thresholds perform well in a wide variety of situations.

Proximal Policy Optimization for Radiation Source Search

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the advantage actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized 20×20 m convex and non-convex simulation environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than 95% median completion rate for up to seven obstructions.

An innovative approach to solve the carsharing demand-supply imbalance problem under demand uncertainty

This paper studies the demand-supply imbalance problem for one-way carsharing systems under a combination of pricing strategy, relocations and access trips considering stochastic demand. A novel concept of a virtual zone is utilized to capture vehicle relocation range and client walking or biking distance constraints in one-way carsharing systems. The vehicle imbalance problem is further addressed by combining a long-term pricing strategy and real-time vehicle relocations in a two-stage stochastic programming model. In the first stage, the tactical decisions including fleet size and trip price are optimized, while anticipating the operational costs from the second stage. The second stage optimizes operational decisions under uncertain demand including vehicle relocations conditional on the tactical decisions in stage one. The model aims to maximize the profit of a carsharing company considering the fleet costs calculated in stage one and the expected operational costs and revenue obtained in stage two. A dedicated gradient search algorithm is developed to solve the two-stage stochastic programming and results are compared to a genetic algorithm and an iterated local search algorithm. The proposed model and corresponding solution approach are applied to a large-scale network with 50 zones and over 1000 vehicles in Suzhou, China. The application allows us to attain additional operational insight. Results suggest that increased prices for high demand stations during peak hours reduce demand while maintaining profitability of the system. It is also found that the real-time vehicle relocations and flexibility of clients to pick up vehicles at farther stations can increase demand service rate by as much as 10%.

Adaptive Gradient Search Algorithm for Displaced Subarrays With Large Element Spacing

In this letter, an adaptive gradient search algorithm for displaced subarray optimization is presented. The displaced subarray technique, which is able to suppress the high grating lobes caused by large interelement spacing (i.e., over one-half wavelength), has attracted much attention. In this case, it could reduce the number of active elements as well as the cost of conventional phased array antennas. However, the optimal solution of each displaced subarray location is hard to achieve. The proposed algorithm is a practical method to solve such a nonconvex problem. By gradually reducing the iteration step size, when the search times of each step are enough, the solution is able to converge to a satisfying solution. The effectiveness and the stable performance of our proposed method are verified by various numerical examples.

An Intelligent Geomagnetic Search Navigation Method Based on Evolutionary Gradient Strategy

Currently, most of the geomagnetic navigation methods are matching navigation algorithms, which require the geomagnetic maps retrieved in advance, and saved in a database. However, there are a great number of unknown environments exist worldwide that limit the extensive application of the geomagnetic matching method in practice. In this paper, an intelligent geomagnetic search navigation method based on the evolutionary gradient search (EGS) algorithm is proposed. The performance of the search and navigation method is analysed with both simulated and real geomagnetic data. And the conclusion is that compared with other intelligent search strategies, the proposed algorithm has better navigation performance with less average navigation error, 161m, which is equivalent to the most traditional geomagnetic matching algorithms. Thus, the EGS algorithm proposed in this paper can effectively improve the performance of geomagnetic navigation without prior geomagnetic information.

Bent-cable quantile regression model

This article considers a bent-cable quantile regression model that comprises two linear segments but is smoothly jointed by a quadratic bend. This model is very flexible to allow the relationship between the response variable and a covariate of interest to change gradually or abruptly across a change point value in the covariate. However, due to the non-differentiability of the objective function in quantile regression, it is challenge to estimate the unknown parameters. Our work aims to develop a gradient-search algorithm to obtain the estimators of the regression coefficients and the change point location. We establish the asymptotic properties of proposed estimators by using the modern empirical processes theory. Monte Carlo simulation studies and an economic empirical application illustrate the good performance of our procedures.

Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration

Smoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nesterov’s acceleration for stochastic optimization problems. The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations’ (o.d.e.) stability for a non-autonomous system. We compare our algorithm with other smoothed functional algorithms such as Quasi-Newton SF, Gradient SF and Jacobi Variant of Newton SF on two different optimization problems: first, on a simple stochastic function minimization problem, and second, on the problem of optimal routing in a queueing network. Additionally, we compared the algorithms on real weather data in a weather prediction task. Experimental results show that our algorithm performs significantly better than these baseline algorithms.

Wing Thickness Optimization for Box Wing Aircraft

Background: In the interest of improving aircraft performance, studies have highlighted the benefits of Box wing configurations over conventional cantilever aircraft configuration. Generally, the greater an aircraft's average thickness to chord ratio (τ), the lower the structural weight as well as volumetric capacity for fuel. On the other hand, the lower the , the greater the drag reduction. A review of patents related to the Box-wing aircraft was carried out. While methodologies for optimizing wing thickness of conventional aircrafts have been studied extensively, limited research work exist on the methodology for optimizing the wing thickness to chord ratio of the Box wing aircraft configurations. Methods: To address this gap, in this work, a two stage optimization methodology based on gradient search algorithm and regression analysis was implemented for the optimization of Box wing aircrafts wing thickness to chord ratio. The first stage involved optimizing the All Up Mass (AUM), Direct Operating Cost (DOC) and Zero Lift Drag Coefficients (CDO), with respect to the aft and fore sweep angle for some selected τ values. At the second stage, a suitability function (γ) was optimized with respect to the aft and fore sweep angle for some selected τ values. A comparative study was further carried out using the proposed methodology on similar size cantilever wing aircraft. Results: From the result, an optimal τ value was reached. Also the τ value for the cantilever aircraft found based on the proposed methodology was similar to the true τ value of the adopted aircraft, thereby validating the methodology. Conclusion: Based on the optimal τ value reached from this work, the Box wing aircraft are suitable for thin airfoils.