A matheuristic for the selection of beam directions and dose distribution in radiotherapy planning

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Within-plant isoprene oxidation confirmed by direct emissions of oxidation products methyl vinyl ketone and methacrolein

Isoprene is emitted from many terrestrial plants at high rates, accounting for an estimated 1/3 of annual global volatile organic compound emissions from all anthropogenic and biogenic sources combined. Through rapid photooxidation reactions in the atmosphere, isoprene is converted to a variety of oxidized hydrocarbons, providing higher order reactants for the production of organic nitrates and tropospheric ozone, reducing the availability of oxidants for the breakdown of radiatively active trace gases such as methane, and potentially producing hygroscopic particles that act as effective cloud condensation nuclei. However, the functional basis for plant production of isoprene remains elusive. It has been hypothesized that in the cell isoprene mitigates oxidative damage during the stress-induced accumulation of reactive oxygen species (ROS), but the products of isoprene-ROS reactions in plants have not been detected. Using pyruvate-2-13C leaf and branch feeding and individual branch and whole mesocosm flux studies, we present evidence that isoprene (i) is oxidized to methyl vinyl ketone and methacrolein (iox) in leaves and that iox/i emission ratios increase with temperature, possibly due to an increase in ROS production under high temperature and light stress. In a primary rainforest in Amazonia, we inferred significant in plant isoprene oxidation (despite the strong masking effect of simultaneous atmospheric oxidation), from its influence on the vertical distribution of iox uptake fluxes, which were shifted to low isoprene emitting regions of the canopy. These observations suggest that carbon investment in isoprene production is larger than that inferred from emissions alone and that models of tropospheric chemistry and biotachemistryclimate interactions should incorporate isoprene oxidation within both the biosphere and the atmosphere with potential implications for better understanding both the oxidizing power of the troposphere and forest response to climate change.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

On arc-routing problems

Das Basisproblem von Arc-Routing Problemen mit mehreren Fahrzeugen ist das Capacitated Arc-Routing Problem (CARP). Praktische Anwendungen des CARP sind z.B. in den Bereichen Müllabfuhr und Briefzustellung zu finden. Das Ziel ist es, einen kostenminimalen Tourenplan zu berechnen, bei dem alle erforderlichen Kanten bedient werden und gleichzeitig die Fahrzeugkapazität eingehalten wird. In der vorliegenden Arbeit wird ein Cut-First Branch-and-Price Second Verfahren entwickelt. In der ersten Phase werden Schnittebenen generiert, die dem Master Problem in der zweiten Phase hinzugefügt werden. Das Subproblem ist ein kürzeste Wege Problem mit Ressourcen und wird gelöst um neue Spalten für das Master Problem zu liefern. Ganzzahlige CARP Lösungen werden durch ein neues hierarchisches Branching-Schema garantiert. Umfassende Rechenstudien zeigen die Effektivität dieses Algorithmus. Kombinierte Standort- und Arc-Routing Probleme ermöglichen eine realistischere Modellierung von Zustellvarianten bei der Briefzustellung. In dieser Arbeit werden jeweils zwei mathematische Modelle für Park and Loop und Park and Loop with Curbline vorgestellt. Die Modelle für das jeweilige Problem unterscheiden sich darin, wie zulässige Transfer Routen modelliert werden. Während der erste Modelltyp Subtour-Eliminationsbedingungen verwendet, werden bei dem zweiten Modelltyp Flussvariablen und Flusserhaltungsbedingungen eingesetzt. Die Rechenstudie zeigt, dass ein MIP-Solver den zweiten Modelltyp oft in kürzerer Rechenzeit lösen kann oder bei Erreichen des Zeitlimits bessere Zielfunktionswerte liefert.

