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Grey prediction evolutionary algorithm (GPE) is an emerging category of meta-heuristic algorithm based on mathematical model. It generates offspring by predicting the macroscopic evolutionary trend of population series. On the contrary, the mining of local evolutionary trend are flawed. To address this imperfection, this paper introduces a quadratic function as a surrogate model to mine the local evolutionary trend of population series for the first time. Thereby an improved grey prediction evolutionary algorithm called grey prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (GPE-QI) is designed. The surrogate model based on quadratic interpolation is regarded as an external auxiliary tool to mine the local evolutionary trend of population series by using currently superior individuals. Through utilizing the mined local trend information, a donor population closer to the optimal solution is formed to improve the prediction direction of the algorithm. The performance of GPE-QI is tested on CEC2019, CEC2020 benchmark functions and six engineering design problems. The experimental results demonstrate the stronger competitiveness of GPE-QI to well-established algorithms in terms of solving accuracy and convergence rate. If this paper is accepted, MATLAB codes associated with this paper will be uploaded to https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE. • Improvement can be made by enhancing local search of grey prediction evolution. • Mine local evolutionary trend of population series by quadratic interpolation. • Construct a surrogate model by using the local evolutionary trend. • Design an improved grey prediction evolutionary algorithm with a surrogate model. • The proposed algorithm is more competitive than the well-established. [ABSTRACT FROM AUTHOR]

• We address a complex single machine scheduling problem. • We consider flexible and variable maintenance activity to be scheduled. • We develop a novel self-adaptive harmony search algorithm. • We compare different heuristic and meta-heuristic algorithms. • We perform a sensitivity analysis involving several influencing factors. A common assumption in the scheduling literature provides that machines are always available, while often they have to be stopped because of preventive maintenance operations. Inspired by a real-life manufacturing context, this paper deals with the single machine scheduling problem with a flexible/variable maintenance to be executed within a specific time window. Differently from other studies in the literature, a set of non-resumable jobs with sequence dependent setup-times and non-zero release dates have to be scheduled along with a maintenance activity whose duration is a non-decreasing function of its starting time, with the objective of minimizing the total tardiness (T-problem). A mathematical model of the problem is proposed and, due to the high computational complexity, several heuristics have been implemented and tested with the aim of using some of them to make metaheuristic algorithms more effective and computationally efficient. Hence, a modified harmony search, powered by several reinforcement strategies and even equipped with a self-adaptive calibration mechanism, has been developed and compared with a set of additional algorithms proposed by the literature. Numerical results reveal that the modified harmony search outperforms the competing algorithms and no performance loss arises by adopting the self-adaptive mechanism. Finally, a proper sensitivity analysis allows assessing the impact of several influencing factors on the total tardiness minimization. [ABSTRACT FROM AUTHOR]