Binary Particle Swarm Optimization Research Articles

Energy-Efficient Joint Scheduling of Pumps and Valves in Water Distribution Network Using Hybrid Optimization Algorithm

Traditionally, pumping efficiency and pressure control have been studied as separate disciplines in water companies, with a focus on optimizing pump operation and managing leakage. Present-day siphons are frequently outfitted with variable speed drives; consequently, the siphon outlet tension could be constrained by controlling siphon speed. If there are siphons upstream from a tension-decreasing valve (PRV) with no moderate tank, the PRV gulf strain could be diminished by changing siphoning in the upstream piece of the organization. In addition, when optimizing pump operation, consideration should be given to the impact of pressure-dependent leakage on the resulting schedules. Thus, this article considers the streamlining of siphon and valve plans for complex huge-scope water circulation organizations (WDN). The review takes care of the siphoning booking issue, which tries to acquire the timetable of on/off switches for each siphon and valve that limits energy power cost, taking into account the energy consumed by the functioning siphons. This schedule generates the flow and pressure through the network and it has to satisfy the demand for all nodes, conserve energy, to minimize head loss. To execute and safeguard clean water assets, functional improvement of WDSs should consider both energy and upkeep costs while deciding the ideal timetable for siphons and valves. The point of this examination is to create and confirm an energy model that can work on the effectiveness of equal siphon frameworks. Accordingly, the research proposed the mathematical model of shaft power consumption using the quadratic polynomial fitting. Additionally, investigated the potential application of Variable Speed Pumps (VSPs) to improve pressure reliability, leakage, and electrical power consumption in Water Distribution Networks (WDNs). To execute and safeguard clean water assets, functional improvement of Water Circulation Frameworks (WDSs) should consider both energy and upkeep costs while deciding the ideal timetable for siphons and valves. The point of this examination is to create and confirm an energy model that can work on the effectiveness of equal siphon frameworks. The hybrid binary dragonfly-enhanced Particle Swarm Optimization (PSO) algorithm is proposed for joint pumping and valve scheduling problems in WDS. The optimal scheduling is conducted based on three different energy tariffs. The Matlab programming climate is utilized to demonstrate this strategy with the assistance of the EPANet Matlab tool compartment. Analyzing a range of scenarios with varying time frames, operational limitations, and network changes, the proposed WDN solution showed its capability to efficiently create and address optimization challenges tailored to diverse needs.

Combined Simulated annealing and Improved Binary PSO based Optimal Corona Ring Design for High Voltage Transmission Line

Combined Simulated annealing and Improved Binary PSO based Optimal Corona Ring Design for High Voltage Transmission Line

Optimal integration and planning of PV and wind renewable energy sources into distribution networks using the hybrid model of analytical techniques and metaheuristic algorithms: A deep learning-based approach

The optimal integration of Renewable Energy Sources (RESs) into distribution networks is crucial for sustainable energy generation. However, existing approaches utilized for optimal RES integration, including metaheuristic and analytical methods, exhibit limitations. Analytical methods are simple to implement, computationally efficient, and able to model power system mechanisms, yet they face scalability issues, making them inefficient for large-scale distribution systems. On the other hand, metaheuristic approaches, while flexible for complex problems, suffer from premature convergence problems, limiting their application in real distribution networks. To address these issues, this paper introduces a novel hybrid model that combines the strengths of analytical and metaheuristic techniques. The proposed model employs a deep learning-based method called bi-directional long short-term memory (B-LSTM) network is utilized to handle the uncertainties associated with the Photovoltaic (PV) and Wind Turbine (WT) generation and load demand. Subsequently, a distinctive analytical multi-objective index-based procedure is developed to minimize the real and reactive energy loss and voltage deviation by analyzing the branch current change caused by the RES penetration in distribution networks. The optimization problem is then solved using the binary particle swarm optimization (BPSO) technique. Importantly, the presented method considers the long-term nature of optimal RES integration and reflects the seasonal impacts of the load and RES output powers. The proposed approach is applied to the IEEE 33-bus test system. The simulation results show that the introduced hybrid model, by addressing the limitations of existing approaches, offers a promising solution for efficient and effective RES integration in distribution systems while requiring low computational effort, thereby advancing the transition towards sustainable energy infrastructure.

