Backtracking Search Algorithm Research Articles

Integrated machine learning for modeling bearing capacity of shallow foundations

Analyzing the stability of footings is a significant step in civil/geotechnical engineering projects. In this work, two novel predictive tools are suggested based on an artificial neural network (ANN) to analyze the bearing capacity of a footing installed on a two-layered soil mass. To this end, backtracking search algorithm (BSA) and equilibrium optimizer (EO) are employed to train the ANN for approximating the stability value (SV) of the system. After executing a set of finite element analyses, the settlement values lower/higher than 5 cm are considered to indicate the stability/failure of the system. The results demonstrated the efficiency of these algorithms in fulfilling the assigned task. In detail, the training error of the ANN (in terms of root mean square error—RMSE)) dropped from 0.3585 to 0.3165 (11.72%) and 0.2959 (17.46%) by applying the BSA and EO, respectively. Moreover, the prediction accuracy of the ANN climbed from 93.7 to 94.3% and 94.1% (in terms of area under the receiving operating characteristics curve—AUROC). A comparison between the elite complexities of these algorithms showed that the EO enjoys a larger accuracy, while BSA is a more time-effective optimizer. Lastly, an explicit mathematical formula is derived from the EO-ANN model to be conveniently used in predicting the SV.

Satin bowerbird optimizer-neural network for approximating the capacity of CFST columns under compression

Concrete-filled steel tube columns (CFSTCs) are important elements in the construction sector and predictive analysis of their behavior is essential. Recent works have revealed the potential of metaheuristic-assisted approximators for this purpose. The main idea of this paper, therefore, is to introduce a novel integrative model for appraising the axial compression capacity (Pu) of CFSTCs. The proposed model represents an artificial neural network (ANN) supervised by satin bowerbird optimizer (SBO). In other words, this metaheuristic algorithm trains the ANN optimally to find the best contribution of input parameters to the Pu. In this sense, column length and the compressive strength of concrete, as well as the characteristics of the steel tube (i.e., diameter, thickness, yield stress, and ultimate stress), are considered input data. The prediction results are compared to five ANNs supervised by backtracking search algorithm (BSA), earthworm optimization algorithm (EWA), social spider algorithm (SOSA), salp swarm algorithm (SSA), and wind-driven optimization. Evaluating various accuracy indicators showed that the proposed model surpassed all of them in both learning and reproducing the Pu pattern. The obtained values of mean absolute percentage error of the SBO-ANN was 2.3082% versus 4.3821%, 17.4724%, 15.7898%, 4.2317%, and 3.6884% for the BSA-ANN, EWA-ANN, SOSA-ANN, SSA-ANN and WDA-ANN, respectively. The higher accuracy of the SBO-ANN against several hybrid models from earlier literature was also deduced. Moreover, the outcomes of principal component analysis on the dataset showed that the yield stress, diameter, and ultimate stress of the steel tube are the three most important factors in Pu prediction. A predictive formula is finally derived from the optimized SBO-ANN by extracting and organizing the weights and biases of the ANN. Owing to the accurate estimation shown by this model, the derived formula can reliably predict the Pu of concrete-filled steel tube columns.

Prediction of CO2 emission for the central European countries through five metaheuristic optimization techniques helping multilayer perceptron

One of the most significant issues in urban design is energy-related CO2 emissions, which are rising quickly as cities expand. The GDP of the Central European countries (from 1990 to 2016) based on several energy sources, such as coal, oil, natural gas, and renewable energy, are used as inputs in this study. To develop a reliable predictive network considering the problem complexity, multilayer perceptron (MLP) is combined with several nature-inspired optimization algorithms, namely, black hole algorithm (BHA), future search algorithm (FSA), backtracking search algorithm (BSA), biogeography-based optimization (BBO), and shuffled complex evolution (SCE). By applying the approaches mentioned above to the synthesis of the MLP, the recommended BBO, BHA, BSA, FSA, and SCE ensembles are obtained. A series of parametric studies are performed to improve the effectiveness of the employed models. It is found that, by combining the BBO, BHA, BSA, FSA, and SCE algorithms, the MLP's accuracy is increased. The result from this parametric analysis showed that SCE and BBO perform better than the other three algorithms as the CO2 emission was computed with the highest level of accuracy using R2 = 0.9999 and 0.9998, RMSE = 1.6781 and 2.0539 for SCE, and R2 = 0.9999 and 0.9998, RMSE = 1.8689 and 2.3833 for BBO.

