Subburaj Brindha, Maheswari J Uma, Ibrahim S P Syed, Kavitha Muthu Subash
School of Computer Science and Engineering, Vellore Institute of Technology, Chennai, India.
School of Information and Data Sciences, Nagasaki University, Nagasaki, Japan.
Sci Rep. 2024 Aug 1;14(1):17863. doi: 10.1038/s41598-024-68436-1.
The objective measurements of the real-world optimization problems are mostly subject to noise which occurs due to several reasons like human measurement or environmental factors. The performance of the optimization algorithm gets affected if the effect of noise is higher than the negligible limit. The previous noise handling optimization algorithms use a large population size or multiple sampling at same region which increases the total count of function evaluations, and few methods work for a particular problem type. To address the above challenges, a Differential Evolution based Noise handling Optimization algorithm (NDE) to solve and optimize noisy bi-objective optimization problems is proposed. NDE is a Differential Evolution (DE) based optimization algorithm where the strategies for trial vector generation and the control parameters of DE algorithm are self-adapted using fuzzy inference system to improve the population diversity along the evolution process. In NDE, explicit averaging based method for denoising is used when the noise level is higher than negligible limit. Extending noise handling method enhances the performance of the optimization algorithm in solving real world optimization problems. To improve the convergence characteristics of the proposed algorithm, a restricted local search procedure is proposed. The performance of NDE algorithm is experimented using DTLZ and WFG problems, which are benchmark bi-objective optimization problems. The obtained results are compared with other SOTA algorithm using modified Inverted Generational Distance and Hypervolume performance metrics, from which it is confirmed that the proposed NDE algorithm is better in solving noisy bi-objective problems when compared to the other methods. To further strengthen the claim, statistical tests are conducted using the Wilcoxon and Friedman rank tests, and the proposed NDE algorithm shows significance over the other algorithms rejecting the null hypothesis.
实际优化问题的客观测量大多受到噪声影响，这些噪声是由多种原因产生的，如人为测量或环境因素。如果噪声影响高于可忽略的限度，优化算法的性能就会受到影响。以往的噪声处理优化算法采用较大的种群规模或在同一区域进行多次采样，这增加了函数评估的总数，而且很少有方法适用于特定类型的问题。为应对上述挑战，提出了一种基于差分进化的噪声处理优化算法（NDE），用于求解和优化有噪声的双目标优化问题。NDE是一种基于差分进化（DE）的优化算法，其中试验向量生成策略和DE算法的控制参数使用模糊推理系统进行自适应调整，以在进化过程中提高种群多样性。在NDE中，当噪声水平高于可忽略限度时，使用基于显式平均的去噪方法。扩展的噪声处理方法提高了优化算法在解决实际优化问题中的性能。为改善所提算法的收敛特性，提出了一种受限局部搜索过程。使用DTLZ和WFG问题对NDE算法的性能进行实验，这两个问题是基准双目标优化问题。使用改进的倒置世代距离和超体积性能指标将所得结果与其他最优算法进行比较，由此证实，与其他方法相比，所提NDE算法在解决有噪声双目标问题方面表现更佳。为进一步强化这一说法，使用威尔科克森和弗里德曼秩检验进行统计测试，所提NDE算法相对于其他算法具有显著性，拒绝了原假设。