Blockchain-based 6G task offloading and cooperative computing resource allocation study

In the upcoming era of 6G, the accelerated development of the Internet of Everything and high-speed communication is poised to provide people with an efficient and intelligent life experience. However, the exponential growth in data traffic is expected to pose substantial task processing challenges. Relying solely on the computational resources of individual devices may struggle to meet the demand for low latency. Additionally, the lack of trust between different devices poses a limitation to the development of 6G networks. In response to this issue, this study proposes a blockchain-based 6G task offloading and collaborative computational resource allocation (CERMTOB) algorithm. The proposed first designs a blockchain-based 6G cloud-network-edge collaborative task offloading model. It incorporates a blockchain network on the edge layer to improve trust between terminals and blockchain nodes. Subsequently, the optimization objective is established to minimize the total latency of offloading, computation, and blockchain consensus. The optimal offloading scheme is determined using the wolf fish collaborative search algorithm(WF-CSA) to minimize the total delay. Simulation results show that the WF-CSA algorithm significantly reduces the total delay by up to 42.58% compared to the fish swarm algorithm, wolf pack algorithm and binary particle swarm optimisation algorithm. Furthermore, the introduction of blockchain to the cloud-side-end offloading system improves the communication success rate by a maximum of 14.93% compared to the blockchain-free system.

A novel solution methodology for electrical vehicles charging schedule in coordinated with full flexible resources in microgrid

This paper proposes a new model for the day-ahead Electric Vehicle charging schedule in Microgrids (MGs) with flexible resources such as Wind Turbine (WT) and Photovoltaic (PV) electrical power, Combined Heat and Power (CHP), Energy Storage Source (ESS), and load Demand Responses (DR). The proposed Mixed Integer Nonlinear Multi-Objective Optimization (MINMO) model considers uncertainty properties with optimal operation objects. The cost function, and power loss minimization are the proposed model's objects for considering optimal operation objects. This model is solved by a three-level decomposition method in master-sub problem presentation and Binary-Continues PSO algorithm (BC PSO) to quickly calculate the optimal solution. In the first layer, the main constraint of electric vehicle aggregators (EVAs) is satisfied by the binary PSO algorithm. According to the top-layer solution, flexible recourses are managed to satisfy the operation objects by the Bi-level Continues PSO algorithm in the second layer. Then, after converging to the optimum solution of these two layers, Electric Vehicles (EVs) charging stations are solved at the last layer by algebraic equations. Finally, the efficiency of the proposed method is illustrated via its application in IEEE 33-bus MG system. The numerical results show that the proposed solution methodology reduces the runtime of the problem up to 95 % compared to intelligence-based and full Newton–Raphson AC power flow method. Also, numerical results illustrate that considering CHP and DR in addition to the other flexible resources reduces the operation cost and power loss up to 21 % and 5 % respectively. In top of that the minimum total cost for day-ahead EV charging schedule by the proposed model and solution methodology is 578,312.7$.

An Image Feature Extraction Algorithm Based on Tissue P System

As digital images continue to generate an increasing amount of data, image feature extraction has become a crucial component of image recognition. This paper proposes an image feature extraction method based on membrane computing to extract image features. The author first uses the rotation invariant local phase quantization (RILPQ) to extract image features and combines the tissue P system with the binary particle swarm optimization (MBPSO) to select the best image features and maximize the classification accuracy. Based on 4 public datasets, 28 datasets are newly constructed, and the proposed method is verified on 28 datasets. Specifically, firstly, local binary pattern (LBP) algorithm and RILPQ are used to extract image features, and then MBPSO, binary particle swarm optimization (BPSO), genetic algorithm (GA) and membrane genetic algorithm (MGA) are used to select the optimal features. The experimental results demonstrate that our proposed image feature extraction method achieves high classification accuracy, stability, and convergence.

A novel unconstrained methodology for economic analysis of the level of repair with a case study of a multi-indenture and multi-echelon repair network