Positioning multiple optical network units in fiber-wireless networks: An efficient hybrid [formula omitted]-harmonic means clustering approach

Wireless-optical broadband access network (WOBAN) or fiber-wireless (FiWi) is a robust and cost-effective solution to provide high bandwidth network connectivity to mobile subscribers. Optical network unit (ONU) placement is a topological optimization problem that plays a vital role in effective deployment of FiWi network. Recently, some artificial intelligence-based approaches for positioning ONUs were proposed and generated promising results. However, the reported performance in the literature is far from the ideal state. This issue emphasizes the necessity of introducing new placement methods or improving the performance of existing methods. This paper presents a hybrid clustering algorithm for finding the optimal position of multiple ONUs. The proposed backtracking K-harmonic means (BKHM) is an integration of K-harmonic means (KHM) and a backtracking search algorithm (BSA). BKHM not only efficiently specifies the optimal positions of ONUs but also significantly decreases the implementation cost. To demonstrate the performance of the BKHM, we evaluate it on well-known placement benchmarks compared with BSA, KHM, whale optimization algorithm (WOA), enhanced backtracking search (EBS), harris hawks optimization (HHO), and chaotic local search-based levy flight distribution (CLF) algorithms. The experimental results and statistical analysis proved that the proposed BKHM algorithm outperformed its counterparts on most benchmarks in terms of cost optimization, convergence accuracy, and solution quality.

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Multi-strategy-based adaptive sine cosine algorithm for engineering optimization problems

Sine Cosine Algorithm(SCA) is a population-based optimization algorithm, to find the optimal solution. However, SCA has problems such as premature convergence, insufficient solution precision for high-dimensional functions, and slow convergence speed. To solve the problems above, this paper proposes a multi-strategy-based Adaptive Sine Cosine Algorithm (ASCA). Firstly, a more uniform initial population is generated by the Halton sequence so that the initial population covers the entire search space to maintain the diversity of the initial population. Secondly, the adaptive grading strategy is adopted to sort according to the fitness value, and the population dynamics are divided into 4 grades: excellent, good, medium and poor. For the purpose of improving the convergence accuracy of the algorithm and enhancing the ability to jump out of the local optimum, hybrid mutation and elite guidance methods are applied to different levels of populations for perturbing mutations. Finally, in order to improve the convergence speed of the algorithm, a dynamic opposition-based learning global search strategy is proposed. The ASCA is tested on a set of 20 functions in low- dimensional and high-dimensional, and the improved algorithm is compared with Particle Swarm Optimization (PSO), Backtracking Search Algorithm(BSA), Genetic Algorithm(GA)and other improved Sine Cosine Algorithms. The results show the improved convergence accuracy and speed of the ASCA. Moreover, the ASCA proposed in this paper is applied to engineering optimization design. The solution results show that the ASCA is better than other algorithms in superiority-seeking ability, and can effectively solve the optimization problems in engineering.

Optimal Reactive Power Flow of AC-DC Power System with Shunt Capacitors Using Backtracking Search Algorithm

In this paper, it is proposed that a two-terminal high voltage direct current (HVDC) be integrated into the power system. Line-commutated converter (LCC)-HVDC is used because of its ability to reduce line losses, which improves overall system efficiency. Shunt capacitors also aid in voltage maintenance by compensating for the reactive power demand. In essence, limiting voltage drops in electrical networks promotes a more efficient power transmission and distribution by lowering resistive losses. In power system investigations, it was discovered that the HVDC link and SCB exist separately. So, for the first time, the backtracking search algorithm (BSA) is used to solve the optimal reactive power flow (ORPF) of a power system with a HVDC link and shunt capacitor banks (SCB). Although BSA simulations on a modified IEEE 30 bus yielded successful results, ABC was also utilized for comparing the outcomes of different methods. Overall, three separate cases of the modified IEEE 30 bus system were examined. When the acquired results are compared to other methods, the suggested algorithm is found to be better at concerning effectiveness as well as performance.

Automating distribution networks: Backtracking search algorithm for efficient and cost-effective fault management

Electricity outages can result in consequences for customers and cause disruptions that result in revenue loss, business productivity reduction, appliance damage, and compromised public safety. To minimize outage duration, locating faults quickly and accurately is crucial. Advanced fault management strategies leverage computational intelligence and deploy fault indicators (FIs) and sectionalizing switches (SSs) to locate faults and isolate faulty parts. Although FIs and SSs can improve distribution network reliability, deploying them at every node is impractical owing to cost and complexity. Therefore, it is important to optimize their placement in strategic locations. This research proposes a new optimization problem for the simultaneous placement of FIs and SSs. The aim is to minimize the cost of equipment placement, dispatching field crews, and service interruption. To solve the proposed formulation, the Backtracking Search Algorithm (BSA), a population-based meta-heuristic method, is used to identify optimal nodes for FIs and SSs placement. The performance of the BSA is evaluated through statistical tests, and the proposed strategy is shown to be effective compared to state-of-the-art methods. The results reveal a significant 7% reduction in device requirement, leading to a substantial 6.69% decrease in equipment expenditures and an overall decline in system costs compared to the established approach implemented in the test system. This research highlights the importance of optimization strategies for fault management systems and demonstrates the potential of meta-heuristic algorithms for solving complex problems.

