The Potential of Restarts for ProbSAT

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.Comment: Eurocast 201

Runtime Distributions and Criteria for Restarts

Randomized algorithms sometimes employ a restart strategy. After a certain number of steps, the current computation is aborted and restarted with a new, independent random seed. In some cases, this results in an improved overall expected runtime. This work introduces properties of the underlying runtime distribution which determine whether restarts are advantageous. The most commonly used probability distributions admit the use of a scale and a location parameter. Location parameters shift the density function to the right, while scale parameters affect the spread of the distribution. It is shown that for all distributions scale parameters do not influence the usefulness of restarts and that location parameters only have a limited influence. This result simplifies the analysis of the usefulness of restarts. The most important runtime probability distributions are the log-normal, the Weibull, and the Pareto distribution. In this work, these distributions are analyzed for the usefulness of restarts. Secondly, a condition for the optimal restart time (if it exists) is provided. The log-normal, the Weibull, and the generalized Pareto distribution are analyzed in this respect. Moreover, it is shown that the optimal restart time is also not influenced by scale parameters and that the influence of location parameters is only linear

Error analysis for hybrid undulators

A general modeling framework is introduced that allows for the solution to magnetic field perturbations due to mechanical and magnetic tolerances in hybrid undulators. For example, both geometric pole errors and permanent magnet block geometry and strength errors can be considered. Of particular significance is the scaling of the various errors with variations in the gap of the device. In this work, the perturbation analysis is presented along with specific examples of errors found in hybrid undulators

Terbutaline and the Prevention of Nocturnal Hypoglycemia in Type 1 Diabetes

OBJECTIVE—Bedtime administration of 5.0 mg of the β2-adrenergic agonist terbutaline prevents nocturnal hypoglycemia but causes morning hyperglycemia in type 1 diabetes. We tested the hypothesis that 2.5 mg terbutaline prevents nocturnal hypoglycemia without causing morning hyperglycemia

atrophy plus syndrome, or costeff optic atrophy syndrome): identification of the OPA3 gene and its

deficiencies in a male with cardiomyopathy and 3-methylglutaconic aciduria, ” J Inherit Metab Dis

A hybrid metaheuristic with learning for a real supply chain scheduling problem

In recent decades, research on supply chain management (SCM) has enabled companies to improve their environmental, social, and economic performance. This paper presents an industrial application of logistics that can be classified as an inventory-route problem. The problem consists of assigning orders to the available warehouses. The orders are composed of items that must be loaded within a week. The warehouses provide an inventory of the number of items available for each day of the week, so the objective is to minimize the total transportation costs and the costs of producing extra stock to satisfy the weekly demand. To solve this problem a formal mathematical model is proposed. Then a hybrid approach that involves two metaheuristics: a greedy randomized adaptive search procedure (GRASP) and a genetic algorithm (GA) is proposed. Additionally, a meta-learning tuning method is incorporated into our hybridized approach, which yields better results but with a longer computation time. Thus, the trade-off of using it is analyzed. An extensive evaluation was carried out over realistic instances provided by an industrial partner. The proposed technique was evaluated and compared with several complete and incomplete solvers from the state of the art (CP Optimizer, Yuck, OR-Tools, etc.). The results showed that our hybrid metaheuristic outperformed the behavior of these well-known solvers, mainly in large-scale instances (2000 orders per week). This hybrid algorithm provides the company with a powerful tool to solve its supply chain management problem, delivering significant economic benefits every week.The authors gratefully acknowledge the financial support of the European Social Fund (Investing In Your Future), the Spanish Ministry of Science (project PID2021-125919NB-I00), and valgrAI - Valencian Graduate School and Research Network of Artificial Intelligence and the Generalitat Valenciana, Spain, and co-funded by the European Union. The authors also thank the industrial partner Logifruit for its support in the problem specification and the permission to generate randomized data for evaluating the proposed algorithm