Optimized scheduling in real-time environments with column generation

Im Bereich sicherheitsrelevanter eingebetteter Systeme stellt sich der Designprozess von Anwendungen als sehr komplex dar. Entsprechend einer gegebenen Hardwarearchitektur lassen sich Steuergeräte aufrüsten, um alle bestehenden Prozesse und Signale pünktlich auszuführen. Die zeitlichen Anforderungen sind strikt und müssen in jeder periodischen Wiederkehr der Prozesse erfüllt sein, da die Sicherstellung der parallelen Ausführung von größter Bedeutung ist. Existierende Ansätze können schnell Designalternativen berechnen, aber sie gewährleisten nicht, dass die Kosten für die nötigen Hardwareänderungen minimal sind. Wir stellen einen Ansatz vor, der kostenminimale Lösungen für das Problem berechnet, die alle zeitlichen Bedingungen erfüllen. Unser Algorithmus verwendet Lineare Programmierung mit Spaltengenerierung, eingebettet in eine Baumstruktur, um untere und obere Schranken während des Optimierungsprozesses bereitzustellen. Die komplexen Randbedingungen zur Gewährleistung der periodischen Ausführung verlagern sich durch eine Zerlegung des Hauptproblems in unabhängige Unterprobleme, die als ganzzahlige lineare Programme formuliert sind. Sowohl die Analysen zur Prozessausführung als auch die Methoden zur Signalübertragung werden untersucht und linearisierte Darstellungen angegeben. Des Weiteren präsentieren wir eine neue Formulierung für die Ausführung mit fixierten Prioritäten, die zusätzlich Prozessantwortzeiten im schlimmsten anzunehmenden Fall berechnet, welche für Szenarien nötig sind, in denen zeitliche Bedingungen an Teilmengen von Prozessen und Signalen gegeben sind. Wir weisen die Anwendbarkeit unserer Methoden durch die Analyse von Instanzen nach, welche Prozessstrukturen aus realen Anwendungen enthalten. Unsere Ergebnisse zeigen, dass untere Schranken schnell berechnet werden können, um die Optimalität von heuristischen Lösungen zu beweisen. Wenn wir optimale Lösungen mit Antwortzeiten liefern, stellt sich unsere neue Formulierung in der Laufzeitanalyse vorteilhaft gegenüber anderen Ansätzen dar. Die besten Resultate werden mit einem hybriden Ansatz erzielt, der heuristische Startlösungen, eine Vorverarbeitung und eine heuristische mit einer kurzen nachfolgenden exakten Berechnungsphase verbindet.

Gap junction channels and cardiac impulse propagation

The role of gap junction channels on cardiac impulse propagation is complex. This review focuses on the differential expression of connexins in the heart and the biophysical properties of gap junction channels under normal and disease conditions. Structural determinants of impulse propagation have been gained from biochemical and immunocytochemical studies performed on tissue extracts and intact cardiac tissue. These have defined the distinctive connexin coexpression patterns and relative levels in different cardiac tissues. Functional determinants of impulse propagation have emerged from electrophysiological experiments carried out on cell pairs. The static properties (channel number and conductance) limit the current flow between adjacent cardiomyocytes and thus set the basic conduction velocity. The dynamic properties (voltage-sensitive gating and kinetics of channels) are responsible for a modulation of the conduction velocity during propagated action potentials. The effect is moderate and depends on the type of Cx and channel. For homomeric-homotypic channels, the influence is small to medium; for homomeric-heterotypic channels, it is medium to strong. Since no data are currently available on heteromeric channels, their influence on impulse propagation is speculative. The modulation by gap junction channels is most prominent in tissues at the boundaries between cardiac tissues such as sinoatrial node-atrial muscle, atrioventricular node-His bundle, His bundle-bundle branch and Purkinje fibers-ventricular muscle. The data predict facilitation of orthodromic propagation.

Aluminum - Bronze Compacts and their Possible Use as a Bearing Material

In the modern aspect of powder metallurgy, the first use of a sintering process was in making filaments for incandescent electric lamps.In the short while from the day of Edison to the pres­ent, the science of working with metal powders has advanced by leaps and bounds.