The multi-indenture and multi-echelon economic analysis of repair levels is commonly modelled as a constrained 0–1 programming problem. However, with the increase in the scale of the decision variables, the proportion of feasible solutions in the solution space sharply decreases, posing a challenge for traditional solution methods. In this paper, the transformation of the initial problem into an unconstrained integer programming problem is demonstrated. Specifically, the total number of feasible decisions can be solved analytically through a decision flow method, and a bijective relationship between decision sequence numbers and feasible decisions is established using a mixed-radix system, converting the optimization variables to feasible decision sequence numbers; in this way, the initial problem becomes unconstrained. The advantages of this approach include the following: (1) All the solutions in the transformed solution space are feasible, which significantly improves the efficiency of the solution and reduces the dimensionality of the decision variables; and (2) the proposed model is highly flexible in terms of considering additional variables, such as decision time, transportation modes, and repair locations. Furthermore, the sequence numbers of each feasible solution are transformed into binary sequences, and the binary particle swarm optimizer (BPSO) algorithm can be employed to solve the model. The proposed methodology is applied to the case of a three-indenture and three-echelon repair network considering multiple fault modes, and the results are compared with those of previous studies. The results validate the rationality and substantial advantages of the proposed methodology for economic analysis in terms of computational speed and convergence performance.

A lightweight BPSO mechanism for topology reconfiguration in data-driven IIoT plants

Wireless Sensor Networks in large-area monitoring applications may be required to deal with emergency events, i.e., events from regions that suddenly require close attention. Nodes in these regions may demand increased data generation rates, and their communication with the base station (BS) should be prioritized. In this sense, a significant challenge is how to reconfigure the network to create paths that offer adequate Quality of Service (QoS) between these sensor nodes and the BSs. Depending on the network’s size, the computational complexity of this problem may become unacceptable; but a meta-heuristic approach could handle it. This work describes a lightweight Binary Particle Swarm Optimization (BPSO) mechanism for the topology reconfiguration of data-driven cluster-tree networks based on IEEE 802.15.4 standard. The goal of this mechanism, called CALiPSO, is to reduce the computational complexity when searching for a suitable network topological configuration that improves network QoS metrics. A simulation assessment and comparison with other approaches were conducted. It was demonstrated that CALiPSO can reconfigure a network of 125 nodes and create an appropriate cluster-tree with fewer cluster-heads in hotspot regions, while improving network QoS. Compared with heuristic and optimization methods, CALiPSO selects around 42% to 55% fewer CHs and forms trees 22% less depth. Concurrently, it diminishes communication delays by about 5% and decreases packet losses by 7.5%, without jeopardizing energy consumption.

Oversampling Framework Based on Sample Subspace Optimization with Accelerated Binary Particle Swarm Optimization for Imbalanced Classification

In response to the need to generate synthetic minority class samples to extend minority classes, the SMOTE-based oversampling methods have been favored for class-imbalanced classification. They usually generate unnecessary noise when training data are not well separated. Although filtering-based oversampling methods are recognized as effective solutions for addressing noise generation through employing specific noise filters based on instance selection methods to remove suspicious noise, they suffer from the following issues: a) noise filters heavily rely on strong assumptions, causing low robustness to different datasets; b) noise filters are specially designed for a specific oversampling method, and are not easily extended to others; and c) noise filters have a relatively high time consumption. To address noise generation while overcoming the above issues a)-c), an oversampling framework based on sample subspace optimization with accelerated binary particle swarm optimization (OF-SSO-ABPSO) is proposed. OF-SSO-ABPSO is a wrapping framework compatible with almost all the oversampling methods. First, in the framework, a SMOTE-based method is used to generate synthetic minority class samples. Second, a novel accelerated binary particle swarm optimization (ABPSO) algorithm with a new search space reduction strategy, a new particle update mechanism, and a new fitness function is proposed. Third, a novel ABPSO-based sample subspace optimization (SSO-ABPSO) method is proposed and used as a noise filter to remove suspicious noise from the training set and synthetic minority class samples. Experiments prove that, a) OF-SSO-ABPSO can improve 6 representative SMOTE variations by addressing noise generation, and b) OF-SSO-ABPSO outperforms 7 state-of-the-art filtering-based oversampling methods.

Operation optimization and performance evaluation of a ventilated heating floor in a nearly-zero-energy building with mixed power

With the proportion of renewable energy in the construction sector increasing and the structure of energy systems becoming increasingly complex, it is crucial to optimize the operation strategy of building energy systems with thermal energy storage for improving multi-performance. However, conventional heuristic optimization algorithm exhibits low searching speed and converges slowly, which is hard for operation optimization of such systems. In this study, with a binary particle swarm optimization (BPSO) algorithm coupled with experience-based searching guiding strategy, the operation of a ventilated floor heating system in a nearly-zero-energy building was optimized . System performance under different optimization objectives and combinations, including reducing operation cost and carbon emission fee, meanwhile increasing wind power consumption and thermal comfort time, was investigated. Results show that with the experience-based accelerating strategy, the BPSO algorithm converged fast and found more reasonable solutions. In contrast, multi-objective optimization yielded better and diverse feasible solutions were found than single-objective optimization. By optimizing operating costs, wind power consumption, and environmental costs, the best comprehensive solution was obtained. The cost range of energy consumption and carbon emissions within 10 days is 19.24–22.17 yuan and 17.45–20.11 yuan, respectively. The proportion of thermal comfort time is 95.39–95.82%. However, due to high thermal insulation level, thermal comfort time under different optimization objectives showed little difference.

