A Hybrid Formal and Optimization Framework for Real-Time Scheduling: Combining Extended Time Petri Nets with Genetic Algorithms

In modern Industry 4.0 environments, real-time scheduling presents a complex challenge requiring both formal correctness guarantees and optimal performance. Background: Traditional approaches fail to provide an optimal integration between formal correctness guaranteeing and optimization, and such failure either produces suboptimal results or a correct result lacking guarantee, and studies have indicated that poor scheduling decisions could cause productivity losses of up to 20–30% and increased operational costs of up to USD 2.5 million each year in medium-scale manufacturing facilities. Methods: This work proposes a new hybrid approach by integrating Extended Time Petri Nets (ETPNs) and Finite-State Automata (FSAs) with formal modeling, abstracting ETPNs by extending conventional Time Petri Nets to deterministic time and priority systems, accompanied by Genetic Algorithms (GAs) to optimize the solution to tackle a multi-objective optimization problem. Our solution tackles indeterministic problems by incorporating suitable priority resolution methods and GA to pursue optimal solutions to very complex scheduling problems and starting accurately from standard real-time scheduling-policy models such as DM, RM, and EDF-EDF. Results: Experimental evaluation has clearly verified performance gains up to 48% above conventional techniques, covering completely synthetic and practical case studies, including 31–48% improvement on synthetic benchmarks, 24% increase on resource allocation, and total elimination of constraint violations. Conclusions: The new proposed hybrid technique is, to a considerable extent, a dramatic advancement within real-time scheduling techniques and Industry 4.0, successfully and effectively integrating optimal correctness guaranteeing and favorable GA-aided optimization techniques, which particularly guarantee optimal correctness to safe-related applications and provide considerable improvements to support efficient and optimal performance, extremely helpful within Industry 4.0.