Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based heuristic solutions to accelerate downstream solvers. While recent generative models have shown promise in learning powerful heuristics, they suffer from a critical limitation. That is, they model the distribution of only the integer variables and fail to capture the intricate coupling between integer and continuous variables, creating an information bottleneck and ultimately leading to suboptimal solutions. To this end, we propose Joint Continuous-Integer Flow for Mixed-Integer Linear Programming (FMIP), which is the first generative framework that models the joint distribution of both integer and continuous variables for MILP solutions. Built upon the joint modeling paradigm, a holistic guidance mechanism is designed to steer the generative trajectory, actively refining solutions toward optimality and feasibility during the inference process. Extensive experiments on eight standard MILP benchmarks demonstrate the superior performance of FMIP against existing baselines, reducing the primal gap by 41.34% on average. Moreover, we show that FMIP is fully compatible with arbitrary backbone networks and various downstream solvers, making it well-suited for a broad range of real-world MILP applications.

Variational quantum algorithms hold the promise to address meaningful quantum problems already on noisy intermediate-scale quantum hardware. In spite of the promise, they face the challenge of designing quantum circuits that both solve the target problem and comply with device limitations. Quantum architecture search (QAS) automates the design process of quantum circuits, with reinforcement learning (RL) emerging as a promising approach. Yet, RL-based QAS methods encounter significant scalability issues, as computational and training costs grow rapidly with the number of qubits, circuit depth, and hardware noise. To address these challenges, we introduce $\textit{TensorRL-QAS}$, an improved framework that combines tensor network methods with RL for QAS. By warm-starting the QAS with a matrix product state approximation of the target solution, TensorRL-QAS effectively narrows the search space to physically meaningful circuits and accelerates the convergence to the desired solution. Tested on several quantum chemistry problems of up to 12-qubit, TensorRL-QAS achieves up to a 10-fold reduction in CNOT count and circuit depth compared to baseline methods, while maintaining or surpassing chemical accuracy. It reduces classical optimizer function evaluation by up to 100-fold, accelerates training episodes by up to 98$\%$, and can achieve 50$\%$ success probability for 10-qubit systems, far exceeding the $<$1$\%$ rates of baseline. Robustness and versatility are demonstrated both in the noiseless and noisy scenarios, where we report a simulation of an 8-qubit system. Furthermore, TensorRL-QAS demonstrates effectiveness on systems on 20-qubit quantum systems, positioning it as a state-of-the-art quantum circuit discovery framework for near-term hardware and beyond.

--We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool-paths of which are usually complex and have a large number of discrete time constraints as waypoints. Kinematic redundancy also exists in these robotic systems. The jerk of motion is optimized in our trajectory planning method at the meanwhile of fabrication process to improve the quality of fabrication. Our method is based on a sampling strategy and consists of two major parts. After determining an initial path by graph-search, a greedy algorithm is adopted to optimize a path by locally applying adaptive filers in the regions with large jerks. The filtered result is obtained by numerical optimization. In order to achieve efficient computation, an adaptive sampling method is developed for learning a collision-indication function that is represented as a support-vector machine. Applications in robot-assisted 3D printing are given in this paper to demonstrate the functionality of our approach. Abstract --In robot-assisted manufacturing applications, robotic arms are employed to realize the motion of workpieces (or machining tools) specified as a sequence of waypoints with the positions of tool tip and the tool orientations constrained. The required degree-of-freedom (DOF) is often less than the robotic hardware system (e.g., a robotic arm has 6-DOF). Specifically, rotations of the workpiece around the axis of a tool can be arbitrary (see Figure 1 for an example). By using this redundancy - i.e., there are many possible poses of a robotic arm to realize a given waypoint, the trajectory of robots can be optimized to consider the performance of motion in velocity, acceleration and jerk in the joint space. In addition, when fabricating complex models each tool-path can have a large amount of waypoints. It is crucial for a motion planning algorithm to compute a smooth and collision-free trajectory of robot to improve fabrication quality. The time taken by the planning algorithm should not significantly lengthen the total manufacturing time; ideally it would remain hidden as computing motions for a layer can be done while the previous layer is printing. The method presented in this paper provides an efficient framework to tackle this problem. The framework has been well tested on our robot-assisted additive manufacturing system to demonstrate its effectiveness and can be generally applied to other robot-assisted manufacturing systems.

