Training Multi-layer Perceptrons Using Chaos Grey Wolf Optimizer
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摘要:
灰狼优化算法(GWO)是一种新的基于灰狼捕食行为的元启发式算法，被证明是一种具有高水平的探索和开发能力的算法。但是存在开发和探索不平衡的问题，以至于其优化性能并不理想。该文将混沌理论引入GWO中，用于平衡GWO的探索和开发，提出一种改进的混沌灰狼优化算法(CGWO)，并应用于多层感知器(MLPs)的训练。首先，基于Cubic混沌理论对GWO的位置更新公式进行改进，以增加个体的多样性，增大跳出局部最优的概率和对解空间进行深入的搜索；其次，设计一种非线性收敛因子，用于协调和平衡CGWO算法在不同迭代进化时期的探索和开发能力；最后，将CGWO算法作为MLPs的训练器，用于对3个复杂分类问题进行分类实验。结果表明：CGWO在分类准确率，避免陷入局部最优，全局收敛速度和鲁棒性方面相较于其他对比算法均具有较好的性能。
Abstract:The Grey Wolf Optimizer (GWO) algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature, and it is an algorithm with high level of exploration and exploitation capability. This algorithm has good performance in searching for the global optimum, but it suffers from unbalance between exploitation and exploration. An improved Chaos Grey Wolf Optimizer called CGWO is proposed, for solving complex classification problem. In the proposed algorithm, Cubic chaos theory is used to modify the position equation of GWO, which strengthens the diversity of individuals in the iterative search process. A novel nonlinear convergence factor is designed to replace the linear convergence factor of GWO, so that it can coordinate the balance of exploration and exploitation in the CGWO algorithm. The CGWO algorithm is used as the trainer of the Multi-Layer Perceptrons (MLPs), and 3 complex classification problems are classified. The statistical results prove the CGWO algorithm is able to provide very competitive results in terms of avoiding local minima, solution precision, converging speed and robustness.
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表 2 5种算法对3 bit XOR问题10次独立运行结果的比较
算法 平均值 中值 标准差 最好值 PSO-MLP 1.48e–04 1.65e–05 2.40e–04 7.67e–09 GSA-MLP 2.35e–01 2.38e–01 1.17e–02 2.10e–01 PSOGSA-MLP 1.27e–02 9.29e–06 2.57e–02 1.64e–09 GWO-MLP 7.00e–03 6.07e–03 1.89e–02 2.90e–05 CGWO-MLP 6.01e–06 1.21e–08 1.33e–05 2.69e–09 
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表 3 5种算法对气球分类问题10次独立运行结果的比较
算法 平均值 中值 标准差 最好值 PSO-MLP 0 0 0 0 GSA-MLP 5.90e–03 4.10e–03 6.00e–03 4.69e–04 PSOGSA-MLP 9.85e–32 9.73e–40 2.94e–31 3.81e–61 GWO-MLP 1.12e–18 3.56e–20 2.38e–18 2.49e–26 CGWO-MLP 2.35e–15 2.07e–18 5.03e–15 1.00e–18
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表 4 5种算法对虹膜分类问题10次独立运行结果的比较
算法 平均值 中值 标准差 最好值 PSO-MLP 2.70e–02 2.47e–02 1.76e–02 6.20e–03 GSA-MLP 1.83e–01 1.89e–01 2.30e–02 1.48e–01 PSOGSA-MLP 4.91e–02 1.84e–02 1.01e–01 1.16e–02 GWO-MLP 2.27e–02 2.19e–02 2.70e–03 1.71e–02 CGWO-MLP 1.90e–02 1.82e–02 4.10e–03 1.39e–02
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