Backtracking Search Algorithm Research Articles

Boosting particle swarm optimization by backtracking search algorithm for optimization problems

Boosting particle swarm optimization by backtracking search algorithm for optimization problems

Backtracking search algorithm with dynamic population for energy consumption problem of a UAV-assisted IoT data collection system

In recent years, collecting data from IoT devices by unmanned aerial vehicles (UAVs) has become a very hot research topic. This paper focuses on the energy consumption problem of a UAV-based IoT data collection system. To solve the considered energy consumption problem, this paper proposes a new population-based optimization algorithm called the backtracking search algorithm with dynamic population (BSADP), which can determine the optimal number and locations of stop points of the UAV simultaneously. In addition, BSADP has a simple framework, which consists of the proposed enhanced backtracking search algorithm (EBSA) and the designed population adjustment mechanism with opposition-based learning (PAMOBL). In the search process, the population is regarded as the entire deployment of the UAV. BSADP firstly generates the trail deployment of the UAV by EBSA and then the next generation deployment of the UAV is produced based on the trail deployment and PAMOBL. The performance of BSADP is investigated by two energy consumption formulations. Experimental results support the superiority of BSADP in optimizing the deployment of the UAV and prove the application value of BSADP in the real scenario. The source code of the proposed algorithm can be found from: https://github.com/jsuzyy/BSADP.

Solving optimal power flow problem for IEEE-30 bus system using a developed particle swarm optimization method: towards fuel cost minimization

ABSTRACT The optimal power flow (OPF) is an important technique for optimizing the control parameters of modern power systems by taking into account the desired objective functions considering system constraints. This paper provides a developed particle swarm optimization (PSO) method for solving the OPF problem with a rigorous objective function of minimizing generation fuel costs for the utility and industrial companies while satisfying a set of system limitations. By reviewing previous OPF investigations, the developed PSO is used in the IEEE 30-bus test system to reduce overall fuel cost, active/reactive power losses, and exhaust. The obtained results are compared to those obtained using a typical PSO technique and other algorithms. In the IEEE 30-bus test system, one of the paper’s key findings is that the cost of fuel is computed as 800.41 $/h, 830.7779 $/h, 825.6922 $/h, 826.54 $/h, 826.3176 $/h, 823.3999 $/h, 786.03 $/h with the conventional PSO, backtracking search algorithm (BSA), hybrid SFLA-SA, differential evolution (DE), enhanced GA (EGA), monarch butterfly optimization (MBO), proposed algorithm, respectively. Moreover, there is a great reduction in the fuel cost by 4.358% compared with the robust MBO algorithm. MATLAB software is used to demonstrate the effectiveness and accuracy of the proposed technique.

Backtracking search algorithm driven by generalized mean position for numerical and industrial engineering problems

Backtracking search algorithm driven by generalized mean position for numerical and industrial engineering problems

An Optimal Multi-Objective Approach for Distributed Generation and AVR Placement in Distribution Networks Using IPMBSA

Inclusion of automatic voltage regulators (AVRs) and distributed generation units (DGs) in the distribution system (DS) will enhance the system performance if allocated optimally. Optimal allocation of AVRs and DGs is a complex combinatorial problem requiring a powerful optimization algorithm for solving the optimization problem. This paper proposes an improved pareto multi-objective backtracking search algorithm (IPMBSA) based Pareto front approach for optimal siting and sizing of DGs and AVRs. The proposed approach considers DS technical (such as minimizing of voltage deviation, power losses and voltage stability index), cost and emission indices as objective functions while solving the allocation problem. To evaluate the performance of the proposed approach, five different operational scenarios are considered for analysis on IEEE 33-bus, IEEE 69-bus and practical 43-bus Indian distribution test systems. The effectiveness of the proposed approach is highlighted by comparison of results obtained using a multi-objective approach based on NSGA-II and weighted sum method (WSM). Results propounded that allocation of DG along with AVR yielded better DS performance compared to the scenarios where only DG or AVRs are placed in DS.

