Swarm Optimization Gravitational Search Algorithm Research Articles

Hybrid game theoretic strategy for optimal relay selection in energy harvesting cognitive radio network

SummaryRelay selection plays a crucial role in enhancing the performance of wireless networks particularly in the context of cognitive radio (CR) systems with energy harvesters. In this paper, we propose a novel approach, namely, CGAPSO Shapley, for the best relay selection while simultaneously optimizing the parameters of signal‐to‐interference‐plus‐noise ratio (SINR), throughput, and outage probability. The CGAPSO Shapley algorithm combines the Shapley value, a cooperative game theory concept, with cellular genetic algorithm particle swarm optimization (CGAPSO) to achieve effective and efficient optimization of relay selection. The CGAPSO framework provides a hybrid structure that integrates cellular genetic algorithm (CGA) and particle swarm optimization (PSO), enabling simultaneous evolution of the population and particles within cells. The incorporation of the Shapley value and the hybrid CGAPSO framework enables effective exploration of the solution space and provides decision‐makers with comprehensive insights for relay selection. By utilizing the Shapley value, we assign weights to the relay nodes based on their contributions to the overall optimization objectives, considering their CR capabilities and energy harvesting capabilities. Some benchmark test functions are used to compare the hybrid algorithm with both the standard CGAPSO, Particle swarm optimization gravitational search algorithm (PSOGSA) and PSO algorithms in evolving best solution. The results show the hybrid algorithm possesses a better capability to escape from local optimums with faster convergence than the standard algorithms. The novel CGAPSO Shapley approach achieves an outage probability of 0.323324, marking a significant improvement of 60% over the outage probability achieved with conventional approach.

Optimal transmission voltage deviation based on Fractional Kinetic Gas Molecular Optimization Symbiotic Organism Search Algorithm for network operational stability improvement

This research applies Fractional Kinetic Gas Molecular Optimization Symbiotic Organism Search (FKGMOSOS) algorithm to optimize Total Voltage Deviation (TVD) while improving the security of an electricity transmission system. Hybrid KGMOSOS has excellent rate of convergence to optimum, but in order to avoid the possibility of getting stuck in local optimum, Fractional Differential Order (FDO) was integrated into the velocity term in the algebraic model of KGMOSOS leading to FKGMOSOS evolution. Using this algorithm, optimal TVD was accomplished by varying the levels of the grid control state variables to attain the finest set of optimal results in IEEE 30 – Bus, 13 – Variable standard network. The optimization competence of this new technique was verified for multiple runs through comparative investigation with that of Fractional Particle Swarm Optimization Gravitational Search Algorithm (FPSOGSA) for each FDO scenario. The results of simulation showed that for 250 successive iterations, FKGMOSOS outperformed FPSOGSA which also outperformed other literary techniques.

Protection coordination of DOCRs for different modes of microgrid operation

The present study is focussed on solving the relay coordination problem. Protection of microgrids is performed through the placement of directional overcurrent relays (DOCR). The efficacy of microgrid protection depends on coordination of all the DOCRs placed in the system. For this purpose, a number of optimization techniques have been employed by the power system researcher. In this paper, Grey Wolf Optimizer (GWO) is proposed for the protection coordination of DOCRs for different modes of microgrid operation. The proposed method is tested and validated on a 7-bus mesh system and a 9-bus radial test system. The proposed method has been compared with other meta-heuristic optimization approaches, namely Genetic Algorithm (GA), Artificial Bee Colony (ABC), Gravitational Search Algorithm (GSA), and Hybrid Particle Swarm Optimization Gravitational Search Algorithm (PSOGSA). Based on the obtained results, the GWO-based approach is very efficient in mitigating the problem of relay coordination as compared to other optimization techniques.

