## 1 Introduction
In the literature, the planning of processes in CPSs were studied. For example, in [27; 28; 29; 30], different approaches were proposed for planning processes in CPS. This study aims to develop a more effective evolutionary algorithm for planning processes in CPS based on an auction mechanism. Auctions have been applied in transportation service procurement on the Cyber-Physical Internet [32] in on-demand logistics trading [33], cloud manufacturing resource trading [34] and task allocation in CPSs [35]. In this study, an auction mechanism will be used in the CPS over the course of the process planning. As the process-planning problem is a constrained discrete optimization problem, an effective approach must be used to tackle its complexity issue. Due to the success of applying various evolutionary computation approaches in the literature to optimize CPSs [36; 37; 38], we will adopt an evolutionary computation approach to solve the planning problem of sustainable CPSs. Well-known evolutionary computation approaches include Particle Swarm Optimization [39] and Differential Evolution [40; 41; 42]. In the literature, the effectiveness of an evolutionary computation algorithm can be assessed based on performance and robustness. Performance is concerned with the quality of solutions found and is usually measured with the average fitness function values of solutions. In addition to performance, robustness is also an important metric in the evaluation of metaheuristic algorithms [43; 44]. The robustness of an evolutionary computation algorithm is measured by the sensitivity of the average fitness function values with respect to the algorithmic parameters. In this study, we will develop an effective evolutionary algorithm for planning production processes in sustainable CPSs and study the computational experiences of the solution algorithm in terms of performance and robustness. In the literature, the neighborhood search mechanism is an effective approach to solving optimization problems. Self-adaptive mechanisms provide an approach to adapting the parameters of a solution method. Combining these two mechanisms has the potential to yield a better solution in the solution space [45]. The effectiveness of this approach has been successfully applied in [46]. To achieve the goal of this study, we focus on developing a self-adaptive neighborhood search-based Differential Evolution method to support the planning of processes in sustainable CPSs. In this study, a self-adaptive mechanism is combined with neighborhood search in the Differential Evolution method. This creates a self-adaptive neighborhood search Differential Evolution (SaNSDE) algorithm. To tackle the constraints of the planning problem, the method used in [47] is adopted. We assess the performance of this approach by performing experiments for several cases. By analyzing the results of these experiments, it shows that the proposed method outperforms several methods in the literature. This paper differs from the previous ones on CPSs in [3; 11] in that both the sustainability factor and efficiency factor are jointly considered in this study. The contributions of this paper are as follows. First, a general problem formulation for planning processes considering time and sustainability factors is proposed. Second, a solution method for the problem based on the self-adaptive mechanism and neighborhood search mechanism is proposed. Third, the proposed method is verified by a special class of production processes. Fourth, the effectiveness of the proposed solution algorithm in terms of performance and robustness is studied and shows that the proposed solution algorithm outperforms several other algorithms. We structure the rest of this paper as follows. In Section 2, we first describe the problem in planning processes in a CPS by briefly introducing the optimization problem. In Section 3, we will propose a SaNSDE algorithm based on the DE approach. We will report the experimental results in Section 4. We will discuss the results in Section 5 and conclude this paper in Section 6.