Higher-order cover cuts from zero–one knapsack constraints augmented by two-sided bounding inequalities

AbstractExtending our work on second-order cover cuts [F. Glover, H.D. Sherali, Second-order cover cuts, Mathematical Programming (ISSN: 0025-5610 1436-4646) (2007), doi:10.1007/s10107-007-0098-4. (Online)], we introduce a new class of higher-order cover cuts that are derived from the implications of a knapsack constraint in concert with supplementary two-sided inequalities that bound the sums of sets of variables. The new cuts can be appreciably stronger than the second-order cuts, which in turn dominate the classical knapsack cover inequalities. The process of generating these cuts makes it possible to sequentially utilize the second-order cuts by embedding them in systems that define the inequalities from which the higher-order cover cuts are derived. We characterize properties of these cuts, design specialized procedures to generate them, and establish associated dominance relationships. These results are used to devise an algorithm that generates all non-dominated higher-order cover cuts, and, in particular, to formulate and solve suitable separation problems for deriving a higher-order cut that deletes a given fractional solution to an underlying continuous relaxation. We also discuss a lifting procedure for further tightening any generated cut, and establish its polynomial-time operation for unit-coefficient cuts. A numerical example is presented that illustrates these procedures and the relative strength of the generated non-redundant, non-dominated higher-order cuts, all of which turn out to be facet-defining for this example. Some preliminary computational results are also presented to demonstrate the efficacy of these cuts in comparison with lifted minimal cover inequalities for the underlying knapsack polytope

Estimating Optimal Thinning and Rotation for Mixed-Species Timber Stands Using a Random Search Algorithm

The problem of optimal density over time for even-aged, mixed-species stands is formulated as a nonlinear-integer programming problem with numbers of trees cut by species and diameter class as decision variables. The model is formulated using a stand-table projection growth model to predict mixed-speciesg rowth and stand-structureO. ptimal thinning and final harvest age are estimated simultaneously using heuristic random search algorithms. For sample problemsw ith two speciesr, andom searchm ethodsp rovide near-optimalc uttings trategiesw ith very little computer time or memory. Optimal solutions are estimated for problems with eight initial species/diameter class groups, projected for up to three discrete growth periods. Such solution methods merit further study for evaluating complex stand- and forest-level decisions. FOREST Scl. 31:303-315

Comparison of TRANSIMS' Light Duty Vehicle Emissions with On-Road Emission Measurements

The Transportation Analysis and Simulation System, TRANSIMS, contains a vehicle emissions module that estimates tailpipe emissions for light and heavy-duty vehicles and evaporative emissions for light-duty vehicles. This paper describes and validates the TRANSIMS emission module and compares its emission estimates to on-road emission-measurements and other state-of-the-art emission models. The trend of the emissions estimated in thirteen different runs in each model are compared. The results indicate that the TRANSIMS model provides consistent trends of estimated carbon monoxide (CO) and hydrocarbons (HC) with field data trends and inconsistent trends of estimated nitrogen lxides (NOx). However, the magnitude of the emission estimated in TRANSIMS is closer to the field data than for other models

Want to Make Your Website Better? Ask a Librarian.

Raise your hand if you have served on a committee in your library. If your hand isn’t raised, just give it some time … libraries definitely like committee work. For instance, I recently had the opportunity to work with a committee consisting mostly of librarians. When the committee’s goals were accomplished, my non-librarian coworker commented that “Librarians sure have a lot of opinions.” Since this article is about usability testing, and is written by and for librarians, let’s test his hypothesis. Let’s also test a few other hypotheses about librarians while we’re at it. (Disclaimer: In this article, “librarians” include staff who work in libraries, and has nothing to do with degrees or job classifications.) Washington County Cooperative Library Services (WCCLS) is a Cooperative of 13 member libraries and two special libraries, each uniquely governed and operated. WCCLS is a primary funding source for member libraries, and our WCCLS “Office” provides other support such as daily courier deliveries, cataloging coordination, and e-book collections. The WCCLS website and Extranet are two other ways the WCCLS Office supports member libraries in Washington County. The WCCLS Extranet is a repository of policies, procedures, and committee meeting documents. It also includes training and promotional materials for WCCLS resources, as well as opportunities for sharing ideas

Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants

Summary Background Comparable global data on health and nutrition of school-aged children and adolescents are scarce. We aimed to estimate age trajectories and time trends in mean height and mean body-mass index (BMI), which measures weight gain beyond what is expected from height gain, for school-aged children and adolescents. Methods For this pooled analysis, we used a database of cardiometabolic risk factors collated by the Non-Communicable Disease Risk Factor Collaboration. We applied a Bayesian hierarchical model to estimate trends from 1985 to 2019 in mean height and mean BMI in 1-year age groups for ages 5–19 years. The model allowed for non-linear changes over time in mean height and mean BMI and for non-linear changes with age of children and adolescents, including periods of rapid growth during adolescence. Findings We pooled data from 2181 population-based studies, with measurements of height and weight in 65 million participants in 200 countries and territories. In 2019, we estimated a difference of 20 cm or higher in mean height of 19-year-old adolescents between countries with the tallest populations (the Netherlands, Montenegro, Estonia, and Bosnia and Herzegovina for boys; and the Netherlands, Montenegro, Denmark, and Iceland for girls) and those with the shortest populations (Timor-Leste, Laos, Solomon Islands, and Papua New Guinea for boys; and Guatemala, Bangladesh, Nepal, and Timor-Leste for girls). In the same year, the difference between the highest mean BMI (in Pacific island countries, Kuwait, Bahrain, The Bahamas, Chile, the USA, and New Zealand for both boys and girls and in South Africa for girls) and lowest mean BMI (in India, Bangladesh, Timor-Leste, Ethiopia, and Chad for boys and girls; and in Japan and Romania for girls) was approximately 9–10 kg/m2. In some countries, children aged 5 years started with healthier height or BMI than the global median and, in some cases, as healthy as the best performing countries, but they became progressively less healthy compared with their comparators as they grew older by not growing as tall (eg, boys in Austria and Barbados, and girls in Belgium and Puerto Rico) or gaining too much weight for their height (eg, girls and boys in Kuwait, Bahrain, Fiji, Jamaica, and Mexico; and girls in South Africa and New Zealand). In other countries, growing children overtook the height of their comparators (eg, Latvia, Czech Republic, Morocco, and Iran) or curbed their weight gain (eg, Italy, France, and Croatia) in late childhood and adolescence. When changes in both height and BMI were considered, girls in South Korea, Vietnam, Saudi Arabia, Turkey, and some central Asian countries (eg, Armenia and Azerbaijan), and boys in central and western Europe (eg, Portugal, Denmark, Poland, and Montenegro) had the healthiest changes in anthropometric status over the past 3·5 decades because, compared with children and adolescents in other countries, they had a much larger gain in height than they did in BMI. The unhealthiest changes—gaining too little height, too much weight for their height compared with children in other countries, or both—occurred in many countries in sub-Saharan Africa, New Zealand, and the USA for boys and girls; in Malaysia and some Pacific island nations for boys; and in Mexico for girls. Interpretation The height and BMI trajectories over age and time of school-aged children and adolescents are highly variable across countries, which indicates heterogeneous nutritional quality and lifelong health advantages and risks

Heterogeneous contributions of change in population distribution of body mass index to change in obesity and underweight NCD Risk Factor Collaboration (NCD-RisC)

From 1985 to 2016, the prevalence of underweight decreased, and that of obesity and severe obesity increased, in most regions, with significant variation in the magnitude of these changes across regions. We investigated how much change in mean body mass index (BMI) explains changes in the prevalence of underweight, obesity, and severe obesity in different regions using data from 2896 population-based studies with 187 million participants. Changes in the prevalence of underweight and total obesity, and to a lesser extent severe obesity, are largely driven by shifts in the distribution of BMI, with smaller contributions from changes in the shape of the distribution. In East and Southeast Asia and sub-Saharan Africa, the underweight tail of the BMI distribution was left behind as the distribution shifted. There is a need for policies that address all forms of malnutrition by making healthy foods accessible and affordable, while restricting unhealthy foods through fiscal and regulatory restrictions