Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

On the mixing set with a knapsack constraint

We study a substructure appearing in mixed-integer programming reformulations of chance-constrained programs with stochastic right-hand-sides over a finite discrete distribution, which we call the mixing set with a knapsack constraint. Recently, Luedtke et al. (Math. Program. 122(2):247–272, 2010) and Küçükyavuz (Math Program 132(1):31–56, 2012) studied valid inequalities for such sets. However, most of their results were focused on the equal probabilities case (when the knapsack constraint reduces to a cardinality constraint). In this paper, we focus on the general probabilities case (general knapsack constraint). We characterize the valid inequalities that do not come from the knapsack polytope and use this characterization to generalize the results previously derived for the equal probabilities case. Our results allow for a deep understanding of the relationship that the set under consideration has with the knapsack polytope. Moreover, they allow us to establish benchmarks that can be used to identify when a relaxation will be useful for the considered types of reformulations of chance-constrained programs

Opposite elements in clutters

Let E be a finite set of elements, and let L be a clutter over ground set E. We say distinct elements e, f are opposite if every member and every minimal cover of L contains at most one of e, f. In this paper, we investigate opposite elements and reveal a rich theory underlying such a seemingly simple restriction. The clutter C obtained from L after identifying some opposite elements is called an identification of L; inversely, L is called a split of C. We will show that splitting preserves three clutter properties, i.e., idealness, the max-flow min-cut property, and the packing property. We will also display several natural examples in which a clutter does not have these properties but a split of them does. We will develop tools for recognizing when splitting is not a useful operation, and as well, we will characterize when identification preserves the three mentioned properties. We will also make connections to spanning arborescences, Steiner trees, comparability graphs, degenerate projective planes, binary clutters, matroids, as well as the results of Menger, Ford and Fulkerson, the Replication Conjecture, and a conjecture on ideal, minimally nonpacking clutters

An integrated personnel allocation and machine scheduling problem for industrial size multipurpose plants

This paper describes the development and implementation of an optimization model to solve the integrated problem of personnel allocation and machine scheduling for industrial size multipurpose plants. Although each of these problems has been extensively studied separately, works that study an integrated approach are very limited, particularly for large-scale industrial applications. We present a mathematical formulation for the integrated problem and show the results obtained from solving large size instances from an analytical services facility. The integrated formulation can improve the results up to 22.1% compared to the case where the personnel allocation and the machine scheduling problems are solved sequentially

Renal fibrosis

Renal fibrosis, characterized by tubulointerstitial fibrosis and glomerulosclerosis, is the final manifestation of chronic kidney disease. Renal fibrosis is characterized by an excessive accumulation and deposition of extracellular matrix components. This pathologic result usually originates from both underlying complicated cellular activities such as epithelial-to-mesenchymal transition, fibroblast activation, monocyte/macrophage infiltration, and cellular apoptosis and the activation of signaling molecules such as transforming growth factor beta and angiotensin II. However, because the pathogenesis of renal fibrosis is extremely complicated and our knowledge regarding this condition is still limited, further studies are needed

Influence of taste disorders on dietary behaviors in cancer patients under chemotherapy

<p>Abstract</p> <p>Objectives</p> <p>To determine the relationship between energy and nutrient consumption with chemosensory changes in cancer patients under chemotherapy.</p> <p>Methods</p> <p>We carried out a cross-sectional study, enrolling 60 subjects. Cases were defined as patients with cancer diagnosis after their second chemotherapy cycle (n = 30), and controls were subjects without cancer (n = 30). Subjective changes of taste during treatment were assessed. Food consumption habits were obtained with a food frequency questionnaire validated for Mexican population. Five different concentrations of three basic flavors --sweet (sucrose), bitter (urea), and a novel basic taste, umami (sodium glutamate)-- were used to measure detection thresholds and recognition thresholds (RT). We determine differences between energy and nutrient consumption in cases and controls and their association with taste DT and RT.</p> <p>Results</p> <p>No demographic differences were found between groups. Cases showed higher sweet DT (6.4 vs. 4.4 μmol/ml; p = 0.03) and a higher bitter RT (100 vs. 95 μmol/ml; <it>p </it>= 0.04) than controls. Cases with sweet DT above the median showed significant lower daily energy (2,043 vs.1,586 kcal; p = 0.02), proteins (81.4 vs. 54 g/day; <it>p </it>= 0.01), carbohydrates (246 vs.192 g/day; <it>p </it>= 0.05), and zinc consumption (19 vs.11 mg/day; <it>p </it>= 0.01) compared to cases without sweet DT alteration. Cases with sweet DT and RT above median were associated with lower completion of energy requirements and consequent weight loss. There was no association between flavors DT or RT and nutrient ingestion in the control group.</p> <p>Conclusion</p> <p>Changes of sweet DT and bitter RT in cancer patients under chemotherapy treatment were associated with lower energy and nutrient ingestion. Taste detection and recognition thresholds disorders could be important factors in malnutrition development on patients with cancer under chemotherapy treatment.</p

Single-row mixed-integer programs: theory and computations

Single-row mixed-integer programming (MIP) problems have been studied thoroughly under many different perspectives over the years. While not many practical applications can be modeled as a single-row MIP, their importance lies in the fact that they are simple, natural and very useful relaxations of generic MIPs. This thesis will focus on such MIPs and present theoretical and computational advances in their study. Chapter 1 presents an introduction to single-row MIPs, a historical overview of results and a motivation of why we will be studying them. It will also contain a brief review of the topics studied in this thesis as well as our contribution to them. In Chapter 2, we introduce a generalization of a very important structured single-row MIP: Gomory's master cyclic group polyhedron (MCGP). We will show a structural result for the generalization, characterizing all facet-defining inequalities for it. This structural result allows us to develop relationships with MCGP, extend it to the mixed-integer case and show how it can be used to generate new valid inequalities for MIPs. Chapter 3 presents research on an algorithmic view on how to maximally lift continuous and integer variables. Connections to tilting and fractional programming will also be presented. Even though lifting is not particular to single-row MIPs, we envision that the general use of the techniques presented should be on easily solvable MIP relaxations such as single-row MIPs. In fact, Chapter 4 uses the lifting algorithm presented. Chapter 4 presents an extension to the work of Goycoolea (2006) which attempts to evaluate the effectiveness of Mixed Integer Rounding (MIR) and Gomory mixed-integer (GMI) inequalities. By extending his work, natural benchmarks arise, against which any class of cuts derived from single-row MIPs can be compared. Finally, Chapter 5 is dedicated to dealing with an important computational problem when developing any computer code for solving MIPs, namely the problem of numerical accuracy. This problem arises due to the intrinsic arithmetic errors in computer floating-point arithmetic. We propose a simple approach to deal with this issue in the context of generating MIR/GMI inequalities.Ph.D.Committee Chair: William J. Cook; Committee Member: Ellis Johnson; Committee Member: George Nemhauser; Committee Member: Robin Thomas; Committee Member: Zonghao G