Learning context-aware adaptive solvers to accelerate quadratic programming

Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter $\rho$. Due to the absence of a general rule for setting $\rho$, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust $\rho$ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses $\rho$ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust $\rho$ considering the stage of the optimization process to accelerate the convergence speed further.Comment: 9 pages, 4 figure

Genetic Algorithms with Neural Cost Predictor for Solving Hierarchical Vehicle Routing Problems

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature

MIMO active vibration control of magnetically suspended flywheels for satellite IPAC service

Theory and simulation results have demonstrated that four, variable speed flywheels could potentially provide the energy storage and attitude control functions of existing batteries and control moment gyros (CMGs) on a satellite. Past modeling and control algorithms were based on the assumption of rigidity in the flywheel’s bearings and the satellite structure. This dissertation provides simulation results and theory which eliminates this assumption utilizing control algorithms for active vibration control (AVC), flywheel shaft levitation and integrated power transfer and attitude control (IPAC) that are effective even with low stiffness active magnetic bearings (AMB), and flexible satellite appendages. The flywheel AVC and levitation tasks are provided by a multi input multi output (MIMO) control law that enhances stability by reducing the dependence of the forward and backward gyroscopic poles with changes in flywheel speed. The control law is shown to be effective even for (1) Large polar to transverse inertia ratios which increases the stored energy density while causing the poles to become more speed dependent and, (2) Low bandwidth controllers shaped to suppress high frequency noise. These two main tasks could be successfully achieved by MIMO (Gyroscopic) control algorithm, which is unique approach. The vibration control mass (VCM) is designed to reduce the vibrations of flexible appendages of the satellite. During IPAC maneuver, the oscillation of flywheel spin speeds, torque motions and satellite appendages are significantly reduced compared without VCM. Several different properties are demonstrated to obtain optimal VCM. Notch, band-pass and low-pass filters are implemented in the AMB system to reduce and cancel high frequency, dynamic bearing forces and motor torques due to flywheel mass imbalance. The transmitted forces and torques to satellite are considerably decreased in the present of both notch and band-pass filter stages. Successful IPAC simulation results are presented with a 12 [%] of initial attitude error, large polar to transverse inertia ratio (IP / IT), structural flexibility and unbalance mass disturbance. Two variable speed control moment gyros (VSCMGs) are utilized to demonstrate simultaneous attitude control and power transfer instead of using four standard pyramid configurations. Launching weights including payload and costs can be significantly reduced

Metabolite concentrations, fluxes and free energies imply efficient enzyme usage.

In metabolism, available free energy is limited and must be divided across pathway steps to maintain a negative ΔG throughout. For each reaction, ΔG is log proportional both to a concentration ratio (reaction quotient to equilibrium constant) and to a flux ratio (backward to forward flux). Here we use isotope labeling to measure absolute metabolite concentrations and fluxes in Escherichia coli, yeast and a mammalian cell line. We then integrate this information to obtain a unified set of concentrations and ΔG for each organism. In glycolysis, we find that free energy is partitioned so as to mitigate unproductive backward fluxes associated with ΔG near zero. Across metabolism, we observe that absolute metabolite concentrations and ΔG are substantially conserved and that most substrate (but not inhibitor) concentrations exceed the associated enzyme binding site dissociation constant (Km or Ki). The observed conservation of metabolite concentrations is consistent with an evolutionary drive to utilize enzymes efficiently given thermodynamic and osmotic constraints

Generating Dispatching Rules for the Interrupting Swap-Allowed Blocking Job Shop Problem Using Graph Neural Network and Reinforcement Learning

The interrupting swap-allowed blocking job shop problem (ISBJSSP) is a complex scheduling problem that is able to model many manufacturing planning and logistics applications realistically by addressing both the lack of storage capacity and unforeseen production interruptions. Subjected to random disruptions due to machine malfunction or maintenance, industry production settings often choose to adopt dispatching rules to enable adaptive, real-time re-scheduling, rather than traditional methods that require costly re-computation on the new configuration every time the problem condition changes dynamically. To generate dispatching rules for the ISBJSSP problem, we introduce a dynamic disjunctive graph formulation characterized by nodes and edges subjected to continuous deletions and additions. This formulation enables the training of an adaptive scheduler utilizing graph neural networks and reinforcement learning. Furthermore, a simulator is developed to simulate interruption, swapping, and blocking in the ISBJSSP setting. Employing a set of reported benchmark instances, we conduct a detailed experimental study on ISBJSSP instances with a range of machine shutdown probabilities to show that the scheduling policies generated can outperform or are at least as competitive as existing dispatching rules with predetermined priority. This study shows that the ISBJSSP, which requires real-time adaptive solutions, can be scheduled efficiently with the proposed method when production interruptions occur with random machine shutdowns.Comment: 14 pages, 10 figures. Supplementary Material not include