Population diversity control based differential evolution algorithm using fuzzy system for noisy multi-objective optimization problems.

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.