## 1 Introduction  
With the continuous improvement of oil and gas exploration and development, the proportion of heterogeneous and low-permeability reservoirs in exploration and development is gradually increasing. Using conventional water injection to develop low-permeability reservoirs results in a low recovery factor [1]. Compared to water, CO\({}_{2}\) is less viscous and can enter into small pores more easily, which can reduce the viscosity of crude oil, expand the volume of crude oil, improve the mobility ratio, and thus increase the oil recovery factor [2,3]. Therefore, CO\({}_{2}\)-enhanced oil recovery (CO\({}_{2}\)-EOR) has great potential for developing low-permeability reservoirs. In addition to this, CO\({}_{2}\)-EOR can sequestrate CO\({}_{2}\) underground, which can help in achieving carbon neutrality [4]. However, in the CO\({}_{2}\) flooding method, during gas injection, the low viscosity of CO\({}_{2}\) may lead to a phenomenon referred to as viscous fingering. This results in an unfavorable mobility ratio, which seriously affects the improvement of swept volume [5]. Moreover, due to its low density, COcan easily escape to the upper part of the reservoir, forming a fugitive flow channel [6]. This also constitutes a drawback for CO2 flooding as it leads to a reduction of the swept volume. In response to the problems of waterflooding and CO2 flooding, researchers proposed CO2-WAG methods [7]. This technology was first used by Mobil in 1957 in a sandstone reservoir in Alberta, Canada. It combines the characteristics of water flooding and CO2 flooding, which increases the macroscopic sweep efficiency and thus improves the overall oil displacement efficiency. In addition, CO2-WAG can mitigate the issue of rapid CO2 flow and increase the gas phase's flow resistance. It can also lower the resistance to the flow of the water phase and increase the mobility ratio. As a result of this, recovery efficiency can be greatly improved [7]. It has been reported that 80% of oilfield projects in the US using WAG technology have achieved good results [8]. [PERSON] et al. [9] studied 59 WAG fields and found that the average recovery of crude oil was improved by 10% for all WAG cases. Recently, WAG has also been used in the Brazilian subsalt oilfield complex [10]. Subsalt oil and gas production was 2739 million barrels of oil equivalent per day (2.739 Mboe/day) by 2020, representing 70.3% of Brazil's total oil equivalent. The Lula field, which conducted the WAG pilot test in April 2011, has a cumulative oil production of 2000 Mboe by 2020 and is the largest extracted/producing field in Brazil, with an average oil and gas production of 988,000 barrels/day and 43.2 Mm\({}^{3}\)/day, respectively [11]. Currently, the optimization of WAG extraction schemes is the focus of many oil fields and related researchers [12; 13; 14; 15; 16; 17; 18; 19; 20]. [PERSON] et al. [21] used CMG reservoir numerical simulation software to optimize the application of WAG in a sub-salt offshore field in Brazil and proposed a design method for CO2-WAG operations in carbonate reservoirs, focusing on the economics, the CO2 cycle efficiency, and project risk. It is worth mentioning that the application of intelligent algorithms such as machine learning, which has developed rapidly in recent years, has been used in petroleum exploration and development [22; 23], especially in optimization problems. For instance, [PERSON] et al. [24] proposed a method for bit optimization with the help of neural networks. [PERSON] and [PERSON] et al. [25] optimized the mud loss problem in Brazilian deepwater subsalt fields with the help of KNN, MLP, and NB algorithms. [PERSON] et al. [26] proposed a joint optimization method for well location and injection and extraction parameters using the random forest as well as a radial basis neural network. In general, memory-based learning algorithms perform better than any other family of algorithms. These methods assume that a given set of terms and class labels can be used as a mapping to identify unlabeled term classes [25].