**2. Preliminaries**

In this section, some basic knowledge on the CBR framework and the distance-based similarity measurements is introduced. Unlike the model-based methods, CBR solves the target problem with several related cases stored in the case base. To be specific, the case base should be constructed with as many historical cases as possible. Each case consists of a problem description and a case solution. Figure 1 gives the basic framework of CBR (also known as the CBR cycle).

**Figure 1.** Basic framework of CBR.

It could be seen from Figure 1 that case retrieval is the first step of the CBR cycle. The task of case retrieval is to retrieve several valuable cases from the constructed case base. Supposing the number of retrieved cases is fixed as *k*, the retrieved cases are the first *k* cases with the most similar problem descriptions to the target problem. After the case retrieval step, the case reuse is performed to obtain a suggested solution according to the retrieved cases. If the suggested solution is not applicable to the target problem, the suggested solution needs revising to adapt to the target problem. In the last step, the experience of solving this target problem is stored to update the case base, which enable CBR to constantly learn during the CBR cycle.

In general, CBR solves the target problem by learning from historical cases with similar problem descriptions to the target problem. Therefore, case retrieval is the foundation of CBR, and the retrieval accuracy directly affects the performance of CBR [29–31]. In previous studies, most case retrievals are based on distance-based similarity. Table 1 lists five most commonly used distances for similarity measurement in CBR.

**Table 1.** The most commonly used distances for similarity measurement in CBR.


As shown in Table 1, several distances can be applied to measure the similarity between two cases. Under the CBR framework, grea<sup>t</sup> attention has been paid to measure the similarity between the target problem and historical problems in the case base. However, due to the complexity of industrial processes, it is still hard to choose an appropriate similarity index that only retrieves valuable cases when facing gross measuring error and multiple working conditions. Therefore, it is necessary to develop an abnormal case removal method so as to obtain the most valuable cases in industrial operational optimization.