Power minimization of gas transmission network in fully transient state using metaheuristic methods

Abstract In gas transmission networks, the pressure drop caused by friction is one of the main operation costs that is compensated through consuming energy in the compressors. In the competitive market of energy, considering the demand variation is inevitable. Hence, the power minimization should be carried out in transient state. Since the minimization problem is severely nonlinear and nonconvex subjected to nonlinear constraints, utilizing a powerful minimization tool with a straightforward procedure is very helpful. In this paper, a novel approach is proposed based on metaheuristic algorithms for power minimization of a gas transmission network in fully transient conditions. The metaheuristic algorithms, unlike the gradient dependent method, can solve the complicated minimization problem without simplification. In the proposed strategy, the cost function is not expressed explicitly as a function of minimization variables; therefore, the transient minimization can be as precise as possible. The minimization is carried out by a straightforward methodology in each time sample, which leads to more precise solutions as compared to the quasi transient minimization. The metaheuristic minimizer, called the particle swarm optimization gravitational search algorithm (PSOGSA), is utilized to find the optimum operating set points. The numerical results also confirm the accuracy and well efficiency of the proposed method.

Transmission Efficiency Optimal Design of Spiral Bevel Gear Based on Hybrid PSOGSA (Particle Swarm Optimization—Gravitational Search Algorithm) Method

Transmission efficiency is a significant index of the transmission system. Even though much research has been carried out to calculate gear transmission efficiency, only a few of them studied spiral bevel gear due to its complexity. Moreover, spiral bevel gear does not have a “standard surface”, which means more complex coupling relations between different parameters and makes efficiency optimal design more difficult. Therefore, an instantaneous transmission efficiency computing model of a spiral bevel gear was set up based on loaded tooth contact analysis and hybrid elasto-hydrodynamic lubrication theory. Then, the particle swarm optimization–gravitational search algorithm (PSOGSA) optimal model was constructed to obtain the best parameters that maximize the average transmission efficiency of spiral bevel gears. Control parameters and machining parameters are optimized in sequence based on the proposed optimal model. The results showed that both optimal designs could help improve transmission efficiency, but the range of machining parameters is limited in a small interval because of the complex coupling relations. Therefore, the machining parameters optimization are conducted after control parameters optimization, which showed good results. Transmission efficiency was finally improved to 98.78%, which increased more than 4% at least. The proposed optimal model could also be applied into other gear design methods or even other fields.

Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties

Optimal reactive power dispatch (ORPD) with integration of renewable energy resources has a growing interest in research community due to its utmost requirements during the operation, planning and design of the modern electrical power networks. The objective of ORPD is to improve the performance of power network by means of reducing the losses in transmission line, improving the voltage profile, and decreasing the overall cost of operation through optimal tuning of the operational variables such as tap position of transformers, generator output voltages and capacitor banks. However, the nonlinear, non-stationary and complex nature of power network, presence of load uncertainties, and dynamic behavior of wind generation introduces a complex optimization task which cannot be readily solved in an efficient manner. In this research work, a new fractional memetic computing paradigm, i.e., the fractional particle swarm optimization gravitational search algorithm with entropy evolution (FPSOGSA-EE), is designed to solve the ORPD problems in power system adopting wind power plants (WPPs) and load uncertainties. The proposed optimization framework FPSOGSA-EE integrates the concept of fractional calculus and Shannon entropy to strengthen the optimization characteristics of canonical algorithm. The exhaustive experimentation endorse the efficacy of FPSOGSA-EE by providing minimum gauge of fitness evaluation function, namely, the line loss and voltage deviation index minimization, in IEEE 30 and 57 bus networks. The stability, consistency and reliability of proposed FPSOGSA-EE is ascertained through statistical interpretations by means of boxplots, probability measures for cumulative distribution function, and histogram illustrations.

Hybrid Particle Swarm Optimization–Gravitational Search Algorithm Based Detection of Graphene Defects With Electrical Impedance Tomography

Recently, graphene has gained a lot of attention in the electronic industry due to its unique properties and to overcome the limits of miniaturization making way for novel devices in the field of electronics. Among the synthesizing methods for growing large graphene films, chemical vapour deposition is one of the promising and common techniques but defects such as cracks, holes, or wrinkles are hard to avoid. The presence of defects influence the electrical properties of graphene thus the local conductivity distribution across the surface of the graphene can characterize its electrical behavior. The difference in conductivity values of the defect and the background can be estimated with electrical impedance tomography. Due to the very high conductivity of graphene, the reconstructed electrical impedance tomography conductivity images suffer from poor spatial resolution. Considering the graphene defect conductivity and the number of defects are known a priori then the unknowns are defect geometry and background conductivity of graphene that are estimated using hybrid particle swarm optimization - gravitational search algorithm. The defect geometries are described by truncated Fourier series coefficient which can represent the complex shapes. Numerical studies are done for graphene characterization with single and multiple defects. Monte Carlo simulations with 20 runs having different noise seed are carried out to evaluate the robustness of the proposed algorithm. Statistical analysis is done and the results of the proposed algorithm are compared against the conventional modified Newton Raphson method and gravitational search algorithm. Experimental studies with graphene sheet 2.5 cm x 2.5 cm with defects are performed for shape estimation. The results showed that the proposed algorithm has a good estimation of background conductivity and defect geometry.

