Improved pigeon-inspired optimization algorithm based on adaptive learning strategy
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摘要:
鸽群优化（PIO）算法已广泛用于无人机编队和控制参数优化等领域，但标准PIO算法容易陷入局部最优。提出了一种基于自适应学习策略的改进鸽群优化（ALPIO）算法。该算法引入了基于容差的搜索方向调整策略、基于自学习的候选者生成策略以及基于竞争学习的预测策略，通过增强种群的多样性，可提高算法全局最优概率，其已在8个基准函数上进行测试。仿真试验结果表明：所提算法在多峰函数优化问题中的收敛精度和收敛速度有了显著提升，并且能够更有效避免陷入局部最优解。
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关键词:
- 鸽群优化(PIO)算法 /
- 局部最优 /
- 自适应学习策略 /
- 种群多样性 /
- 全局最优
Abstract:Pigeon-Inspired Optimization (PIO) algorithm has been widely used in the field of UAV formation and control parameter optimization, but the standard PIO algorithm is easy to fall into local optimum. This paper proposes an Adaptive Learning Pigeon-Inspired Optimization (ALPIO) algorithm. The algorithm introduces a tolerance-based search direction adjustment strategy, a self-learning candidate generation strategy, and a competitive learning based prediction strategy. By enhancing the diversity of the population, the global optimal probability of the algorithm can be improved. The algorithm has been tested on eight benchmark functions. The simulation results show that the convergence accuracy and convergence speed of the algorithm in the multi-peak function optimization problem are significantly improved, and it can effectively avoid falling into the local optimal solution.
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表 1 测试函数
Table 1. Test functions
函数类别 No. 函数名称 fi*=fi(x*) 定义域 单峰函数 1 Sphere Function -1400 [-100, 100]D 5 Different Powers Function -1000 多峰函数 11 Rastrigin’s Function -400 14 Schwefel’s Function -100 17 Lunacek Bi_Rastrigin Function 300 18 Rotated Lunacek Bi_Rastrigin Function 400 组合函数 22 Composition Function 2 (n=3, Unrotated) 800 28 Composition Function 8 (n=5, Rotated) 1400 注：D为搜索空间维度；fi*为函数fi的全局最优解。 
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表 2 参数设置
Table 2. Parameter setting
参数 数值 适用算法 地图与指南针算子最大迭代次数T1 400/1 200/2 000, D=10/30/50 PIO，ALPIO 地标算子最大迭代次数T2 MaxIter-T1 全局最大迭代次数MaxIter 1000/3000/5000, D=10/30/50 所有算法 种群数量Ncmax 30/100/200, D=10/30/50 指南针因子R 0.3 PSO, SCPIO, EGTPIO, ALPIO 导航过渡因子tr 2 EGTPIO 每次迭代减少数量Ndec 1 学习因子c1 1.49445 PSO 学习因子c2 1.49445 惯性因子ω 0.5
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表 3 D=10时测试函数上算法的性能比较
Table 3. Performance comparison of algorithms on test functions at D=10
基准函数 算法 最好值 最差值 中位数 平均值 方差 1 PIO -1.4000×103 -1.3493×103 -1.3983×103 -1.3927×103 1.3182×102 PSO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 SCPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 EGTPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 ALPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 5 PIO -1.0000×103 -9.6351×102 -9.9882×102 -9.9719×102 30.264 PSO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 SCPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 4.3495 EGTPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 ALPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 11 PIO -4.0000×102 -2.8845×102 -3.6360×102 -3.5356×102 1.7683×103 PSO -4.0000×102 -3.9403×102 -3.9901×102 -3.9809×102 4.7455 SCPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 EGTPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 ALPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 14 PIO -99.466 3.1140×103 1.8499×102 8.6975×102 1.3738×106 PSO -1.0000×102 1.4396×102 -99.750 -75.268 2.8283×103 SCPIO -1.0000×102 -99.998 -1.0000×102 -1.0000×102 8.0483×10-8 EGTPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 ALPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 17 PIO 3.6426×102 3.9355×102 3.8136×102 3.8053×102 66.988 PSO 3.0323×102 3.1785×102 3.1029×102 3.1014×102 24.856 SCPIO 3.0000×102 3.0097×102 3.0000×102 3.0010×102 0 EGTPIO 3.6502×102 3.6721×102 3.6622×102 3.6610×102 43.345 ALPIO 3.0000×102 3.6616×102 3.0000×102 3.0000×102 0 18 PIO 4.0000×102 4.1002×102 4.0043×102 4.0136×102 5.5533 PSO 4.0000×102 4.1000×102 4.0000×102 4.0078×102 7.3725 SCPIO 4.0000×102 4.0005×102 4.0000×102 4.0000×102 0 EGTPIO 4.0000×102 4.1000×102 4.0000×102 4.0039×102 3.8432 ALPIO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 22 PIO 9.0011×102 4.1978×103 1.2728×103 1.9899×103 1.3803×106 PSO 9.0000×102 1.3791×103 9.0012×102 9.4073×102 9.2495×103 SCPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 EGTPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 ALPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 28 PIO 1.6000×103 1.6070×103 1.6001×103 1.6010×103 4.5682 PSO 1.6000×103 1.6002×103 1.6000×103 1.6000×103 5.5234×10-3 SCPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 EGTPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 ALPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0
