Recent advancements have introduced machine learning frameworks to enhance the Branch and Bound (B\&B) branching policies for solving Mixed Integer Linear Programming (MILP). These methods, primarily relying on imitation learning of Strong Branching, have shown superior performance. However, collecting expert samples for imitation learning, particularly for Strong Branching, is a time-consuming endeavor. To address this challenge, we propose \textbf{C}ontrastive Learning with \textbf{A}ugmented \textbf{M}ILPs for \textbf{Branch}ing (CAMBranch), a framework that generates Augmented MILPs (AMILPs) by applying variable shifting to limited expert data from their original MILPs. This approach enables the acquisition of a considerable number of labeled expert samples. CAMBranch leverages both MILPs and AMILPs for imitation learning and employs contrastive learning to enhance the model's ability to capture MILP features, thereby improving the quality of branching decisions. Experimental results demonstrate that CAMBranch, trained with only 10\% of the complete dataset, exhibits superior performance. Ablation studies further validate the effectiveness of our method.

A new iterative learning control method is presented for the trajectory tracking control of linear time-variant systems. This new method does not need detailed knowledge of the controlled system. However, a reference batch is designed, in which some small change of the input trajectory in the current batch is applied to the controlled system, and then its output trajectory is obtained. The ratio of the input change and corresponding output change in the current and reference batch is used as the gain in the learning law for calculating the inputs of the next batch. Thus the method can track the desired trajectory successfully while the iteration is running on. The convergence of the proposed method is analyzed, and the method is validated on a typical linear time-variant system.

This paper presents an iterative learning control strategy for a fed-batch fermentation process using linearised models identified from process operational data. Off-line calculated control policies for batch fermentation processes may not be optimal when implemented on the processes due to model plant mismatches and/or the presence of unknown disturbances. In order to overcome the effect of model plant mismatches and unknown disturbances, a batch to batch iterative learning control strategy is developed to modify the control actions for the next batch using the information obtained form current and previous batches. The control policy updating is calculated using a model linearised around a reference batch. In order to cope with process variations and disturbances, the reference batch can be taken as the immediate previous batch. After each batch, the newly obtained process operation data is added to the historical process data base and an updated linearised model is re-identified. Since the control actions during different stages of a batch are usually correlated, it is proposed in this paper that the linearised model can be identified from partial least square regression. The proposed technique has been successfully applied to a simulated fed-batch fermentation process.