A novel gaussian based particle swarm optimization gravitational search algorithm for feature selection and classification

A Gaussian based Particle Swarm Optimization Gravitational Search Algorithm (GPSOGSA) is being proposed for extensive feature selection that serves highly in making effective predictions. GPSOGSA helps to overcome the problem of being stuck into the local optima and influences the local searching ability, thus it aims to bridge the gap of exploration and exploitation. The algorithm also limits the usage of too many parameters like acceleration factors, maximum velocity, inertia weight that plays a vital role in PSO, GSA and PSOGSA. The efficacy of the algorithm has been tested upon unimodal and multimodal benchmark functions. We have also evaluated the performance of the algorithm by applying it on various benchmark datasets. The algorithm uses a wrapper-based approach that includes Support Vector Machine as a learner algorithm, and improves both the execution time and the performance accuracy. The findings show that the proposed algorithm could escape from local optimum and converges faster than the PSO, GSA and PSOGSA algorithms.

Optimized Harmonic Reduction PWM based Control Technique for Three-Phase quasi Z-Source Inverter

This paper proposes an optimized harmonic reduction pulse width modulation (HRPWM) control strategy for three-phase quasi Z-source inverter (qZSI). In traditional sinusoidal or space vector pulse width modulation techniques, the flexibility in adjustment of individual switching angles is not possible and thus, these techniques are not optimum choices for low switching frequency operations of high/medium power qZSI. In the proposed technique, adjustments of switching angles of HRPWM waveform are possible to achieve optimum performance. The optimum performance is targeted as maximization of boosting factor and simultaneous minimization of weighted total harmonic distortion (WTHD) at the output voltage of qZSI. The hybrid particle swarm optimization gravitational search algorithm (PSOGSA) is used for computation of optimum switching angles of suggested HRPWM waveform at various modulation indices. The obtained WTHDs up to 49th order harmonics and boosting factors of optimized HRPWM methodology are compared with that of the maximum boost control (MBC) technique for qZSI to justify superior performances of the suggested method in low switching frequency range. The proposed concept has been verified via simulation study. The experimentation (qZSI controlled by microcontroller) validates the working of optimized HRPWM based qZSI which agrees with software results.

An Improved PSOGSA for Clustering and Routing in WSNs

Wireless sensor network (WSN) is an integration of sensing, communicating, computing in a board range environment. Efficient energy consumption becomes the most challenging task for sensor nodes. The clustering and routing techniques are promising methods to resolve the issue and extend the network’s lifespan. The clustering technique is defined as grouping data into classes, every cluster sharing a high degree of similarity in between them, and each cluster being dissimilar with others. This technique is the best data processing model for WSN, and it controls the redundant data inside the network. The nomination of the appropriate cluster head is a major factor in the clustering technique. The object of this proposed paper is to equipoise the energy of the clustering nodes and route the data from cluster head to sink. We propose an improved particle swarm optimization gravitational search algorithm for clustering and routing in WSNs. Here clustering algorithm makes equal energy in the entire network by the uniform distribution of cluster head, routing algorithm decides the ideal routing path to convey data packet between cluster head and sink. The proposed paper integrates the exploration capacity of GSA and the exploitation capability of PSO. Detailed simulation performs using MATLAB based simulator in terms of residual energy, network lifespan, and convergence rate. In comparing our proposed algorithm to other existing algorithms, it outperforms significantly.

