A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, the first deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at https://miralab-ustc.github.io/L2O-G2MILP

Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation

Machine learning has been successfully applied to improve the efficiency of Mixed-Integer Linear Programming (MILP) solvers. However, the learning-based solvers often suffer from severe performance degradation on unseen MILP instances -- especially on large-scale instances from a perturbed environment -- due to the limited diversity of training distributions. To tackle this problem, we propose a novel approach, which is called Adversarial Instance Augmentation and does not require to know the problem type for new instance generation, to promote data diversity for learning-based branching modules in the branch-and-bound (B&B) Solvers (AdaSolver). We use the bipartite graph representations for MILP instances and obtain various perturbed instances to regularize the solver by augmenting the graph structures with a learned augmentation policy. The major technical contribution of AdaSolver is that we formulate the non-differentiable instance augmentation as a contextual bandit problem and adversarially train the learning-based solver and augmentation policy, enabling efficient gradient-based training of the augmentation policy. To the best of our knowledge, AdaSolver is the first general and effective framework for understanding and improving the generalization of both imitation-learning-based (IL-based) and reinforcement-learning-based (RL-based) B&B solvers. Extensive experiments demonstrate that by producing various augmented instances, AdaSolver leads to a remarkable efficiency improvement across various distributions

Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically

Differentiation of canine distemper virus isolates in fur animals from various vaccine strains by reverse transcription-polymerase chain reaction-restriction fragment length polymorphism according to phylogenetic relations in china

In order to effectively identify the vaccine and field strains of Canine distemper virus (CDV), a new differential diagnostic test has been developed based on reverse transcription-polymerase chain reaction (RT-PCR) and restriction fragment length polymorphism (RFLP). We selected an 829 bp fragment of the nucleoprotein (N) gene of CDV. By RFLP analysis using BamHI, field isolates were distinguishable from the vaccine strains. Two fragments were obtained from the vaccine strains by RT-PCR-RFLP analysis while three were observed in the field strains. An 829 nucleotide region of the CDV N gene was analyzed in 19 CDV field strains isolated from minks, raccoon dogs and foxes in China between 2005 and 2007. The results suggest this method is precise, accurate and efficient. It was also determined that three different genotypes exist in CDV field strains in fur animal herds of the north of China, most of which belong to Asian type. Mutated field strains, JSY06-R1, JSY06-R2 and JDH07-F1 also exist in Northern China, but are most closely related to the standard virulent strain A75/17, designated in Arctic and America-2 genetype in the present study, respectively

Molecular and Paleontological Evidence for a Post-Cretaceous Origin of Rodents

The timing of the origin and diversification of rodents remains controversial, due to conflicting results from molecular clocks and paleontological data. The fossil record tends to support an early Cenozoic origin of crown-group rodents. In contrast, most molecular studies place the origin and initial diversification of crown-Rodentia deep in the Cretaceous, although some molecular analyses have recovered estimated divergence times that are more compatible with the fossil record. Here we attempt to resolve this conflict by carrying out a molecular clock investigation based on a nine-gene sequence dataset and a novel set of seven fossil constraints, including two new rodent records (the earliest known representatives of Cardiocraniinae and Dipodinae). Our results indicate that rodents originated around 61.7–62.4 Ma, shortly after the Cretaceous/Paleogene (K/Pg) boundary, and diversified at the intraordinal level around 57.7–58.9 Ma. These estimates are broadly consistent with the paleontological record, but challenge previous molecular studies that place the origin and early diversification of rodents in the Cretaceous. This study demonstrates that, with reliable fossil constraints, the incompatibility between paleontological and molecular estimates of rodent divergence times can be eliminated using currently available tools and genetic markers. Similar conflicts between molecular and paleontological evidence bedevil attempts to establish the origination times of other placental groups. The example of the present study suggests that more reliable fossil calibration points may represent the key to resolving these controversies.Organismic and Evolutionary Biolog