Dynamic reconfiguration of active distribution network based on improved backtracking search algorithm

This research proposes a dynamic reconfiguration model (DRM) and method for the distribution network, considering wind power, photovoltaic distributed generation (DG), and demand-side response. The reconfiguration goal is to minimize the total operating cost of the distribution network. The electricity purchase costs, DG operation costs, participation in demand response programs, network losses, and voltage deviations are selected to construct the optimization function. The DRM is established by clustered load data segments. An improved backtracking search algorithm incorporating a differential evolution learning strategy and adaptive chaotic elite search strategy is adopted to solve the DRM. The viability of the proposed method is validated by an IEEE 30-node simulation distributed system.

A novel problem-solving method by multi-computational optimisation of artificial neural network for modelling and prediction of the flow erosion processes

This research aims to forecast, using various criteria, the flow of soil erosion that will occur at a particular geographical location. As for the training dataset, 80% of the dataset from the sample sites, four hybrid algorithms, namely heap-based optimizer (HBO), political optimizer (PO), teaching-learning based optimization (TLBO), and backtracking search algorithm (BSA) combined with artificial neural network (ANN) was used to create an erosion susceptibility model and establishes a unique and original approach. After it was confirmed to be successful, the algorithms were applied to create a susceptibility map for this area, demonstrating the integrity of the results. The AUC values were computed for every optimisation algorithm used in this study. The optimal estimated accuracy indices for populations of 450 were determined to be 0.9846 using the BSA-MLP training databases. The maximum AUC value for the HBO-MLP training databases with different swarm sizes was 0.9736. A swarm size of 350–300 is considered optimal for forecasting erosion susceptibility mapping in hybrid models. With the same swarm size constraints, the AUC value for training in the TLBO-MLP scenario was 0.996. After 150 swarm size conditions were used to train the PO-MLP model, the AUC values were 0.9845. According to these findings, the TLBO-MLP and PO-MLP algorithms worked best with populations of 50 and 150, respectively.

An Enhanced Backtracking Search Algorithm for the Flight Planning of a Multi-Drones-Assisted Commercial Parcel Delivery System

Using drones to carry out commercial parcel delivery can significantly promote the transformation and upgrading of the logistics industry thanks to the saving of human labor source, which is becoming a new component of intelligent transportation systems. However, the flight distance of drones is often constrained due to the limited battery capacity. To address this challenge, this paper designs a multi-drones-assisted commercial parcel delivery system, which supports long-distance delivery by a generalized service network (GSN). Each node of the GSN is equipped with charging piles to provide a charging service for drones. Given the limited number of charging piles at each node and the limited battery capacity of a drone, to ensure the efficient operation of the system, the flight planning problem of drones is converted into a large-scale optimization problem by a priority-based encoding mechanism. To solve this problem, an enhanced backtracking search algorithm (EBSA) is reported, which is inspired by the characteristics of the considered flight planning problem and the weak ability of the backtracking search algorithm to escape from a local optimum. The core components of EBSA are the designed comprehensive learning mechanism and local escape operator. Experimental results prove the validity of the improved strategies and the excellent performance of EBSA on the considered flight planning problem.

Optimal allocation of photovoltaic generations in buildings‐to‐distribution‐network integration system using improved backtracking search optimization algorithm

AbstractA novel optimal allocation framework for photovoltaic generations in an integration system of buildings‐to‐distribution‐network using improved backtracking search optimization algorithm is proposed here. In the proposed framework, photovoltaic generations are optimally allocated to optimize the overall performance of a buildings‐to‐distribution‐network regarding the efficient active power usage of photovoltaic generations, the energy savings, and voltage profile improvement of distribution network. The effects of building active demand response on the photovoltaic generations' optimal allocation are considered in the proposed framework. An improved backtracking search algorithm using two new operators is developed to optimize the active power reduction factors and locations of photovoltaic generations. The test results of IEEE 33‐bus and 69‐bus systems demonstrate that the developed framework can take full advantage of photovoltaic generation power and the active demand response of buildings to coordinate the efficient active power usage of photovoltaic generations, the voltage profile improvement and energy savings of a buildings‐to‐distribution‐network. In addition, the improved backtracking search optimization algorithm converges faster than genetic algorithm, classical backtracking search optimization algorithm, and bird swarm algorithm.

