Bi-stage restriction-handling method for the preventive maintenance of a complex machine using differential evolution algorithm

Abstract

With the increasing complexity of manufacturing equipment, reliability is facing increasingly serious challenges. To ensure its safe operation, this paper considers the preventive maintenance scheme of a complex machine considering production, variable maintenance instants, and deterioration. To begin with, a stochastic dynamical system is proposed to describe the machine’s deterioration process. Further, this problem is modeled as a stochastic dynamical system optimal control model (SDSOCM) including restrictions. It is challenging to directly achieve a high-quality solution of the SDSOCM due to its non-convexity, strong non-linearity, and randomness. To obtain a global optimal solution, the SDSOCM is analytically transformed into a deterministic dynamical system optimal control model (DDSOCM) with restrictions. Following that, a differential evolution algorithm with bi-stage restriction-handling method (DEA-BSRHM) is proposed to solve this DDSOCM via integrating the exterior point approach (EPA) and the interior point approach (IPA) into a differential evolution algorithm (DEA). In the first stage, the EPA involving a dynamic penalty parameter is proposed for comparing candidate members to drive them into the feasible domain. To enhance the search capability and decrease the calculation cost, the IPA including a dynamic penalty parameter is employed for choosing the candidate members in the second stage. Finally, the validity of the proposed method is illustrated via comprehensive experiments and comparative studies. Numerical results on a machine preventive maintenance problem and test functions from IEEE CEC 2010, IEEE CEC 2017, and IEEE CEC 2020 show that compared with other algorithms, DEA-BSRHM can obtain a better solution with smaller standard deviation and less number of function evaluations.