A Hybrid Modified Method of the Sine Cosine Algorithm Using Latin Hypercube Sampling with the Cuckoo Search Algorithm for Optimization Problems

The metaheuristic algorithm is a popular research area for solving various optimization problems. In this study, we proposed two approaches based on the Sine Cosine Algorithm (SCA), namely, modification and hybridization. First, we attempted to solve the constraints of the original SCA by developing a modified SCA (MSCA) version with an improved identification capability of a random population using the Latin Hypercube Sampling (LHS) technique. MSCA serves to guide SCA in obtaining a better local optimum in the exploitation phase with fast convergence based on an optimum value of the solution. Second, hybridization of the MSCA (HMSCA) and the Cuckoo Search Algorithm (CSA) led to the development of the Hybrid Modified Sine Cosine Algorithm Cuckoo Search Algorithm (HMSCACSA) optimizer, which could search better optimal host nest locations in the global domain. Moreover, the HMSCACSA optimizer was validated over six classical test functions, the IEEE CEC 2017, and the IEEE CEC 2014 benchmark functions. The effectiveness of HMSCACSA was also compared with other hybrid metaheuristics such as the Particle Swarm Optimization–Grey Wolf Optimization (PSOGWO), Particle Swarm Optimization–Artificial Bee Colony (PSOABC), and Particle Swarm Optimization–Gravitational Search Algorithm (PSOGSA). In summary, the proposed HMSCACSA converged 63.89% faster and achieved a shorter Central Processing Unit (CPU) duration by a maximum of up to 43.6% compared to the other hybrid counterparts.

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

This paper proposes a novel hybrid algorithm called Fractional-order Particle Swarm optimization Gravitational Search Algorithm (FPSOGSA) and applies it to the trajectory planning of the hypersonic lifting reentry flight vehicles. The proposed method is used to calculate the control profiles to achieve the two objectives, namely a smoother trajectory and enforcement of the path constraints with terminal accuracy. The smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide (QEG) scheme. The aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement scheme. The maximum heating rate path constraint is enforced through the angle of attack parameterization. The Common Aero Vehicle (CAV) flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization (PSO) method and the standard Gravitational Search Algorithm (GSA). The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.

A new compound wind speed forecasting structure combining multi-kernel LSSVM with two-stage decomposition technique

The aims of this study are to develop a novel compound structure that consists of two-stage decomposition (TSD), hybrid particle swarm optimization gravitational search algorithm (HPSOGSA) and multi-kernel least square support vector machine (MLSSVM) for improving forecasting accuracy. In the most previous wind speed forecasting studies, only one wind speed signal decomposition method is considered, which is insufficient. To better deal with the wind speed time series, TSD method combining complementary ensemble empirical mode decomposition with adaptive noise with wavelet transform is firstly employed in the proposed model to preprocess the wind speed samples; then, binary-valued particle swarm optimization gravitational search algorithm is exploited as feature selection to identify and eliminate the abnormal noise signal within the input candidate matrix that is determined by partial autocorrelation function. The kernel function and the kernel parameters have great influence on the regression performance of LSSVM. To solve these problems, integrations of radial basis function, polynomial (poly) and linear kernel functions by optimal weighted coefficients are constructed as multi-kernel function for LSSVM, namely MKLSSVM, and the parameter combination is tuned by conventional PSOGSA. The feature selection and parameter optimization are realized by hybrid PSOGSA (HPSOGSA) simultaneously. Finally, comprehensive comparison and analysis are carried out using the historical wind speed data from one wind farm of China to illustrate the excellent forecasting performance of TSD–HPSOGSA–MKLSSVM.

Design of Fractional Particle Swarm Optimization Gravitational Search Algorithm for Optimal Reactive Power Dispatch Problems

In fact, optimal RPD is one of the most critical optimization matters related to electrical power stability and operation. The minimization of overall real power losses is obtained by adjusting the power systems control variables, for instance; generator voltage, compensated reactive power and tap changing of the transformer. In this search, a new heuristic computing method named as fractional particle swarm optimization gravitational search algorithm (FPSOGSA) is presented by introducing fractional derivative of velocity term in standard optimization mechanism. The designed FPSOGSA is implemented for the optimal RPD problems with IEEE-30 and IEEE-57 standards by attaining the near finest outcome sets of control variables along with minimization of two fitness objectives; active power transmission line losses ($P_{loss,}$ MW) and voltage deviation ($\text{V}_{\mathrm {D}}$ ). The superior performance of the proposed FPSOGSA is verified for both single and multiple runs through comparative study with state of art counterparts for each scenario of optimal RPD problems.