Multilayer Perceptron and Their Comparison with Two Nature-Inspired Hybrid Techniques of Biogeography-Based Optimization (BBO) and Backtracking Search Algorithm (BSA) for Assessment of Landslide Susceptibility

Regarding evaluating disaster risks in Iran’s West Kurdistan area, the multi-layer perceptron (MLP) neural network was upgraded with two novel techniques: backtracking search algorithm (BSA) and biogeography-based optimization (BBO). Utilizing 16 landslide conditioning elements such as elevation (aspect), plan (curve), profile (curvature), geology, NDVI (land use), slope (degree), stream power index (SPI), topographic wetness index (TWI), rainfall, and sediment transport index (STI), and 504 landslides as target variables, a large geographic database is constructed. Applying the techniques mentioned above to the synthesis of the MLP results in the suggested BBO-MLP and BSA-MLP ensembles. As accuracy standards, we benefit from mean absolute error, mean square error, and area under the receiving operating characteristic curve to assess the utilized models, we have also designed a scoring system. The MLP’s accuracy increases thanks to the application of the BBO and BSA algorithms. Comparing the BBO with the BSA, we find that the former achieves higher average MLP optimization ranks (20, 15, and 14). A further finding showed that the BBO is superior to the BSA at maximizing the MLP.

Start-up process optimization of pumped-storage unit with Tilt–Integral–Derivative controller

Focused on the hydraulic–mechanical coupled transient behaviors of the pumped-storage unit (PSU), this paper discusses the theoretical implementation and the parameter optimization of tilt–integral–derivative (TID) controller in turbine start-up processes. A novel learning backtracking search algorithm (LBSA) is adapted to optimize the control parameters, and a comprehensive index combining the relative deviation of the rotational speed and the relative deviation of the volute’s water pressure is designed as the objective function. A nonlinear mathematical model which can reflect hydraulic and mechanical dynamic characteristics of the pumped-storage governing system (PSGS) is established for the simulation of the transient period. Simulation experiments of two typical operating conditions are carried out under no-load condition. The simulation results show that the TID controller attaches significance to suppressing the amplitude of water hammer pressure and damping the hydraulic fluctuations. It will also restrain the trend of state trajectories oscillating back and forth in the unstable “S” shaped regions.

Optimization Using Backtracking Search Algorithm for the Design of Magnetron Anode Block and Pill-Box RF Window

Optimization Using Backtracking Search Algorithm for the Design of Magnetron Anode Block and Pill-Box RF Window

An Optimized Machine Learning Approach for Forecasting Thermal Energy Demand of Buildings

Recent developments in indirect predictive methods have yielded promising solutions for energy consumption modeling. The present study proposes and evaluates a novel integrated methodology for estimating the annual thermal energy demand (DAN), which is considered as an indicator of the heating and cooling loads of buildings. A multilayer perceptron (MLP) neural network is optimally trained by symbiotic organism search (SOS), which is among the strongest metaheuristic algorithms. Three benchmark algorithms, namely, political optimizer (PO), harmony search algorithm (HSA), and backtracking search algorithm (BSA) are likewise applied and compared with the SOS. The results indicate that (i) utilizing the properties of the building within an artificial intelligence framework gives a suitable prediction for the DAN indicator, (ii) with nearly 1% error and 99% correlation, the suggested MLP-SOS is capable of accurately learning and reproducing the nonlinear DAN pattern, and (iii) this model outperforms other models such as MLP-PO, MLP-HSA and MLP-BSA. The discovered solution is finally expressed in an explicit mathematical format for practical uses in the future.

Aeroelastic tailoring of composite rudder skin considering variable angle tow laminates by a hybrid backtracking search-JAYA-Sine Cosine Algorithm

Flutter is a typical dynamic instability phenomenon of the wing or rudder structure. Besides, the phenomenon of aerodynamic heating will be quite significant and temperature can rise rapidly with the increase of the flight speed, thermal flutter characteristics should be taken into consideration for the rudder structure of supersonic vehicle. To improve the thermal flutter characteristics of the rudder structure and meet the design requirements of a lightweight structure, this article optimizes the variable stiffness laminates of the skin on the premise of keeping the thickness of the skin unchanged, so as to improve the critical flutter speed of the rudder. A novel intelligent optimization algorithm named BJASCA, which is a hybrid algorithm coupling of Backtracking Search Algorithm, Sine Cosine Algorithm, and JAYA Algorithms is proposed in this article to improve the efficiency of structural optimization and this algorithm shows obvious advantages in searching global optima compared with several other algorithms. The finite element model and aerodynamic model of the rudder are established to calculate the critical flutter speed. The results represent that the rudder structure optimized by the BJASCA algorithm shows better flutter characteristics and the critical flutter speed can be increased by 76.4% compared with the un-optimized structure.

