###### Abstract  
A moving window decision-making algorithm is proposed for the cleaning schedule optimization of heat exchanger network system subject to fouling in refinery crude preheat train. This algorithm is designed by incorporating the moving window scheme into a conventional multi-period optimal control problem (OCP) framework and has a distinct feature that it can efficiently handle a complex problem where a long-time horizon is considered. When compared with the conventional multi-period OCP method using fixed time horizon, our algorithm always shows an excellent performance regarding the computational time, still finding a compatible optimal solution. In our moving window decision-making algorithm, it is important to determine the optimal moving window size for the given time horizon as it  
presented a MINLP framework with a multi-period time discretization, which was widely adopted in the optimization studies of the preheat train afterwards. They used a lumped parameter model and compared two optimization methods, i.e., a commercial deterministic MINLP solver and a simple heuristic greedy algorithm (GrA), concluding that both methods could not guarantee a global optimum because the problem itself was highly nonconvex. Although stochastic techniques such as outer approximation-extended relaxation algorithm [22] and backtracking threshold accepting algorithm [23] were explored, they all found only local minimum and even suffered from failure in convergence with a large-scale problem [21]. To find a global solution, mixed-integer linear programming (MILP) approaches have also been employed [15; 24; 25; 26]. [PERSON] and [PERSON] [27] presented a MINLP model considering cyclic cleaning actions and attempted to find a global solution after reformulating it into a MILP model. [PERSON] and [PERSON] [15] also presented a rigorous MILP model based on the multi-period time discretization and proposed a decomposition procedure to obtain a global solution. The MILP approach, however, has a critical drawback that the problem scale becomes much larger by the linearization [1; 17]. In addition, the linearization itself has been argued in the real situations. More recently, several advanced stochastic optimization techniques such as imperialist competitive algorithm [6; 28], genetic algorithm [4; 11], particle swarm optimization [11], duelist algorithm [11], etc. have also received great attention along with the advances in computer hardware technology. However, it seems that the global optimality of the solutions obtained by these stochastic methods should be further confirmed because their performance could be varied depending on parameter tuning [17]. Moreover, they still require too much computational resources to make a rapid decision in the actual fields. The difficulty in identifying a global solution has made the researchers rather focus on more robust optimization techniques capable of handling a large-scale HEN cleaning schedule problem. This practical need has been emphasized as the mathematical model has become more complex with the deepened understandings about the effects of varied operating conditions on the fouling and the different types of fouling mechanisms/cleaning actions. For example, the effect of wall temperature and flow velocity [29], controlling the desalter inlet temperature [2], distinguishing the foulant deposit into two layers, i.e., soft (fresh) and hard (aged) layers [3], cleaning-in-place methods and off-line mechanical cleaning [30], etc. were successfully incorporated into the model. It is noteworthy, however, there has been any significant improvement for the optimization techniques in these studies. Most of them still adopted heuristic approaches such as GrA or its modifications. In recent, [PERSON] et al. [18] proposed a simple but robust algorithm for the HEN cleaning schedule optimization problem, which is quite different from the previous approaches.