Solution Techniques for Classes of Biobjective and Parametric Programs

Mathematical optimization, or mathematical programming, has been studied for several decades. Researchers are constantly searching for optimization techniques which allow one to de-termine the ideal course of action in extremely complex situations. This line of scientific inquiry motivates the primary focus of this dissertation — nontraditional optimization problems having either multiple objective functions or parametric input. Utilizing multiple objective functions al-lows one to account for the fact that the decision process in many real-life problems in engineering, business, and management is often driven by several conflicting criteria such as cost, performance, reliability, safety, and productivity. Additionally, incorporating parametric input allows one to ac-count for uncertainty in models’ data, which can arise for a number of reasons, including a changing availability of resources, estimation or measurement errors, or implementation errors caused by stor-ing data in a fixed precision format. However, when a decision problem has either parametric input or multiple objectives, one cannot hope to find a single, satisfactory solution. Thus, in this work we develop techniques which can be used to determine sets of desirable solutions. The two main problems we consider in this work are the biobjective mixed integer linear program (BOMILP) and the multiparametric linear complementarity problem (mpLCP). BOMILPs are optimization problems in which two linear objectives are optimized over a polyhedron while restricting some of the decision variables to be integer. We present a new data structure in the form of a modified binary tree that can be used to store the solution set of BOMILP. Empirical evidence is provided showing that this structure is able to store these solution sets more efficiently than other data structures that are typically used for this purpose. We also develop a branch-and-bound (BB) procedure that can be used to compute the solution set of BOMILP. Computational experiments are conducted in order to compare the performance of the new BB procedure with current state-of-the-art methods for determining the solution set of BOMILP. The results provide strong evidence of the utility of the proposed BB method. We also present new procedures for solving two variants of the mpLCP. Each of these proce-dures consists of two phases. In the first phase an initial feasible solution to mpLCP which satisfies certain criteria is determined. This contribution alone is significant because the question of how such an initial solution could be generated was previously unanswered. In the second phase the set of fea-sible parameters is partitioned into regions such that the solution of the mpLCP, as a function of the parameters, is invariant over each region. For the first variant of mpLCP, the worst-case complex-ity of the presented procedure matches that of current state-of-the-art methods for nondegenerate problems and is lower than that of current state-of-the-art methods for degenerate problems. Addi-tionally, computational results show that the proposed procedure significantly outperforms current state-of-the-art methods in practice. The second variant of mpLCP we consider was previously un-solved. In order to develop a solution strategy, we first study the structure of the problem in detail. This study relies on the integration of several key concepts from algebraic geometry and topology into the field of operations research. Using these tools we build the theoretical foundation necessary to solve the mpLCP and propose a strategy for doing so. Experimental results indicate that the presented solution method also performs well in practice

Branch-and-bound for biobjective mixed-integer linear programming

We present a generic branch-and-bound method for finding all the Pareto solutions of a biobjective mixed integer program. Our main contribution is new algorithms for obtaining dual bounds at a node, for checking node fathoming, presolve and duality gap measurement. Our various procedures are implemented and empirically validated on instances from literature and a new set of hard instances. We also perform comparisons against the triangle splitting method of Boland et al. [\emph{INFORMS Journal on Computing}, \textbf{27} (4), 2015], which is a objective space search algorithm as opposed to our variable space search algorithm. On each of the literature instances, our branch-and-bound is able to compute the entire Pareto set in significantly lesser time. Most of the instances of the harder problem set were not solved by either algorithm in a reasonable time limit, but our algorithm performs better on average on the instances that were solved.Comment: 35 pages, 12 figures. Original preprint at Optimization Online, October 201

Punish or pardon? En undersökning av amnestiers påverkan på demokratiutvecklingen i Argentina, Brasilien och Paraguay.

Ett stort dilemma för länder som är på väg att lämna ett repressivt styre bakom sig är hur man ska handskas med de övergrepp som drabbat befolkningen under den tidigare regimen. Hur ska de överlevande offrens krav på upprättelse tillgodoses utan att det äventyrar den stabilitet som nya demokratier ofta är beroende av? Inflytelserik forskning tenderar att förmedla en förenklad syn på amnestier i detta sammanhang, bland annat eftersom man ofta bortser från de överlevande offrens perspektiv. För att försöka problematisera detta synsätt jämförs i denna uppsats utvecklingen i Argentina, Paraguay och Brasilien – tre länder som alla drabbades av militärdiktaturer under senare delen av 1900-talet, men som efteråt hanterat frågan om amnestier olika. Jag finner att amnestier inte är oproblematiska för ett lands demokratiutveckling. Uppsatsen indikerar ett möjligt negativt samband mellan denna sorts straffrihet och medborgares förtroende för statliga institutioner. En metodik för att närmare studera denna problemställning presenteras

Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming

In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer. Since many of the techniques for finding or approximating the Pareto set of a BOMILP use and update a subset of nondominated solutions, it is highly desirable to efficiently store this subset. We present a new data structure, a variant of a binary tree that takes as input points and line segments in $\R^2$ and stores the nondominated subset of this input. When used within an exact solution procedure, such as branch-and-bound (BB), at termination this structure contains the set of Pareto optimal solutions. We compare the efficiency of our structure in storing solutions to that of a dynamic list which updates via pairwise comparison. Then we use our data structure in two biobjective BB techniques available in the literature and solve three classes of instances of BOMILP, one of which is generated by us. The first experiment shows that our data structure handles up to $10^7$ points or segments much more efficiently than a dynamic list. The second experiment shows that our data structure handles points and segments much more efficiently than a list when used in a BB

In-process control of protein levels in formula feeds

Call number: LD2668 .T4 1964 A22Master of Scienc

Dinheiro, de Victoria Benedictsson: Uma tradução a quatro mãos e quatro línguas

Victoria Benedictsson foi uma das figuras-chaves do “Grande Avanço Moderno” sueco, que precedeu mudanças essenciais para que a sociedade escandinava se tornasse mais igualitária – e uma das mais igualitárias do mundo – em termos de gênero. O trecho do romance Pengar (“Dinheiro”) vertido aqui pela primeira vez ao português brasileiro é fundamental para se compreender também o pensamento da autora e seu suicídio, que destituiu a cena literária e feminista prematuramente de um de seus ícones

The Effects of Lead, Copper, and Iron Corrosion Products on Antibiotic Resistant Bacteria and Antibiotic Resistance Genes

Antibiotic resistance is a public health crisis. Antibiotic resistant bacteria (ARB) and antibiotic resistance genes (ARGs) are present in drinking water distribution systems. Metals are known selective pressures for antibiotic resistance, and metallic corrosion products are found within drinking water distribution systems due to the corrosion of metal pipes. While corrosion products are a source of metals, the impact of specific corrosion products on antibiotic resistance has not been investigated. The objective of this study was to determine the impact of six corrosion products—CuO, Cu2O, Pb5(PO4)3OH, β-PbO2, Fe3O4, and α-FeOOH—on the abundance of ARB and ARGs. Lab-scale microcosms were seeded with source water from Lake Michigan and amended with individual corrosion products. In general, copper and lead corrosion products increased antibiotic resistance, although not universally across different ARB and ARG types. Concentration and speciation of copper and lead corrosion products were found to have an impact on antibiotic resistance profiles. Meanwhile, iron corrosion products had minimal impact on antibiotic resistance. Overall, this study sheds light on how pipe materials may impact antibiotic resistance as a result of corrosion products