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With the increasing uncertainty in production environments and changes in market demand, flexible and efficient scheduling solutions have become particularly critical. However, existing research mainly focuses on static scheduling or relatively simple dynamic scheduling problems, which are inadequate to address the complexities of actual production processes. This paper considers the dynamic flexible flow shop scheduling problem (DFFSP) characterized by diverse processes, complexity, and high flexibility, and proposes a multi-agent reinforcement learning algorithm based on cross-attention networks (MARL_CA). First, this paper proposes a novel state feature representation method, which represents the job processing data and the production Gantt chart as a state matrix, fully reflecting the environment state in the scheduling process. In addition, a cross-attention network is proposed to extract state features, enabling efficient discovery of complex relationships between jobs and machines, thereby enhancing the model's ability to understand intricate features. The model is trained using an independent proximal policy optimization (IPPO) based on the actor-critic method to help agents learn accurate and efficient scheduling strategies. Experimental results on a large number of static and dynamic scheduling instances demonstrate that the proposed algorithm outperforms traditional heuristic rules and other advanced algorithms, exhibiting strong learning efficiency and generalization capability.

Federated learning (FL) emerges as a promising approach to empower vehicular networks, composed by intelligent connected vehicles equipped with advanced sensing, computing, and communication capabilities. While previous studies have explored the application of FL in vehicular networks, they have largely overlooked the intricate challenges arising from the mobility of vehicles and resource constraints. In this paper, we propose a framework of mobility-aware decentralized federated learning (MDFL) for vehicular networks. In this framework, nearby vehicles train an FL model collaboratively, yet in a decentralized manner. We formulate a local iteration and leader selection joint optimization problem (LSOP) to improve the training efficiency of MDFL. For problem solving, we first reformulate LSOP as a decentralized partially observable Markov decision process (Dec-POMDP), and then develop an effective optimization algorithm based on multi-agent proximal policy optimization (MAPPO) to solve Dec-POMDP. Finally, we verify the performance of the proposed algorithm by comparing it with other algorithms.

Passively cooled base stations (PCBSs) have emerged to deliver better cost and energy efficiency. However, passive cooling necessitates intelligent thermal control via traffic management, i.e., the instantaneous data traffic or throughput of a PCBS directly impacts its thermal performance. This is particularly challenging for outdoor deployment of PCBSs because the heat dissipation efficiency is uncertain and fluctuates over time. What is more, the PCBSs are interference-coupled in multi-cell scenarios. Thus, a higher-throughput PCBS leads to higher interference to the other PCBSs, which, in turn, would require more resource consumption to meet their respective throughput targets. In this paper, we address online decision-making for maximizing the total downlink throughput for a multi-PCBS system subject to constraints related on operating temperature. We demonstrate that a reinforcement learning (RL) approach, specifically soft actor-critic (SAC), can successfully perform throughput maximization while keeping the PCBSs cool, by adapting the throughput to time-varying heat dissipation conditions. Furthermore, we design a denial and reward mechanism that effectively mitigates the risk of overheating during the exploration phase of RL. Simulation results show that our approach achieves up to 88.6% of the global optimum. This is very promising, as our approach operates without prior knowledge of future heat dissipation efficiency, which is required by the global optimum.

Caching popular contents at cell edge has been recognized as a promising way to facilitate rapid content delivery and alleviate backhaul burden. The content popularity is greatly influenced by recommendations by content providers. In this paper, we leverage this fact to jointly optimize caching and recommendation towards higher caching efficiency. We focus on both personalized and incumbent-aware recommendation. The incumbent content refers to the content that a user is currently browsing, resulted by the user's short-term interest. We model and formulate the resulting cache efficiency maximization problem subject to user satisfaction requirements. We prove the NP-hardness of the problem, and reformulate it using integer linear programming, enabling to solve optimally small-scale instances. Based on problem analysis with a graph representation, we derive three polynomial-time algorithms, where the recommendation sub-problem is solved to global optimum. Among these algorithms, the first two are based on sub-modularity, with  1−e⁻¹ approximation guarantee under mild conditions, while the last one is an alternation-based algorithm with fast convergence. Numerical results show the close-to-optimal performance of the proposed algorithms.

Passively cooled base stations (PCBSs) are highly relevant for achieving better efficiency in cost and energy. However, dealing with the thermal issue via load management, particularly for outdoor deployment of PCBS, becomes crucial. This is a challenge because the heat dissipation efficiency is subject to (uncertain) fluctuation over time. Moreover, load management is an online decision-making problem by its nature. In this paper, we demonstrate that a reinforcement learning (RL) approach, specifically Soft Actor-Critic (SAC), enables to make a PCBS stay cool. The proposed approach has the capability of adapting the PCBS load to the time-varying heat dissipation. In addition, we propose a denial and reward mechanism to mitigate the risk of overheating from the exploration such that the proposed RL approach can be implemented directly in a practical environment, i.e., online RL. Numerical results demonstrate that the learning approach can achieve as much as 88.6% of the global optimum. This is impressive, as our approach is used in an online fashion to perform decision-making without the knowledge of future heat dissipation efficiency, whereas the global optimum is computed assuming the presence of oracle that fully eliminates uncertainty. This paper pioneers the approach to the online PCBSs load management problem.

