Neural methods have shown significant merit in solving combinatorial optimization (CO) problems, including the Bin Packing Problem (BPP). However, most existing ML-based approaches focus on geometric BPP like 3DBPP, neglecting complex vector BPP. In this study, we introduce a vector BPP variant called Class-Constrained Bin Packing Problem (CCBPP), dealing with items of both classes and sizes, and the objective is to pack the items in the least amount of bins respecting the bin capacity and the number of different classes that it can hold. To enhance the efficiency and practicality of solving CCBPP, we propose a learning-based Encoder-Decoder Model. The Encoder employs a Graph Convolution Network (GCN) to generate a heat-map, representing probabilities of different items packing together. The Decoder decodes and fine-tunes the solution through Cluster Decode and Active Search methods, thereby producing high-quality solutions for CCBPP instances. Extensive experiments demonstrate that our proposed method consistently yields high-quality solutions for various kinds of CCBPP with a very small gap from the optimal. Moreover, our Encoder-Decoder Model also shows promising performance on one practical application of CCBPP, the *Manufacturing Order Consolidation Problem* (OCP).

In the multirate sampling processes, the process data are usually collected from various operating conditions and display multimodal characteristics. To monitor these multirate multimode processes, a multirate mixture probability principal component analysis model is proposed for process modeling and fault detection. In this model, the local multirate models are built first for each mode and all of them are subsequently fused with the mixture modeling approach. Such model is able to deal with multirate data with various amount of sampling rates, contributing to a remarkable fault detection and mode identification performance by utilizing all the available measurements even if some variables are unobserved. Then the expectation$-$maximum algorithm is utilized to estimate all the model parameters in the probabilistic framework and the corresponding monitoring method is also developed based on the constructed models. Finally, the effectiveness of the proposed method is demonstrated through a PRONTO benchmark and a real multimode ammonia synthesis process.Note to Practitioners—Motivated by the practical problem of ununiform sampling intervals in multimode processes, this paper proposes a novel multirate mixture probability principle component analysis model for processes modeling and monitoring. In this model, all the available observations with different sampling rates can be incorporated, which contributes greatly to capturing the multimodal characteristics within the industrial processes. Such ability is the key to realize multimode process monitoring, evaluation, fault diagnosis, and process optimization. In addition, although this paper only focuses on the continuous multirate data in industry, it is equally applicable to other forms of multirate data, such as images and videos.

Multi-agent coordination involves both the individual reward and team reward, where the former guides the agent to learn basic skills and the latter measures how well such a team cooperatively completes final tasks. However, in many complex scenarios, these two aspects can be contradictory, due to that one agent excessively pursuing its own profits may suppress the performance of other teammates and lead to the reduction of overall profits. Besides, such dual rewards are generally entangled which make the learning swing between optimizing either the former or latter, which further leads to the sub-optimal and unstable solutions. Moreover, the sparse reward problem commonly encountered in the multi-agent system would further exacerbate this contradiction. In the present work, we address these challenges by proposing CEMARL, a novel framework combining cross-entropy method (CEM) and off-policy multi-agent reinforcement learning (MARL). CEM is gradient-free and learns from the whole episode, whereas MARL is gradient-based and learns from the experiences of agents. The core idea behind CEMARL is that it explicitly decomposes the individual reward and team reward, and deals with them through gradient-based learning and gradient-free evolution, respectively. By means of this, it can simultaneously maximize the individual and team reward, and reconciles the contradiction between individual and team as well as the sparse reward problem. CEMARL shows both conciseness in framework and stability in training, and achieves significantly better performances than state-of-the-art baselines on a range of complex tasks.

Recently, Reinforcement Learning (RL) has shown superior performance in traffic signal control (TSC) and can effectively mitigate traffic congestion. However, two key challenges still need to be addressed. First, a clear mechanism to coordinate different intersections is essential for efficient TSC, and the investigation of diverse coordination mechanisms is needed in various traffic scenarios, which remains unsolved in current works. Second, existing research tries to optimize area traffic efficiency by manually designing rewards with local short-time-horizon metrics based on different expert experiences, which requires cumbersome work and may not align with the area control objective. To address these challenges, a novel cooperation skill motivated TSC algorithm (CoST) with a modular framework is proposed in this paper. Cooperation skill in CoST is an innovative method to directly investigate diverse coordination mechanisms between neighboring intersections without manually reward design. The cooperation skill is formulated in a hierarchical structure with a cooperative policy and an execution policy, which are used to determine the cooperative probabilities between intersections and to realize such cooperation, respectively. Besides, a distinguishable feature extraction network is introduced to encourage the learning of diverse functionalities. Then based on learned cooperation skills, a meta policy is formulated to choose skills of different intersections to achieve optimum area transportation efficiency. We evaluate our method on two synthetic networks and two real-world networks using SUMO, and the results show the superiority of our method over the state-of-the-art methods.

Multivariate statistical process monitoring (MSPM) has been widely used in modern industries and most of traditional MSPM methods are developed using uniformly sampled measurements. However, process variables are often sampled with different rates in practical industries. On the other hand, most of the industries are dynamic processes in which the measurements are highly autocorrelated. Thus, it is difficult to build a dynamic process model with incomplete data sets in multirate processes. In this paper, a multirate linear Gaussian state-space model is exploited to deal with the above issues. Both the offline model training and online process monitoring schemes are developed in the present of incomplete multirate process data sets. The proposed method is validated through a numerical example and the Tennessee Eastman benchmark process.