Chance constrained dynamic optimization approach for single machine scheduling involving flexible maintenance, production, and uncertainty

• Published in: Engineering applications of artificial intelligence Vol. 114; p. 105024
• Main Authors: Wu, Xiang, Zhang, Kanjian
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2022
• Subjects: Chance constraints; Convergence analysis; Dynamic optimization; Non-convex optimization; Single machine scheduling; Stochastic search algorithm; Chance constraints; Stochastic search algorithm; Non-convex optimization; Single machine scheduling; Dynamic optimization; Convergence analysis
• ISSN: 0952-1976
• DOI: 10.1016/j.engappai.2022.105024

Chance constraints are suitable for industrial process modeling under uncertain conditions, where constraints cannot be strictly satisfied or do not need to be fully satisfied. In this paper, a single machine scheduling problem involving flexible maintenance, production, and uncertainty is modeled as a chance constrained dynamic optimization problem (CCDOP). A novel method is proposed for transforming the CCDOP into an equivalent deterministic dynamic optimization problem (DOP) with fixed state jump times. Furthermore, by using the idea of l1 penalty function and a smooth approximation technique, the resulting deterministic DOP becomes a smoothing penalty problem, which is a non-convex nonlinear parameter optimization problem (NNPOP) with simple bounds on the variables. To solve the NNPOP, a gradient-based stochastic search algorithm (GSSA) is developed based on a gradient-based adaptive search algorithm (GASA) and a novel stochastic search algorithm (NSSA). The convergence analysis result shows that the GSSA is a globally convergent algorithm. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method. Numerical results show that the GSSA has excellent convergence behavior with robust computation feature, providing better results compared with the other typical methods. •A CCDOA is developed for the single machine scheduling problem.•Propose a novel technique to transform the CCDOP into an equivalent CDPOP.•Design a GASA, which is effective for ill-conditioned problems.•Design a NSSA, in which no parameters tuning is required.•Propose a GSSA for the NNPOP and comparison results imply its superiority.