Hybrid optimization for integration of renewable energy systems into smart grids

The significant increase in the human population, energy consumption in daily living is increasing. One approach is to raise the amount of power produced to match the growth in human population, although this is typically practically unfeasible. By controlling demand, electricity consumption and associated expenses may be reduced. As a consequence, we employ Demand-side Management (DSM) to plan different gadgets on loads to reduce energy usage. Incorporating renewable energy sources and reducing energy costs are two significant roles that the smart grid plays. As a result, we suggest a hybrid swarm based Harris Hawks' optimization (S–HHO) algorithm to overcome the optimization difficulties. The suggested approach includes loads of home and business variety. The proposed technique was compared to binary particle swarm optimization (BPSO), multi-objective particle swarm optimization (MOPSO), wind driven optimization (WDO), and multi-objective genetic algorithms (MOGA). Results from simulations were produced using MATLAB software. The results show that the improved hybrid optimization S–HHO reduces the Peak-to-average ratio (PAR) and computational time better than other methods such as WDO, BPSO, MOPSO, and MOGA.

Smart home energy management using demand response with uncertainty analysis of electric vehicle in the presence of renewable energy sources

In this article, smart home energy management is proposed using real-time pricing (RTP) based demand response for effective utilization of renewable-based distributed generation (DGs), battery, and electric vehicle (EV) to reduce grid dependency. The smart home consists of eighteen smart appliances and EV. The EV can be operated either in vehicle-to-home or home-to-vehicle. The smart appliances in the smart home are categorized into two types: electrical and thermal loads. Each smart appliance’s operating time slots and durations are scheduled based on the tariff, availability of DGs, and storage devices using the Binary Particle Swarm Optimization (BPSO) algorithm without affecting user preferences. Due to the proposed method, the grid dependency of the smart home in each time slot is reduced, which shall reduce the net electricity cost. Different cases are analyzed based on the various combinations of renewable-based DGs such as wind power, solar photovoltaic (PV), and battery in the smart home to showcase the effectiveness of the proposed method. The performance of the proposed system is analyzed under uncertain EV and DG operations. A detailed comparison is made with and without appliance scheduling in the proposed smart home to showcase the necessity of appliance scheduling and reduce the grid dependency. The simulation results show the profit of ₹13.046 and the grid dependency reduced by 9.636 kW in case 5 with appliance scheduling compared to case 5 without appliance scheduling. Therefore, the electricity cost and grid dependency are reduced using the BPSO algorithm for appliance scheduling in the smart home under normal and uncertain conditions.

FOLD: Fog-dew infrastructure-aided optimal workload distribution for cloud robotic operations

In our fast-paced, technology-driven world, multi-robot systems have emerged as crucial solutions to tackle contemporary challenges, from industrial automation to disaster response, especially where the scope of human interventions is significantly constrained. In such scenarios, a notable number of event-driven operations trigger robots to perform a substantial amount of tasks. Nonetheless, completion of the tasks proves challenging due to the limited computational capabilities inherent to many robotic systems. Although cloud computing solutions can be integrated to address these limitations by distributing the workload to clouds, ensuring optimized performance remains a formidable challenge due to the communication bottlenecks encountered by the robots. Moreover, the presence of robots’ energy constraints and stringent real-time service requirements further exacerbate this workload distribution problem. In response to the aforementioned challenges, this paper introduces a fog-dew-enabled robotic system designed to mitigate latency and energy consumption while orchestrating crucial workload distribution decisions among robots. The execution of decision-making tasks is conceptualized as a multi-objective optimization problem. Due to the NP-hardness of the multi-objective optimization, we propose an innovative solution based on a meta-heuristic Binary Particle Swarm Optimization algorithm. Through rigorous experimentation conducted via simulation within the iFogSim2 simulator, our results demonstrate that the proposed algorithm surpasses the current state-of-the-art in simultaneously optimizing latency and energy consumption.