A generalized adaptive Levenberg–Marquardt method for solving nonlinear ill-posed problems

We investigate the method of regularization for the stable approximate solution to nonlinear ill-posed problems whose forward operators may not be Gâteaux differentiable. The method is designed by combining the classical Levenberg–Marquardt method with the two-point gradient iteration, and the adaptive stepsize which is related to the Tikhonov regularization parameter and the structure of the forward operator. In order to further enhance the acceleration effect, we employ a modified discrete backtracking search algorithm to determine the combination parameters involved. With the help of the concept of asymptotic stability and a generalized tangential cone condition, the convergence analysis of the proposed method is studied. Moreover, several numerical experiments are performed to illustrate the effectiveness and acceleration effect.

Optimizing DNN Compilation for Distributed Training With Joint OP and Tensor Fusion

This article proposes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisCo</i> , an automatic deep learning compilation module for data-parallel distributed training. Unlike most deep learning compilers that focus on training or inference on a single device, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisCo</i> optimizes a DNN model for distributed training over multiple GPU machines. Existing single-device compilation strategies do not work well in distributed training, due mainly to communication inefficiency that they incur. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisCo</i> generates optimized, joint computation operator and communication tensor fusion strategies to enable highly efficient distributed training. A GNN-based simulator is built to effectively estimate per-iteration training time achieved by operator/tensor fusion candidates. A backtracking search algorithm is driven by the simulator, navigating efficiently in the large strategy space to identify good operator/tensor fusion strategies that minimize distributed training time. We compare <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisCo</i> with existing DL fusion schemes and show that it achieves good training speed-up close to the ideal, full computation-communication overlap case.

An enhanced grey wolf optimizer with fusion strategies for identifying the parameters of photovoltaic models

Identifying photovoltaic (PV) parameters accurately and reliably can be conducive to the effective use of solar energy. The grey wolf optimizer (GWO) that was proposed recently is an effective nature-inspired method and has become an effective way to solve PV parameter identification. However, determining PV parameters is typically regarded as a multimodal optimization, which is a challenging optimization problem; thus, the original GWO still has the problem of insufficient accuracy and reliability when identifying PV parameters. In this study, an enhanced grey wolf optimizer with fusion strategies (EGWOFS) is proposed to overcome these shortcomings. First, a modified multiple learning backtracking search algorithm (MMLBSA) is designed to ameliorate the global exploration potential of the original GWO. Second, a dynamic spiral updating position strategy (DSUPS) is constructed to promote the performance of local exploitation. Finally, the proposed EGWOFS is verified by two groups of test data, which include three types of PV test models and experimental data extracted from the manufacturer’s data sheet. Experiments show that the overall performance of the proposed EGWOFS achieves competitive or better results in terms of accuracy and reliability for most test models.

Sparse measures with swarm-based pliable hidden Markov model and deep learning for EEG classification.

In comparison to other biomedical signals, electroencephalography (EEG) signals are quite complex in nature, so it requires a versatile model for feature extraction and classification. The structural information that prevails in the originally featured matrix is usually lost when dealing with standard feature extraction and conventional classification techniques. The main intention of this work is to propose a very novel and versatile approach for EEG signal modeling and classification. In this work, a sparse representation model along with the analysis of sparseness measures is done initially for the EEG signals and then a novel convergence of utilizing these sparse representation measures with Swarm Intelligence (SI) techniques based Hidden Markov Model (HMM) is utilized for the classification. The SI techniques utilized to compute the hidden states of the HMM are Particle Swarm Optimization (PSO), Differential Evolution (DE), Whale Optimization Algorithm (WOA), and Backtracking Search Algorithm (BSA), thereby making the HMM more pliable. Later, a deep learning methodology with the help of Convolutional Neural Network (CNN) was also developed with it and the results are compared to the standard pattern recognition classifiers. To validate the efficacy of the proposed methodology, a comprehensive experimental analysis is done over publicly available EEG datasets. The method is supported by strong statistical tests and theoretical analysis and results show that when sparse representation is implemented with deep learning, the highest classification accuracy of 98.94% is obtained and when sparse representation is implemented with SI-based HMM method, a high classification accuracy of 95.70% is obtained.