Effective LSTMs with seasonal-trend decomposition and adaptive learning and niching-based backtracking search algorithm for time series forecasting

Long short-term memory faces challenges in information mining and parameter selection due to inherent uncertainty and randomness. In this study, we propose a novel hybrid model called ‘STL-ALN_BSA-LSTM’ that aims to tackle this issue. In the proposed model, data is first prepossessed using seasonal-trend decomposition to extract informative features. Next, we propose an adaptive learning and niching-based backtracking search algorithm to enhance the robustness and learning ability of the original backtracking search algorithm, which affords a balance between exploration and exploitation. Subsequently, the weights and thresholds within each LSTM are optimized by our optimization algorithm automatically, leading to improved interpretability and accuracy of the model. Finally, the proposed optimization algorithm was evaluated using five benchmark functions, and the hybrid model was compared with sixteen baselines on two real-world datasets. For rainfall forecasting, the hybrid model achieved the root mean square error of 7.3772, mean absolute error of 2.6187, and R2 of 0.8388. For power generation forecasting, our model outperformed the second-best model by 29.6%, 34.4%, and 16 ‰, respectively, as in the above metrics. These results demonstrate that the proposed hybrid model can attain higher accuracy in real-life applications than previous models, which contributes in-depth insights into parameter optimization for time series forecasting, and provides valuable suggestions in resource planning, risk reduction, and decision-making. The core code of this work can be found from https://github.com/zjuml/STL-ALNBSA-LSTM.

Five Phases Algorithm: A Novel Meta-heuristic Algorithm and Its Application on Economic Load Dispatch Problem

<p>A new meta-heuristic algorithm named the five phases algorithm (FPA) is presented in this paper. The proposed method is inspired by the five phases theory in traditional Chinese thought. FPA updates agents based on the generating and overcoming strategy as well as learning strategy from the agent with the same label. FPA has a simple structure but excellent performance. It also does not have any predefined control parameters, only two general parameters including population size and terminal condition are required. This provides flexibility to users to solve different optimization problems. For global optimization, 10 test functions from the CEC2019 test suite are used to evaluate the performance of FPA. The experimental results confirm that FPA is better than the 6 state-of-the-art algorithms including particle swarm optimization (PSO), grey wolf optimizer (GWO), multi-verse optimizer (MVO), differential evolution (DE), backtracking search algorithm (BSA), and slime mould algorithm (SMA). Furthermore, FPA is applied to solve the Economic Load Dispatch (ELD) from the real power system problem. The experiments give that the minimum cost of power system operation obtained by the proposed FPA is more competitive than the 14 counterparts. The source codes of this algorithm can be found in https://ww2.mathworks.cn/matlabcentral/fileexchange/118215-five-phases-algorithm-fpa.</p> <p> </p>

A new combined approach of neural-metaheuristic algorithms for predicting and appraisal of landslide susceptibility mapping.

In this research, to predict landslide susceptibility mapping (LSM), we have studied and optimized an artificial neural network (ANN) by utilizing the backtracking search algorithm (BSA) as well as the Cuckoo optimization algorithm (COA). Multiple research studies have shown that ANN-based techniques can be used to figure out the LSM. Still, ANN computing models have big problems, like slow system learning and getting stuck in their local minimums. Optimization strategies may improve ANN performance results. Existing uses of the BSA and COA models in ANN training have not been used to map landslides, nor have the best ways to set up networks or other factors that affect this problem been examined. Consequently, the present research focuses on predicting landslide susceptibility for hazardous mapping using hybrid BSA and COA-based ANN algorithms (BSA-MLP and COA). A large data set was provided from an area in the province of Kurdistan, west of Iran, to provide training and testing datasets for the algorithms. All of the BSA and COA algorithms' parameters and weights, for instance, were fine-tuned to make the utmost accurate maps of landslide risk. The input dataset consists of elevation, slope angle, slope orientation, NDVI, fault tolerance, profile curvature, plan curvature, distance to the river, rainfall, far from the road, SPI, STI, TRI, TWI, land use, and geology; the output is landslide susceptibility value. In the testing phase, the AUC rose significantly from 0.701 to 0.864 for BSA-MLP and 0.738 to 0.822 for COA-MLP after using the abovementioned techniques. We have used the area under the curve (AUC) to evaluate how well the probabilistic models worked. In addition, the computed AUCs for the BSA-MLP available databases and the actual AUCs were 0.864, 0.857, 0.833, 0.778, 0.777, 0.769, 0.763, 0.758, 0.727, and 0.701 and 0.822, 0.808, 0.807, 0.805, 0.804, 0.777, and 0.769 for the COA-MLP combination. The integrated models can produce beneficial results for this area of research. The results suggest that the BSA-ANN model is better than the COA-ANN in optimizing an artificial neural network model's structure and computational parameters. The collected landslide susceptibility maps are significant for figuring out how dangerous landslides are in the studied area.

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.