A wide range of sustainability and grid-integration strategies depend on workload shifting, which aligns the timing of energy consumption with external signals such as grid curtailment events, carbon intensity, or time-of-use electricity prices. The main challenge lies in the online nature of the problem: operators must make real-time decisions (e.g., whether to consume energy now) without knowledge of the future. While forecasts of signal values are typically available, prior work on learning-augmented online algorithms has relied almost exclusively on simple point forecasts. In parallel, the forecasting research has made significant progress in uncertainty quantification (UQ), which provides richer and more fine-grained predictive information. In this paper, we study how online workload shifting can leverage UQ predictors to improve decision-making. We introduce $\texttt{UQ-Advice}$, a learning-augmented algorithm that systematically integrates UQ forecasts through a $\textit{decision uncertainty score}$ that measures how forecast uncertainty affects optimal future decisions. By introducing $\textit{UQ-robustness}$, a new metric that characterizes how performance degrades with forecast uncertainty, we establish theoretical performance guarantees for $\texttt{UQ-Advice}$. Finally, using trace-driven experiments on carbon intensity and electricity price data, we demonstrate that $\texttt{UQ-Advice}$ consistently outperforms robust baselines and existing learning-augmented methods that ignore uncertainty.

Group-fairness metrics (e.g., equalized odds) can vary sharply across resamples and are especially brittle under distribution shift, undermining reliable audits. We propose a Wasserstein distributionally robust framework that certifies worst-case group fairness over a ball of plausible test distributions centered at the empirical law. Our formulation unifies common group fairness notions via a generic conditional-probability functional and defines $\varepsilon$-Wasserstein Distributional Fairness ($\varepsilon$-WDF) as the audit target. Leveraging strong duality, we derive tractable reformulations and an efficient estimator (DRUNE) for $\varepsilon$-WDF. We prove feasibility and consistency and establish finite-sample certification guarantees for auditing fairness, along with quantitative bounds under smoothness and margin conditions. Across standard benchmarks and classifiers, $\varepsilon$-WDF delivers stable fairness assessments under distribution shift, providing a principled basis for auditing and certifying group fairness beyond observational data.

In modern logistics management systems, route planning requires high efficiency. The Open Capacitated Vehicle Routing Problem (OCVRP) deals with finding optimal delivery routes for a fleet of vehicles serving geographically distributed customers, without requiring the vehicles to return to the depot after deliveries. The present study is comparative in nature and speaks of two algorithms for OCVRP solution: Ant Colony Optimization (ACO), a nature-inspired metaheuristic; and Google OR-Tools, an industry-standard toolkit for optimization. Both implementations were developed in Python and using a custom dataset. Performance appraisal was based on routing efficiency, computation time, and scalability. The results show that ACO allows flexibility in routing parameters while OR-Tools runs much faster with more consistency and requires less input. This could help choose among routing strategies for scalable real-time logistics systems.

Aiming at the problem of driver's perception lag and low utilization efficiency of space-time resources in expressway ramp confluence area, based on the preemptive spatiotemporal trajectory Adjustment system, from the perspective of coordinating spatiotemporal resources, the reasonable value of safe space-time distance in trajectory pre-preparation is quantitatively analyzed. The minimum safety gap required for ramp vehicles to merge into the mainline is analyzed by introducing double positioning error and spatiotemporal trajectory tracking error. A merging control strategy for autonomous driving heterogeneous vehicles is proposed, which integrates vehicle type, driving intention, and safety spatiotemporal distance. The specific confluence strategies of ramp target vehicles and mainline cooperative vehicles under different vehicle types are systematically expounded. A variety of traffic flow and speed scenarios are used for full combination simulation. By comparing the time-position-speed diagram, the vehicle operation characteristics and the dynamic difference of confluence are qualitatively analyzed, and the average speed and average delay are used as the evaluation indices to quantitatively evaluate the performance advantages of the preemptive cooperative confluence control strategy. The results show that the maximum average delay improvement rates of mainline and ramp vehicles are 90.24 % and 74.24 %, respectively. The proposed strategy can effectively avoid potential vehicle conflicts and emergency braking behaviors, improve driving safety in the confluence area, and show significant advantages in driving stability and overall traffic efficiency optimization.

In stochastic optimal control the distribution of the exogenous noise is typically unknown and must be inferred from limited data before dynamic programming (DP)-based solution schemes can be applied. If the conditional expectations in the DP recursions are estimated via kernel regression, however, the historical sample paths enter the solution procedure directly as they determine the evaluation points of the cost-to-go functions. The resulting data-driven DP scheme is asymptotically consistent and admits efficient computational solution when combined with parametric value function approximations. If training data is sparse, however, the estimated cost-to-go functions display a high variability and an optimistic bias, while the corresponding control policies perform poorly in out-of-sample tests. To mitigate these small sample effects, we propose a robust data-driven DP scheme, which replaces the expectations in the DP recursions with worst-case expectations over a set of distributions close to the best estimate.

Variational inference algorithms provide the most effective framework for large-scale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization.

We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require maximizing a certain submodular function (like coverage or diversity) while simultaneously minimizing another (like cooperative cost). These problems are often posed as minimizing the difference between submodular functions [9, 23] which is in the worst case inapproximable. We show, however, that by phrasing these problems as constrained optimization, which is more natural for many applications, we achieve a number of bounded approximation guarantees. We also show that both these problems are closely related and, an approximation algorithm solving one can be used to obtain an approximation guarantee for the other.