A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains

We present a new model formulation for a multi-product lot-sizing problem with product returns and remanufacturing subject to a capacity constraint. The given external demand of the products has to be satisfied by remanufactured or newly produced goods. The objective is to determine a feasible production plan, which minimizes production, holding, and setup costs. As the LP relaxation of a model formulation based on the well-known CLSP leads to very poor lower bounds, we propose a column-generation approach to determine tighter bounds. The lower bound obtained by column generation can be easily transferred into a feasible solution by a truncated branch-and-bound approach using CPLEX. The results of an extensive numerical study show the high solution quality of the proposed solution approach.

Scheduling of continuous and discontinuous material flows with intermediate storage restrictions

This paper deals with scheduling batch (i.e., discontinuous), continuous, and semicontinuous production in process industries (e.g., chemical, pharmaceutical, or metal casting industries) where intermediate storage facilities and renewable resources (processing units and manpower) of limited capacity have to be observed. First, different storage configurations typical of process industries are discussed. Second, a basic scheduling problem covering the three above production modes is presented. Third, (exact and truncated) branch-and-bound methods for the basic scheduling problem and the special case of batch scheduling are proposed and subjected to an experimental performance analysis. The solution approach presented is flexible and in principle simple, and it can (approximately) solve relatively large problem instances with sufficient accuracy.

Scheduling the production of rolling ingots: Industrial context, model, and solution method

We study a real-world scheduling problem arising in the context of a rolling ingots production. First we review the production process and discuss peculiarities that have to be observed when scheduling a given set of production orders on the production facilities. We then show how to model this scheduling problem using prescribed time lags between operations, different kinds of resources, and sequence-dependent changeovers. A branch-and-bound solution procedure is presented in the second part. The basic principle is to relax the resource constraints by assuming infinite resource availability. Resulting resource conflicts are then stepwise resolved by introducing precedence relationships among operations competing for the same resources. The algorithm has been implemented as a beam search heuristic enumerating alternative sets of precedence relationships.

Patient classification system: An integrated method for measuring nursing intensity and optimizing resource allocation

A patient classification system was developed integrating a patient acuity instrument with a computerized nursing distribution method based on a linear programming model. The system was designed for real-time measurement of patient acuity (workload) and allocation of nursing personnel to optimize the utilization of resources.^ The acuity instrument was a prototype tool with eight categories of patients defined by patient severity and nursing intensity parameters. From this tool, the demand for nursing care was defined in patient points with one point equal to one hour of RN time. Validity and reliability of the instrument was determined as follows: (1) Content validity by a panel of expert nurses; (2) predictive validity through a paired t-test analysis of preshift and postshift categorization of patients; (3) initial reliability by a one month pilot of the instrument in a practice setting; and (4) interrater reliability by the Kappa statistic.^ The nursing distribution system was a linear programming model using a branch and bound technique for obtaining integer solutions. The objective function was to minimize the total number of nursing personnel used by optimally assigning the staff to meet the acuity needs of the units. A penalty weight was used as a coefficient of the objective function variables to define priorities for allocation of staff.^ The demand constraints were requirements to meet the total acuity points needed for each unit and to have a minimum number of RNs on each unit. Supply constraints were: (1) total availability of each type of staff and the value of that staff member (value was determined relative to that type of staff's ability to perform the job function of an RN (i.e., value for eight hours RN = 8 points, LVN = 6 points); (2) number of personnel available for floating between units.^ The capability of the model to assign staff quantitatively and qualitatively equal to the manual method was established by a thirty day comparison. Sensitivity testing demonstrated appropriate adjustment of the optimal solution to changes in penalty coefficients in the objective function and to acuity totals in the demand constraints.^ Further investigation of the model documented: correct adjustment of assignments in response to staff value changes; and cost minimization by an addition of a dollar coefficient to the objective function. ^

Associating optical measurements and estimating orbits of geocentric objects through population-based meta-heuristic methods

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both, the correct associations among the observations and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. The number S corresponds to the number of fences involved in the problem. Each fence consists of a set of observations where each observation belongs to a different object. The S ≥ 3 MTT problem is an NP-hard combinatorial optimization problem. There are two general ways to solve this. One way is to seek the optimum solution, this can be achieved by applying a branch-and- bound algorithm. When using these algorithms the problem has to be greatly simplified to keep the computational cost at a reasonable level. Another option is to approximate the solution by using meta-heuristic methods. These methods aim to efficiently explore the different possible combinations so that a reasonable result can be obtained with a reasonable computational effort. To this end several population-based meta-heuristic methods are implemented and tested on simulated optical measurements. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to efficiently process large data sets with minimal manual intervention.

