## 1 Introduction
In this mechanism, the reactive scheduling is normally motivated by disturbances beyond a specific level in order to reduce the rescheduling for frequently occurring events. However, it is currently challenging to find out a method that can achieve a good balance between solution quality as well as computational time when it is necessary to consider rescheduling in HFSs. Heuristic methods obtain a feasible solution quickly, but can hardly ensure the solution quality because they fail to take all the aspects of HFS scheduling into account. Alternatively, metaheuristic methods are capable of finding out optimal solutions owing to their general procedures. Nevertheless, these procedures require too much computational effort and will make the rescheduling plan not a real-time one. Consequently, it is necessary to develop an efficient rescheduling method for the dynamic scheduling of HFS. The Genetic Regulatory Network (GRN) is a structured network that describes the regulation of gene expression in cells [38]. It has been attracting increased attention because of its excellent description capacity, and various methods, including directed graphs, Boolean networks, rule-based formalisms, qualitative differential equations, Bayesian networks and partial differential equations are currently alternative to construct such a network [39]. A GRN has at least the following three elements in common: genes, gene regulations and gene expression procedures [40]. Each gene has two alternative states (i.e., the expressed state and the unexpressed state). If a gene is in the expressed state, it has inhibitory effects on the states of other ones, which is the primary form of gene regulations. Based upon these regulations, the gene expression procedure converts iteratively certain genes in the unexpressed state into ones in the expressed state if there are few inhibitory effects on these genes. According to genes in the expressed state, the GRN finally determines a specific morphology for the related cell. For instance, Figure 1 illustrates a GRN composed of three genes and constructed by differential equations. In this network, \(\mu_{z}\) (\(z\) = 1-3) represents the state of gene \(z\); \(\sigma_{z}\) (\(z\) = 1-3) is the inhibition coefficient that describes quantitatively the inhibitory effects on gene \(z\); \(\epsilon_{1}\), \(\epsilon_{2}\) and \(\epsilon_{3}\) are regulatory parameters in gene regulation equations. At the beginning, all genes are in the unexpressed state. Based on the inhibition coefficients determined by regulatory parameters, the gene expression procedure converts certain genes to the expressed state at discrete moments, and finally ends with the gene states (0,1,1). In a HFS scheduling problem, the binary decision variable is similar to the state of a gene. The decision variable interaction in constraints and objectives has an analogous form with gene regulations. Therefore, genes in a GRN are used to express decision variables, and gene regulations are adopted to describe constraints and objectives. In this way, a gene expression procedure depending on the regulations appropriately can obtain a feasible solution, in which the state of a gene indicates the assigned value of a related decision variable. In general, the differential equation method is most suitable for such a GRN because it provides the detailed description of gene regulations in a quantitative way [41]. In such an equation, undetermined regulatory parameters can be further optimized to obtain a near-optimal solution within the reasonable computational time because the number of these parameters is limited. Based on the mapping relationship illustrated in Figure 2, a GRN-based method is thus proposed for HFS rescheduling. Figure 1: An example of GRN (Genetic Regulatory Network) composed of three genes. Figure 2: Mapping between the HFS (Hybrid Flow Shop) scheduling problem and a GRN.