Optimal planning of Cross-regional hydrogen energy storage systems considering the uncertainty

The cross-regional consumption of renewable energy can effectively solve the problem of the uneven spatial distribution of renewable energy. To explore the application of hydrogen energy storage systems (HESS) for cross-regional consumption of renewable energy, optimal planning of cross-regional HESS considering the uncertainty is researched in this study. Firstly, a two-layer planning model is proposed to consider investment and operation costs. The upper layer of the model aims to determine a feasible planning strategy for HESS based on existing conditions. The purpose of the lower layer is then to determine the optimal scheduling strategy and minimum operating cost of the system considering uncertainty based on distributionally robust optimization. Furthermore, the solution method that combines the modified Backtracking Search Algorithm (MBSA) and Yalmip/Cplex is utilized to determine the optimal placement and sizing of the HESS. Finally, the simulation experiment is performed with the case of Southwest China to verify the effectiveness of the proposed planning model and corresponding solution method. The simulation results show that the MBSA has a better convergence speed and stronger global search capability performance than the traditional BSA. MBSA converges at 44th, which is quicker than the 60th of BSA; the optimal objective value obtained by MBSA is $1,038,929,953.66, which is better than that of BSA of $1,051,512,303.18. In addition, the resulting HESS planning scheme can effectively reduce the network loss of the system, reduce the peak-to-valley load difference, and improve renewable energy consumption. Specifically, the system network loss is reduced from 1.56 MWh to 1.47 MWh, the peak-to-valley difference is reduced from 245.61 MW to 225.88 WM, and the total renewable energy consumption of four typical days is increased from 6582.07 MW to 7626.03 MW.

Stability improvement of the PSS-connected power system network with ensemble machine learning tool

Stability is a primary requirement of the electrical power system for its flawless, secure, and economical operation. Low-frequency oscillations (LFOs), commonly seen in interconnected power systems, initiate the possibility of instability and, therefore, require sophisticated care to deal with. This paper proposes an original approach to tuning the parameters of the power system stabilizer (PSS), which plays a crucial role in the power system networks to dampen unwanted oscillations. The ensemble method combines multiple machine learning techniques and has been used for tuning the PSS parameters in real-time for two PSS-connected power system networks. The first system is a single-machine infinite bus power system, while the second is a unified power flow controller (UPFC) device. The backtracking search algorithm (BSA) based proposed ensemble model is formed by combining three machine learning (ML) techniques, namely the extreme learning machine (ELM), neurogenetic (NG) system, and multi-gene genetic programming (MGGP). To validate the stability of the network, Eigenvalues, well-recognized statistical parameters, and minimum damping ratios were analyzed, besides the time-domain simulation results. Furthermore, results for various loading conditions were prepared to check the robustness of the proposed model. A comparative study of the proposed approach with NG, ELM, MGGP models, and two reference cases along with the conventional method will validate the superiority of the employed ML approach.

Forecasting of future greenhouse gas emission trajectory for India using energy and economic indexes with various metaheuristic algorithms

The accelerating increment of greenhouse gas (GHG) concentration in the atmosphere already reached an alarming level, and nowadays its adverse impacts on the living organisms, environment, and ecological balance of nature have been well-understood. India is one of the top countries that contribute the most to global GHG emissions . Therefore, it is of great significance to forecast the future GHG trends of the country in advance and accordingly take measures against the parameters that cause these emissions, considerably. In this direction, the present research has centered on forecasting the greenhouse gas trajectory of India with various metaheuristic algorithms. In this framework, marine predators algorithm (MPA), lightning search algorithm (LSA), equilibrium optimizer (EO), symbiotic organisms search (SOS), and backtracking search algorithm (BSA) are used for modeling the future GHG emission trajectory of India. Accordingly, the significant economic and energy indicators of India such as renewable energy generation , electricity generation from coal, electricity generation from gas, electricity generation from oil, gross domestic product, and population between 1990 and 2018 are collected to make a nexus with GHG emissions. As GHG emissions, CO 2 , CH 4 , F-gases, N 2 O, as well as total GHG emissions are separately forecasted by the year 2050. To make a better comparison, each GHG emission data in the last year five years is used for the testing phase of the algorithms, and then statistically discussed in terms of R 2 , MBE , rRMSE , and MAPE benchmarks. In the results, it is found that the R 2 value changes between 0.8822 and 0.9923 for CO 2 , 0.2855–0.9945 for CH 4 , 0.9–0.9904 for F-gases, 0.4655–0.9964 for N 2 O, and 0.9016–0.9943 for total GHG emission, and the results in terms of rRMSE are very satisfying for all algorithms. In the study, it is forecasted that the two greenhouse gas emissions with the highest increase rate in 2050 will be between 2.5 and 2.87 times for CO 2 emissions and between 2.8 and 3.5 times for F-gases, compared to today's data. According to the results of the present paper, the total GHG emission for India is forecasted to be 2.1–2.4 times higher in the year 2050 as compared to today. Given all forecasting results together, it is seen that the MPA algorithm generally gives the best results according to the statistical metric results, while the LSA algorithm generally gives the worst results. Consequently, the present paper strongly reports that the decision-makers and policy-makers should take some serious steps in advance for the mitigation of GHG emissions, and to revise their energy investments in the upcoming years.