Mesozooplankton size data from the fjord branch Kapisigdlit located in the Godthaabsfjord system, West Greenland, 2010

Sampling was conducted from March 24 to August 5 2010, in the fjord branch Kapisigdlit located in the inner part of the Godthåbsfjord system, West Greenland. The vessel "Lille Masik" was used during all cruises except on June 17-18 where sampling was done from RV Dana (National Institute for Aquatic Resources, Denmark). A total of 15 cruises (of 1-2 days duration) 7-10 days apart was carried out along a transect composed of 6 stations (St.), spanning the length of the 26 km long fjord branch. St. 1 was located at the mouth of the fjord branch and St. 6 was located at the end of the fjord branch, in the middle of a shallower inner creek . St. 1-4 was covering deeper parts of the fjord, and St. 5 was located on the slope leading up to the shallow inner creek. Mesozooplankton was sampled by vertical net tows using a Hydrobios Multinet (type Mini) equipped with a flow meter and 50 µm mesh nets or a WP-2 net 50 µm mesh size equipped with a non-filtering cod-end. Sampling was conducted at various times of day at the different stations. The nets were hauled with a speed of 0.2-0.3 m s**-1 from 100, 75 and 50 m depth to the surface at St. 2 + 4, 5 and 6, respectively. The content was immediately preserved in buffered formalin (4% final concentration). All samples were analyzed in the Plankton sorting and identification center in Szczecin (www.nmfri.gdynia.pl). Samples containing high numbers of zooplankton were split into subsamples. All copepods and other zooplankton were identified down to lowest possible taxonomic level (approx. 400 per sample), length measured and counted. Copepods were sorted into development stages (nauplii stage 1 - copepodite stage 6) using morphological features and sizes, and up to 10 individuals of each stage was length measured.

Mesozooplankton abundance data from the fjord branch Kapisigdlit located in the Godthaabsfjord system, West Greenland, 2010

Sampling was conducted from March 24 to August 5 2010, in the fjord branch Kapisigdlit located in the inner part of the Godthåbsfjord system, West Greenland. The vessel "Lille Masik" was used during all cruises except on June 17-18 where sampling was done from RV Dana (National Institute for Aquatic Resources, Denmark). A total of 15 cruises (of 1-2 days duration) 7-10 days apart was carried out along a transect composed of 6 stations (St.), spanning the length of the 26 km long fjord branch. St. 1 was located at the mouth of the fjord branch and St. 6 was located at the end of the fjord branch, in the middle of a shallower inner creek . St. 1-4 was covering deeper parts of the fjord, and St. 5 was located on the slope leading up to the shallow inner creek. Mesozooplankton was sampled by vertical net tows using a Hydrobios Multinet (type Mini) equipped with a flow meter and 50 µm mesh nets or a WP-2 net 50 µm mesh size equipped with a non-filtering cod-end. Sampling was conducted at various times of day at the different stations. The nets were hauled with a speed of 0.2-0.3 m s**-1 from 100, 75 and 50 m depth to the surface at St. 2 + 4, 5 and 6, respectively. The content was immediately preserved in buffered formalin (4% final concentration). All samples were analyzed in the Plankton sorting and identification center in Szczecin (www.nmfri.gdynia.pl). Samples containing high numbers of zooplankton were split into subsamples. All copepods and other zooplankton were identified down to lowest possible taxonomic level (approx. 400 per sample), length measured and counted. Copepods were sorted into development stages (nauplii stage 1 - copepodite stage 6) using morphological features and sizes, and up to 10 individuals of each stage was length measured.