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表 4 D=30时测试函数上算法的性能比较
Table 4. Performance comparison of algorithms on test functions at D=30
基准函数 算法 最好值 最差值 中位数 平均值 方差 1 PIO -1.4000×103 -1.1955×103 -1.3949×103 -1.3759×103 1.6455×103 PSO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 SCPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 EGTPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 ALPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 5 PIO -9.9998×102 -9.5253×102 -9.9787×102 -9.9364×102 1.0811×102 PSO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 SCPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 EGTPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 ALPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 11 PIO -3.9994×102 -1.1362×102 -3.4789×102 -3.2648×102 6.0677×103 PSO -4.0000×102 -3.5722×102 -3.9005×102 -3.8763×102 1.5583×102 SCPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 EGTPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 ALPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 14 PIO -99.995 1.0678×104 1.6731×103 3.5922×103 1.4467×107 PSO -1.0000×102 1.3613×103 -98.612 1.6715×102 1.9816×105 SCPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 EGTPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 ALPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 17 PIO 3.0396×102 5.9754×102 5.8832×102 5.6157×102 8.2231×103 PSO 3.0284×102 3.5431×102 3.2714×102 3.3142×102 3.2705×102 SCPIO 3.0000×102 3.0000×102 3.0000×102 3.0000×102 0 EGTPIO 5.7408×102 5.9003×102 5.7463×102 5.7685×102 26.065 ALPIO 3.0000×102 3.0000×102 3.0000×102 3.0000×102 0 18 PIO 4.0001×102 4.1697×102 4.0413×102 4.0631×102 44.777 PSO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 SCPIO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 EGTPIO 4.0000×102 4.3000×102 4.0000×102 4.0600×102 1.6001×102 ALPIO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 22 PIO 9.0567×102 1.0038×104 3.7923×103 4.8606×103 1.7354×107 PSO 9.0000×102 1.6773×103 9.6100×102 1.0725×103 6.6626×104 SCPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 EGTPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 ALPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 28 PIO 1.6000×103 1.6189×103 1.6014×103 1.6042×103 41.089 PSO 1.6000×103 1.6098×103 1.6013×103 1.6024×103 9.6456 SCPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 EGTPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 ALPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0
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表 5 D=50时测试函数上算法的性能比较
Table 5. Performance comparison of algorithms on test functions at D=50
基准函数 算法 最好值 最差值 中位数 平均值 方差 1 PIO -1.3993×103 -1.3242×103 -1.3864×103 -1.3803×103 5.2769×102 PSO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 SCPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 EGTPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 ALPIO -1.4000×103 -1.4000×103 -1.4000×103 -1.4000×103 0 5 PIO -9.9906×102 -9.9038×102 -9.9742×102 -9.9606×103 11.036 PSO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 SCPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 EGTPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 ALPIO -1.0000×103 -1.0000×103 -1.0000×103 -1.0000×103 0 11 PIO -3.9954×102 1.1811×102 51.466 -89.763 4.9059×104 PSO -4.0000×102 -3.4030×102 -3.9154×102 -3.7622×102 7.0296×102 SCPIO -4.0000×102 -3.8009×102 -4.0000×102 -3.9639×102 58.637 EGTPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 ALPIO -4.0000×102 -4.0000×102 -4.0000×102 -4.0000×102 0 14 PIO -96.729 1.4799×104 7.5448×103 6.8965×103 3.9397×107 PSO -1.0000×102 2.2040×103 8.8665×102 9.1588×102 5.4392×105 SCPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 EGTPIO -1.0000×102 -1.0000E×102 -1.0000×102 -1.0000×102 0 ALPIO -1.0000×102 -1.0000×102 -1.0000×102 -1.0000×102 0 17 PIO 4.6652×102 8.3597×102 7.8375×102 7.7430×102 2.9637×103 PSO 3.0000×102 4.2347×102 3.5955×102 3.5744×102 9.7055×102 SCPIO 3.0000×102 3.0000×102 3.0000×102 3.0000×102 0 EGTPIO 3.0000×102 8.0084×102 7.8518×102 7.6805×102 9.1350×103 ALPIO 3.0000×102 3.0000×102 3.0000×102 3.0000×102 0 18 PIO 4.0006×102 4.5189×102 4.0243×102 4.1314×102 4.1925×102 PSO 4.0000×102 4.5000×102 4.0000×102 4.0500×102 2.5000×102 SCPIO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 EGTPIO 4.0000×102 4.5000×102 4.2718×102 4.2544×102 6.7213×102 ALPIO 4.0000×102 4.0000×102 4.0000×102 4.0000×102 0 22 PIO 9.0453×102 8.1386×103 2.4321×103 3.3507×103 8.0341×106 PSO 9.0000×102 2.8655×103 2.1728×103 1.8437×103 7.1144×105 SCPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 EGTPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 ALPIO 9.0000×102 9.0000×102 9.0000×102 9.0000×102 0 28 PIO 1.6000×103 1.6230×103 1.6015×103 1.6038×103 48.631 PSO 1.6000×103 1.6029×103 1.6001×103 1.6009×103 1.3128 SCPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 EGTPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0 ALPIO 1.6000×103 1.6000×103 1.6000×103 1.6000×103 0