Fractional PSOGSA Algorithm Approach to Solve Optimal Reactive Power Dispatch Problems With Uncertainty of Renewable Energy Resources

The optimal reactive power dispatch (ORPD) is a major tool, and it plays a vital role for enhancement of the power system performance. ORPD is one multimodal, non-convex, and non-linear problem. Many elegant benefits can be obtained by using the renewable energy resources (RERs), but many technical issues related to the RERs including the stochastic characteristics of these resources due to continuous variations of solar irradiance and the wind speed lead to increasing the uncertainties of system. Thus, solving the ORPD problem with RERs is a crucial task. The contribution of the paper includes application a modified hybrid algorithm for solving the ORPD considering the uncertainties of the RERs and the load demand. The proposed algorithm is based on Fractional Calculus with Particle Swarm Optimization Gravitational Search Algorithm (FPSOGSA) which aims to enhance the searching capabilities of the conventional PSOGSA algorithm and overcome its tendency to stagnation. The proposed algorithm is tested on IEEE 30-bus system for reducing power losses and voltage deviation as well as enhancing voltage stability. The scenario-based method is employed to produce a set of scenarios from the uncertainties of load, wind speed and solar irradiance. The simulation results verify the effectiveness of the proposed algorithm for solving the ORPD problem with and without considering the uncertainties in the system. Furthermore, the proposed algorithm is superior compared with the state-of-the-art techniques in terms of the reduction of power losses and voltage deviations as well as the stability enhancement.

New Approach for Sediment Yield Forecasting with a Two-Phase Feedforward Neuron Network-Particle Swarm Optimization Model Integrated with the Gravitational Search Algorithm

Predicting sediment yield is an important task for decision-makers in environmental monitoring and water management since the benefits of applying non-linear, artificial intelligence (AI) models for optimal prediction can be far reaching in real-life decision support systems. AI-based models are considered to be favorable predictive tools since the nonlinear nature of suspended sediment data series warrants the utilization of nonlinear predictive methods for feature extraction, and for accurate simulation of suspended sediment load. In this study, Artificial Neural Network (ANN) approaches are employed to estimate the monthly sediment load where the two-phase Feed-forward Neuron Network Particle Swarm Optimization Gravitational Search Algorithm (FNN-PSOGSA) is developed, and then evaluated in respect to 3 distinct algorithms: the Adaptive Neuro-Fuzzy Inference System (ANFIS), Feed-forward Neuron Network (FNN) and the single-phase Feed-forward Neuron Network Particle Swarm Optimization (FNN-PSO). The study is carried out using the monthly rainfall, runoff and sediment data spanning a 10 year period (2000–2009) where about 75% of data are used in model training phase, 25% in testing phase. Three statistical performance criteria namely: the mean absolute error (MAE), Nash-Sutcliffe coefficient (NSE) and the Willmott’s Index (WI) and diagnostic plots visualizing the tested results are used to evaluate the performance of four AI-based models. The results reveal that the objective model (the two-phase FNN-PSOGSA model) and the single-phase FNN-PSO model yielded more precise results compared to the other forecast models. This result accorded to an NSE value of 0.612 (for the FNN-PSOGSA model) vs. an NS value of 0.500, 0.331 and 0.244 for the FNN-PSO, FNN and ANFIS models, and WI = 0.832 vs. 0.771, 0.692 and 0.726, respectively The study also demonstrated that the FNN model generated slightly better results than the ANFIS model for the estimation of sediment load data but overall, the two-phase FNN-PSOGSA model outperformed all comparison models. In light of the superior performance, this research advocates that the fully-optimized two-phase FNN-PSOGSA model can be explored as a decision-support tool for monthly sediment load forecasting using the rainfall and runoff values as the predictor datasets.