An Efficient Heap Based Optimizer Algorithm for Feature Selection

The heap-based optimizer (HBO) is an innovative meta-heuristic inspired by human social behavior. In this research, binary adaptations of the heap-based optimizer B_HBO are presented and used to determine the optimal features for classifications in wrapping form. In addition, HBO balances exploration and exploitation by employing self-adaptive parameters that can adaptively search the solution domain for the optimal solution. In the feature selection domain, the presented algorithms for the binary Heap-based optimizer B_HBO are used to find feature subsets that maximize classification performance while lowering the number of selected features. The textitk-nearest neighbor (textitk-NN) classifier ensures that the selected features are significant. The new binary methods are compared to eight common optimization methods recently employed in this field, including Ant Lion Optimization (ALO), Archimedes Optimization Algorithm (AOA), Backtracking Search Algorithm (BSA), Crow Search Algorithm (CSA), Levy flight distribution (LFD), Particle Swarm Optimization (PSO), Slime Mold Algorithm (SMA), and Tree Seed Algorithm (TSA) in terms of fitness, accuracy, precision, sensitivity, F-score, the number of selected features, and statistical tests. Twenty datasets from the UCI repository are evaluated and compared using a set of evaluation indicators. The non-parametric Wilcoxon rank-sum test was used to determine whether the proposed algorithms’ results varied statistically significantly from those of the other compared methods. The comparison analysis demonstrates that B_HBO is superior or equivalent to the other algorithms used in the literature.

Pretrained Cost Model for Distributed Constraint Optimization Problems

Distributed Constraint Optimization Problems (DCOPs) are an important subclass of combinatorial optimization problems, where information and controls are distributed among multiple autonomous agents. Previously, Machine Learning (ML) has been largely applied to solve combinatorial optimization problems by learning effective heuristics. However, existing ML-based heuristic methods are often not generalizable to different search algorithms. Most importantly, these methods usually require full knowledge about the problems to be solved, which are not suitable for distributed settings where centralization is not realistic due to geographical limitations or privacy concerns. To address the generality issue, we propose a novel directed acyclic graph representation schema for DCOPs and leverage the Graph Attention Networks (GATs) to embed graph representations. Our model, GAT-PCM, is then pretrained with optimally labelled data in an offline manner, so as to construct effective heuristics to boost a broad range of DCOP algorithms where evaluating the quality of a partial assignment is critical, such as local search or backtracking search. Furthermore, to enable decentralized model inference, we propose a distributed embedding schema of GAT-PCM where each agent exchanges only embedded vectors, and show its soundness and complexity. Finally, we demonstrate the effectiveness of our model by combining it with a local search or a backtracking search algorithm. Extensive empirical evaluations indicate that the GAT-PCM-boosted algorithms significantly outperform the state-of-the-art methods in various benchmarks.

Minimum weight design of reinforced concrete beams utilizing grey wolf and backtracking search optimization algorithms

In this study, optimal weight design of a reinforced concrete beam subjected to various loading conditions is investigated. The purpose of the optimization is to attain the minimum weight design of the reinforced concrete beam under distributed and two-point loads. The design problem is handled under three different design load cases. The two-point loads are affected on beam-to-beam connection nodes of reinforced concrete beams. Thus, while the magnitudes of distributed load and two-points load are remained constant, the distances between two-points loads are taken as 2m, 3m and 4m, respectively. The width and height of the rectangular cross-section of the concrete beam, and the diameters of the longitudinal and confinement steel rebars are treated as design variables of the optimum design problem. The design constraints of the optimization problem consist of the geometric constraints and necessities of the Turkish Requirements for Design and Construction of Reinforced Concrete Structures (TS500), and Turkish Building Earthquake Code (TBEC). As two novel metaheuristics, grey wolf (GW) and backtracking search (BS) optimization algorithms are selected as optimizers. Both algorithms are independently operated five times for three different design problems. Thus, the obtained results are examined statistically to compare in accordance with algorithmic performances. The optimal findings from optimization algorithms show that the GW algorithm is a little bit more robust on the exploitation phase, while the BS algorithm is stronger on the exploration phase. Moreover, it can be deducted from optimal beam designs that the GW algorithm is more viable to minimize reinforced concrete beam design.