Optimal scheduling and demand response implementation for home energy management

The optimal scheduling of the loads based on dynamic tariffs and implementation of a direct load control (DLC) based demand response program for the domestic consumer is proposed in this work. The load scheduling is carried out using binary particle swarm optimization and a newly prefaced nature-inspired discrete elephant herd optimization technique, and their effectiveness in minimization of cost and the peak-to-average ratio is analyzed. The discrete elephant herd optimization algorithm has acceptable characteristics compared to the conventional algorithms and has determined better exploring properties for multi-objective problems. A prototype hardware model for a home energy management system is developed to demonstrate and analyze the optimal load scheduling and DLC-based demand response program. The controller effectively schedules and implements DLC on consumer devices. The load scheduling optimization helps to improve PAR by a value of 2.504 and results in energy cost savings of ₹ 12.05 on the scheduled day. Implementation of DLC by 15% results in monthly savings of ₹ 204.18. The novelty of the work is the implementation of discrete elephant herd optimization for load scheduling and the development of the prototype hardware model to show effects of both optimal load scheduling and the DLC-based demand response program implementation.

Quantum binary particle swarm optimization for optimal on-load tap changing and power loss reduction

Quantum binary particle swarm optimization for optimal on-load tap changing and power loss reduction

Lithium-ion battery: Battery sizing with charge scheduling for load levelling, ramp rate control and peak shaving using metaheuristic algorithms

Renewable energy sources (RES) are considered the most promising alternatives to fossil fuels, especially solar photovoltaic (PV). However, the variation in solar irradiance leads to power mismatching with load demand based on the required power distribution. Hybrid solar PV battery is a clean and reliable technology for compensating the load demand during peak hours. In this research, the solar PV is modelled by Nasik Wani substation datasets, and the lithium-ion battery is considered for power scheduling. The proposed work used the emperor penguin optimization (EPO) for battery scheduling to provide the required power to the load during increasing demand and to store the excess energy during lower demand. This proposed work schedules the battery by considering peak shaving and load levelling constraints. Optimum sizing of the battery is an important factor in achieving cost-effective units based on battery operation. In this regard, battle royale optimization (BRO) is used for optimum battery sizing to consider the capital cost, operating cost and maintenance cost. The proposed work is modelled through the MATLAB platform, and the results will be compared using existing Binary Particle Swarm Optimization (BPSO), Teach and Learn Based Optimization (TLBO) and Chimp Optimization Algorithm (COA) for battery scheduling; moreover, the PSO and simulated annealing (SA) approaches for optimum sizing. The capital cost of the proposed method is 821,400$, and the operational and maintenance cost is 11,625.5($/year). The comparative analysis shows that the proposed method outperforms existing approaches for proper scheduling and sizing the battery to meet the load demand.

Integrated Approach for ECG Signal Classification Using Fused Slantlet Transform and Autoregressive Features

Sudden cardiac death remains a significant concern, emphasizing the critical need for intelligent diagnostic techniques in cardiac disease detection. Cardiologic Vascular Diseases (CVD) pose a significant global health challenge, often associated with unhealthy lifestyle habits. Electrocardiogram (ECG) monitoring plays a crucial role in assessing heart function, but its interpretation can be challenging due to signal complexity. This study proposes a novel approach utilizing fused Slantlet-Spatial features alongside Auto Regression (AR) coefficients to classify electrocardiogram (ECG) signals. Leveraging the Slantlet Transform (SLT) for its superior time localization capabilities and the simplicity of AR coefficients, this methodology aims to enhance the accuracy of cardiac illness classification. Nineteen distinct features were extracted from 300 ECG signals, each comprising 512 samples, enriching the classification scheme's efficacy. The fused feature extraction technique demonstrated success in improving overall accuracy. Employing Binary Particle Swarm Optimization (BPSO), irrelevant features were pruned, resulting in a refined feature vector of only 14 relevant features. This reduction in feature dimensionality significantly influenced the classification accuracy. Subsequently, the refined feature vector was introduced to the classification stage, employing four distinct classifiers: Support Vector Machine (SVM) with various kernel functions, K-Nearest Neighbors (K-NN), Naïve Bayes (NB), and Decision Tree (DT). Simulation results revealed the feasibility of achieving an average classification accuracy of 99.67% across ECG signal categories. Notably, the polynomial kernel function-SVM classifier, with only 2-fold cross-validation, yielded optimal performance. This study emphasizes the potential of fused Slantlet-Spatial and AR features in enhancing the accuracy of cardiac disease classification. Moreover, the efficacy of BPSO in feature selection and the superior performance of the SVM classifier highlight promising avenues for further research in intelligent cardiac diagnosis systems. The proposed approach outperforms existing methods and contributes to the early detection of cardiovascular abnormalities, potentially improving patient outcomes.

