Using machine learning to predict the number of alternative solutions to a minimum cardinality set covering problem

Although the characterization of alternative optimal solutions for linear programming problems is well known, such characterizations for combinatorial optimization problems are essentially non-existent. This is the first article to qualitatively predict the number of alternative optima for a classic NP-hard combinatorial optimization problem, namely, the minimum cardinality (also called unicost) set covering problem (MCSCP). For the MCSCP, a set must be covered by a minimum number of subsets selected from a specified collection of subsets of the given set. The MCSCP has numerous industrial applications that require that a secondary objective is optimized once the size of a minimum cover has been determined. To optimize the secondary objective, the number of MCSCP solutions is optimized. In this article, for the first time, a machine learning methodology is presented to generate categorical regression trees to predict, qualitatively (extra-small, small, medium, large, or extra-large), the number of solutions to an MCSCP. Within the machine learning toolbox of MATLAB®, 600,000 unique random MCSCPs were generated and used to construct regression trees. The prediction quality of these regression trees was tested on 5000 different MCSCPs. For the 5-output model, the average accuracy of being at most one off from the predicted category was 94.2%.Â

Generating bounded solutions for multi-demand multidimensional knapsack problems: a guide for operations research practitioners

A generalization of the 0-1 knapsack problem that is hard-to-solve both theoretically (NP-hard) and in practice is the multi-demand multidimensional knapsack problem (MDMKP). Solving an MDMKP can be difficult because of its conflicting knapsack and demand constraints. Approximate solution approaches provide no guarantees on solution quality. Recently, with the use of classification trees, MDMKPs were partitioned into three general categories based on their expected performance using the integer programming option of the CPLEX® software package on a standard PC: Category A—relatively easy to solve, Category B—somewhat difficult to solve, and Category C—difficult to solve. However, no solution methods were associated with these categories. The primary contribution of this article is that it demonstrates, customized to each category, how general-purpose integer programming software (CPLEX in this case) can be iteratively used to efficiently generate bounded solutions for MDMKPs. Specifically, the simple sequential increasing tolerance (SSIT) methodology will iteratively use CPLEX with loosening tolerances to efficiently generate these bounded solutions. The real strength of this approach is that the SSIT methodology is customized based on the particular category (A, B, or C) of the MDMKP instance being solved. This methodology is easy for practitioners to use because it requires no time-consuming effort of coding problem specific-algorithms. Statistical analyses will compare the SSIT results to a single-pass execution of CPLEX in terms of execution time and solution quality

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

Role of NKX2-1 in N-bis(2-hydroxypropyl)-nitrosamine-induced thyroid adenoma in mice

NKX2-1 is a homeodomain transcription factor that is critical for genesis of the thyroid and transcription of the thyroid-specific genes. Nkx2-1-thyroid-conditional hypomorphic mice were previously developed in which Nkx2-1 gene expression is lost in 50% of the thyroid cells. Using this mouse line as compared with wild-type and Nkx2-1 heterozygous mice, a thyroid carcinogenesis study was carried out using the genotoxic carcinogen N-bis(2-hydroxypropyl)-nitrosamine (DHPN), followed by sulfadimethoxine (SDM) or the non-genotoxic carcinogen amitrole (3-amino-1,2,4-triazole). A significantly higher incidence of adenomas was obtained in Nkx2-1-thyroid-conditional hypomorphic mice as compared with the other two groups of mice only when they were treated with DHPN + SDM, but not amitrole. A bromodeoxyuridine incorporation study revealed that thyroids of the Nkx2-1-thyroid-conditional hypomorphic mice had >2-fold higher constitutive cell proliferation rate than the other two groups of mice, suggesting that this may be at least partially responsible for the increased incidence of adenoma in this mouse line after genotoxic carcinogen exposure. Thus, NKX2-1 may function to control the proliferation of thyroid follicular cells following damage by a genotoxic carcinogen