A hybrid structure of an extreme learning machine combined with feature selection, signal decomposition and parameter optimization for short-term wind speed forecasting

Influenced by various environmental and meteorological factors, wind speed presents stochastic and unstable characteristics, which makes it difficult to forecast. To enhance the forecasting accuracy, this study contributes to short-term multi-step hybrid wind speed forecasting (WSF) models using wavelet packet decomposition (WPD), feature selection (FS) and an extreme learning machine (ELM) with parameter optimization. In the model, the WPD technique is applied to decompose the empirical wind speed data into different, relatively stable components to reduce the influence of the unstable characteristics of wind speed. A hybrid particle swarm optimization gravitational search algorithm (HPSOGSA) combining conventional PSOGSA with binary PSOGSA (BPSOGSA) is utilized to realize the FS and parameter optimization simultaneously. The PSOGSA is employed to tune the parameter combination of input weights and biases in ELM, while BPSOGSA is exploited to select the most suitable features from the candidate input variables determined by a partial autocorrelation function for reconstruction of the input matrix for ELM. The proposed forecasting strategy carries out multi-step short-term WSF using mean half-hour historical wind speed data collected from a wind farm situated in Anhui, China. To investigate the forecasting results of the hybrid model, a lot of comparisons and analyses are executed. Simulation results illustrate that the proposed WPD-ELM model with FS and parameter optimization can effectively catch the non-linear characteristics hidden in wind speed data and provide satisfactory WSF performance.

Use of modified hybrid PSOGSA for optimum design of RC frame

ABSTRACTA realistic and optimum design of reinforced concrete structural frame, by hybridizing enhanced versions of standard particle swarm optimization (PSO) and standard gravitational search algorithm (GSA) is presented in this paper. PSO has been democratized by considering all good and bad experiences of the particles, whereas GSA has been made self-adaptive by considering a specific range for certain parameters like ‘gravitational constant’ and ‘set of agents with best fitness value.’ Optimal size and reinforcement of the members have been found by employing the technique in a computer-aided environment. Use of self-adaptive GSA together with democratic PSO technique has been found to provide two distinct advantages over standard PSO and GSA, namely better capability to escape from local optima and faster convergence rate. The entire formulation for optimal cost design of frame includes the cost of beams and columns. In this approach, variables of each element of structural frame have been considered as continuous functions and rounded off appropriately to imbibe practical relevance to the study. An example has been considered to emphasize the validity of this optimum design procedure and results have been compared with earlier studies.

Stochastic optimal reactive power planning and active power dispatch with large penetration of wind generation

In this paper, an optimal probabilistic reactive power planning and active power dispatch method considering uncertain loads and intermittent wind generation is proposed. Four types of wind generator models, viz, simple PQ model of an induction generator and pitch regulated fixed speed, semi-variable speed, and doubly fed induction generator models, have been considered in this work. The objective of the planning strategy adopted is to maximize the annual profit of the utility. To maximize the profit, a modified particle swarm optimization gravitational search algorithm based optimization technique has been developed. The performance of this developed technique has been compared with those obtained from genetic algorithm, gravitational search algorithm, and modified particle swarm optimization gravitational search algorithm optimization methods. Extensive simulation studies on IEEE-30, IEEE-57, and IEEE-118 bus systems show that the performance of the modified algorithm technique is superior to that of other methods in terms of the value of both the objective function and the reproducibility of results.

Optimization of collision avoidance maneuver planning for cluster satellites in space debris explosion situation

In this study, the conjunction situation when a number of explosion fragments approach four cluster satellites was simulated, and an optimum avoidance maneuver plan that mitigates this risk was established. The orbits of four deputy satellites around a virtual chief satellite were defined using the Hill–Clohessy–Wiltshire equation, and NASA’s breakup model was applied to similar altitude rocket body to simulate explosions situation. The distribution of 230 explosion fragments after an explosion was simulated, and the size and direction of the Delta-V were applied to each fragment. In this situation, the collision avoidance maneuver planning strategy that uses heuristic algorithm was proposed to establish efficient avoidance maneuver plan for approaching fragments after the explosion. Avoidance maneuver plans using four heuristic algorithms were established to minimize the fuel consumption of the four cluster satellites within several constraints including conjunction risk, ground track and formation between cluster satellites. Eight simulations were performed with different combinations of the four heuristic algorithms and different generations and populations. As a result, all avoidance maneuver plan satisfied conjunction risk constraint as well as the other complex constraints. In particular, particle swarm optimization–gravitational search algorithm established the most efficient maneuver plan with the least fuel consumption and fastest convergence speed.