The optimization of sawing processes in the wood industry is critical for maximizing efficiency and profitability. The introduction of computerized tomography scanners provides sawmill operators with three-dimensional internal models of logs, which can be used to assess value and yield more accurately. We present a methodology for solving the sawing optimization problem employing a flexible sawing scheme that allows greater flexibility in cutting logs into products while considering product quality classes influenced by wane defects. The methodology has two phases: preprocessing and optimization. In the preprocessing phase, two alternative algorithms are given that generate and evaluate the potential sawing positions of products by considering the 3D surface of the log, product size requirements, and product quality classes. In the optimization phase, a maximum set-packing problem is solved for the preprocessed data using mixed-integer programming (MIP), aiming to obtain a feasible cut pattern that maximizes value yield. This is implemented in a system named FlexSaw, which takes advantage of parallel computation during the preprocessing phase and utilizes a MIP solver during the optimization phase. The proposed sawing methods are evaluated on the Swedish Pine Stem Bank. Additionally, FlexSaw is compared with an existing tool that utilizes cant sawing. Results demonstrate the superiority of flexible sawing. While the practical feasibility of implementing a flexible way of sawing logs is constrained by the limitations of current sawmill machinery, the potential increase in yield promotes the exploration of alternative machinery in the wood industry.

In multi-access edge computing (MEC) systems, there are multiple local cache servers caching contents to satisfy the users' requests, instead of letting the users download via the remote cloud server. In this paper, a multi -cell content scheduling problem (MCSP) in MEC systems is considered. Taking into account jointly the freshness of the cached contents and the traffic data costs, we study how to schedule content updates along time in a multi -cell setting. Different from single -cell scenarios, a user may have multiple candidate local cache servers, and thus the caching decisions in all cells must be jointly optimized. We first prove that MCSP is NP -hard, then we formulate MCSP using integer linear programming, by which the optimal scheduling can be obtained for small-scale instances. For problem solving of large scenarios, via a mathematical reformulation, we derive a scalable optimization algorithm based on repeated column generation. Our performance evaluation shows the effectiveness of the proposed algorithm in comparison to an off -the -shelf commercial solver and a popularity -based caching.

We study a radio resource allocation problem in mobile communication systems. As the distinct characteristic of this problem, a common data transmission rate is used on all channels allocated to a user. Because the channels differ in their quality, for each user the achievable rate varies by channel. Thus allocating more channels does not necessarily increase the total rate, as the common rate is constrained to be the lowest one supported by the allocated channels. Radio resource allocation subject to the common-rate constraint is of practical relevance, though little attention has been paid to modeling and solving the problem. We take a mathematical optimization perspective with focus on modeling. We first provide a complexity analysis. Next, several integer linear programming (ILP) formulations for the problem, including compact as well as non-compact models, are derived. The bulk of our analysis consists in a rigorous comparative study of their linear programming (LP) relaxations, to reveal the relationship between the formulations in terms of bounding. Computational experiments are presented to illustrate the numerical performance in bounding and LP-assisted problem solving. Our theoretical analysis and numerical results together serve the aim of setting a ground for the next step of developing model-based and tailored optimization methods.

Content caching at the network edge is an effective way of mitigating backhaul load and improving user experience. Caching efficiency can be enhanced by content recommendation and by keeping the information fresh. By content recommendation, a requested content that is not in the cache can be alternatively satisfied by a related cached content recommended by the system. Information freshness can be quantified by age of information (AoI). This article has the following contributions. First, we address optimal scheduling of cache updates for a time-slotted system accounting for content recommendation and AoI, and to the best of our knowledge, there is no work that has jointly taken into account these aspects. Next, we rigorously prove the problem's NP-hardness. Then, we derive an integer linear formulation, by which the optimal solution can be obtained for small-scale scenarios. On the algorithmic side, our contributions include the development of an effective algorithm based on Lagrangian decomposition, and efficient algorithms for solving the resulting subproblems. Our algorithm computes a bound that can be used to evaluate the performance of any suboptimal solution. We conduct simulations to show the effectiveness of our algorithm.

In this paper, we investigate the deployment and service of pre-trained foundation models (PFMs) in mobile edge networks with cell coupling. We formulate a joint resource allocation and request routing optimization problem (RARP) to achieve a trade-off between the accuracy loss and cost of artificial intelligence-generated content (AIGC). For problem solving, we propose an alternating optimization algorithm (AOA) that decomposes RARP into two sub-problems and iteratively optimizes them. Specifically, for the first sub-problem, we reformulate it as a linear programming problem and use the off-the-shelf optimization solver to solve it. For the other sub-problem, we propose a deep reinforcement learning based algorithm to optimize the deployment to PFMs. Performance evaluations validate the efficiency of AOA.