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[1] DUAN H B, QIAO P X.Pigeon-inspired optimization:A new swarm intelligence optimizer for air robot path planning[J].International Journal of Intelligent Computing and Cybernetics, 2014, 7(1):24-37. [2] ZHANG X M, DUAN H B, YANG C.Pigeon-inspired optimization approach to multiple UAVs formation reconfiguration controller design[C]//Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference.Piscataway: IEEE Press, 2014: 2707-2712. [3] SUN Y B, XIAN N, DUAN H B.Linear-quadratic regulator controller design for quadrotor based on pigeon-inspired optimization[J].Aircraft Engineering and Aerospace Technology, 2016, 88(6):761-770. [4] DOU R, DUAN H B.Pigeon inspired optimization approach to model prediction control for unmanned air vehicles[J].Aircraft Engineering and Aerospace Technology:An International Journal, 2016, 88(1):108-116. [5] DENG Y M, DUAN H B.Control parameter design for automatic carrier landing system via pigeon-inspired optimization[J].Nonlinear Dynamics, 2016, 85(1):97-106. [6] ZHANG D F, DUAN H, YANG Y J, et al.Active disturbance rejection control for small unmanned helicopters via levy flight-based pigeon-inspired optimization[J].Aircraft Engineering and Aerospace Technology, 2017, 89(8):946-952. [7] DUAN H B, WANG X H.Echo state networks with orthogonal pigeon-inspired optimization for image restoration[J].IEEE Transanctions on Neural Networks and Learning Systems, 2016, 27(11):2413-2425. [8] DUAN H B, QIU H X, FAN Y M.Unmanned aerial vehicle close formation cooperative control based on predatory escaping pigeon-inspired optimization[J].Scientia Sinica, 2015, 45(6):559. [9] YANG Z Y, DUAN H B, FAN Y M, et al.Automatic carrier landing system multilayer parameter design based on cauchy mutation pigeon-inspired optimization[J].Aerospace Science and Technology, 2018, 79:518-530. [10] ZHANG D F, DUAN H B.Social-class pigeon-inspired optimization and time stamp segmentation for multi-UAV cooperative path planning[J].Neurocomputing, 2018, 313(3):229-246. [11] HUA B, HUANG Y, WU Y, et al.Spacecraft formation reconfiguration trajectory planning with avoidance constraints using adaptive pigeon-inspired optimization[J].Science China Information Sciences, 2019, 62(7):98-100. [12] XIANG S, XING L, WANG L, et al.Comprehensive learning pigeon-inspired optimization with tabu list[J].Science China Information Sciences, 2019, 62(7):95-97. [13] HUO M, DUAN H, LUO D, et al.Parameter estimation for a VTOL UAV using mutant pigeon inspired optimization algorithm with dynamic OBL strategy[C]//2019 IEEE 15th International Conference on Control and Automation (ICCA).Piscataway: IEEE Press, 2019: 669-674. [14] HU C, XIA Y, ZHANG J.Adaptive operator quantum-behaved pigeon-inspired optimization algorithm with application to UAV path planning[J].Algorithms, 2019, 12(1):3. [15] LIU H, YAN X, WU Q.An improved pigeon-inspired optimization algorithm and its application in parameter inversion[J].Symmetry, 2019, 11(10):1291. [16] XU X, DUAN H, DENG Y, et al.Hybrid ISMC-PIO and receding horizon control for UAVs formation[C]//2019 IEEE Congress on Evolutionary Computation (CEC).Piscataway: IEEE Press, 2019: 3277-3284. [17] CHEN B, LEI H, SHEN H, et al.A hybrid quantum-based PIO algorithm for global numerical optimization[J].Science China Information Sciences, 2019, 62(7):33-44. [18] HAI X S, WANG Z L, REN Y, et al.A novel adaptive pigeon-inspired optimization algorithm based on evolutionary game theory[J].Science China Information Sciences, 2020, 64(3):24-37. [19] ZHANG S J, DUAN H B.Gaussian pigeon-inspired optimization approach to orbital spacecraft formation reconfiguration[J].Chinese Journal of Aeronautics, 2015, 28(1):200-205. [20] WANG F, ZHANG H, LI K S, et al.A hybrid particle swarm optimization algorithm using adaptive learning strategy[J].Information Sciences, 2018:162-177. [21] LIANG J J, QU B Y, SUGANTHAN P N, et al.Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization[J].Computational Intelligence Laboratory, 2013, 12(34):281-295. [22] LIANG J J, SUGANTHAN P N.Dynamic multi-swarm particle swarm optimizer with a novel constraint-handling mechanism[C]//IEEE International Conference on Evolutionary Computation.Piscataway: IEEE Press, 2006: 16-21. -
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