A robust state estimation by optimal placement of measurement units considering loads/renewable generations and measurements uncertainty

AbstractThe supervisory control and data acquisition (SCADA) system is one of the key requirements for monitoring the power systems state. The power system state is estimated from the state estimation (SE) function, which uses the measurements results from different points. Inaccurate estimation may cause inefficient management of power systems and making decisions. Usually, the number of measurement units (MUs) is limited so the optimal location of MUs is very important in successful and accurate state estimation. The optimal placement of MUs gets more complicated when the actual state of the power system is uncertain due to the high penetration of renewable generation and load uncertainties. Considering the power system's actual state uncertainty and measurement units’ inherent error, this work presents a probabilistic model for the uncertainty of measuring based on the K‐medoids data clustering technique. Then the probabilistic optimal placement of MUs is solved by a binary particle swarm optimization (PSO) method. Considering the mentioned uncertainties makes the obtained solution robust against all the probable scenarios. The proposed technique is implemented on the IEEE 14‐bus test system and the results are discussed. Results show the effectiveness of the proposed method in improving the accuracy of power system state estimation.

Improved Binary Meerkat Optimization Algorithm for efficient feature selection of supervised learning classification

Feature selection (FS) is a crucial step in machine learning and data mining projects. It aims to remove redundant and uncorrelated features, thus improving the accuracy of models. However, it can be challenging to select the optimal features, especially for datasets with many features. This paper proposes the Binary Meerkat Optimization Algorithm (BMOA) to address the issue of FS. The BMOA selects the most related and useful features. Additionally, an improved BMOA (IBMOA) is introduced, which enhances exploration and exploitation capabilities by incorporating the Periodic Mode Boundary Handling (PMBH) strategy and the Local Search (LS) process. This helps to reduce dimensionality and enhance classification accuracy. To evaluate the significance of selected features, two widely used classifiers, namely k-nearest Neighbor (k-NN) and Support Vector Machine (SVM), were used as quality raters. The proposed IBMOA and the original BMOA were compared on 21 multi-scale and multi-faceted benchmark datasets. The binary structures of eight contemporary algorithms, including Binary Artificial Bee Colony (BABC), Binary Grey Wolf Optimization (BGWO), Binary Sailfish Optimizer (BSFO), Binary Particle Swarm Optimizer (BPSO), Binary Bird Swarm Algorithm (BBSA), Binary Whale Optimization Algorithm (BWOA), Binary Grasshopper Optimization Algorithm (BGOA), and Binary Bat Algorithm (BBA), were also analyzed and compared. The proposed IBMOA algorithm outperforms competitors on small and large datasets, obtaining optimal solutions within a reasonable timeframe. This is true for the proposed IBMOA, which has been statistically proven to be highly competitive using the Wilcoxon rank sum test (with alpha=0.05).

A Competitive Bilevel Programming Model for Green, CLSCs in Light of Government Incentives

The growth of world population has fueled environmental, legal, and social concerns, making governments and companies attempt to mitigate the environmental and social implications stemming from supply chain operations. The state-run Environmental Protection Agency has initially offered financial incentives (subsidies) meant to encourage supply chain managers to use cleaner technologies in order to minimize pollution. In today’s competitive markets, using green technologies remains vital. In the present project, we have examined a class of closed-loop supply chain competitive facility location-routing problems. According to the framework of the competition, one of the players, called the Leader, opens its facilities first. The second player, called the Follower, makes its decision when Leader’s location is known. Afterwards, each customer chooses an open facility based on some preference huff rules before returning the benefits to one of the two companies. The follower, under the influence of the leader’s decisions, performs the best reaction in order to obtain the maximum capture of the market. So, a bilevel mixed-integer linear programming model is formulated. The objective function at both levels includes market capture profit, fixed and operating costs, and financial incentives. A metaheuristic quantum binary particle swarm optimization (PSO) is developed via Benders decomposition algorithm to solve the proposed model. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.