Research on low-carbon flexible job shop scheduling problem based on improved Grey Wolf Algorithm

As a significant branch of production scheduling problem, the Flexibility Job Shop Scheduling Problem (FJSP) is a typical NP-hard problem. Most conventional flexible workshop scheduling primarily focuses on performance aspects involving production efficiency such as time and quality. In recent years, due to increased energy costs and environmental pollution, 'low-carbon scheduling' has garnered attention as a new scheduling paradigm among scholars and engineers. This paper investigates a low-carbon flexible Job shop scheduling problem, proposing a Grey Wolf Optimization algorithm (SC-GWO), aiming to minimize the sum of carbon emission costs and makespan costs. This algorithm employs the Grey Wolf Algorithm (GWO) as the fundamental optimization method, adaptively choosing between global and local searches based on the dispersion degree of individuals. Firstly, integrating the Sine Cosine Algorithm (SCA), the sinusoidal cosine search mechanism is applied to GWO to enhance its local search capability. Secondly, a new leader selection mechanism is introduced to prevent leaders from falling into local optima, thus improving the algorithm's global exploration capability. Utilizing a nonlinear convergence factor strategy controls the global exploration and local exploitation capabilities in different algorithm stages, enhancing optimization accuracy and accelerating convergence, achieving a dynamic balance between the two. Finally, validation of the SC-GWO algorithm's ability to solve low-carbon scheduling problems in flexible job shop scheduling instances is conducted. Experimental results demonstrate the superior performance of SC-GWO in solving low-carbon flexible workshop scheduling instances. Comparative experiments against four other advanced algorithms on 22 classic benchmark test functions confirm SC-GWO's better convergence. Through standard test functions like Bandimarte instances applied to solve FJSP, experimental results showcase the excellent optimization performance of SC-GWO. Compared to HGWO and GWO, the makespan time is reduced by 22.25% and 39.27%, respectively. The proposed SC-GWO algorithm demonstrates favorable solving effects on flexible job shop scheduling instances, meeting actual production scheduling needs.