Title: Robustification of statistical and econometrical regression methods Author: Mgr. Tomáš Jurczyk Department: Department of probability and mathematical statistics Supervisor: prof. RNDr. Jan Ámos Víšek CSc., IES FSV UK Praha Abstract: Multicollinearity and outlier presence are two problems of data which can occur during the regression analysis. In this thesis we are interested mainly in situations where combined outlier-multicollinearity problem is present. We will show first the behavior of classical methods developed for overcoming one of these problems. We will investigate the functionality of methods proposed as robust multicollinearity detectors as well. We will prove that proposed two-step procedures (in one step typically based on robust regression methods) are failing in outlier detection and therefore also multicollinearity detection, if the strong multicollinearity is present in the majority of the data. We will propose a new one-step method as a candidate for the robust detector of multicollinearity as well as the robust ridge regression estimate. We will derive its properties, behavior and propose the diagnostic tools derived from that method. Keywords: multicollinearity, outliers, robust detector of multicollinearity, ro- bust ridge regression 1

The main aim of this research project is to extend theories of four-wheel-steering as developed by J. Ackermann to include an individually steered four-wheel steering system for passenger vehicles. Ackermann’s theories, including theories available in this subject area, dwell much on vehicle system dynamics developed from what is called single track model and some call it a bicycle model. In the bicycle model, the front two wheels are bundled together. Similarly, the rear wheels are bundled together. The problem with this is that it assumes two front wheels or two rear wheels to be under the same road, vehicle and operating conditions. The reality on the ground and experiments that are conducted are to the contrary. Therefore this study discusses vehicle disturbance rejection through robust decoupling of yaw and lateral motions of the passenger vehicle. A mathematical model was developed and simulated using Matlab R2008b. The model was developed in such a way that conditions can be easily changed and simulated. The model responded well to variations in road and vehicle conditions. Focus was in the ability of the vehicle to reject external disturbances. To generate yaw moment during braking, the brake on the left front wheel was disconnected. This was done because lateral wind generators, as used by Ackermann, were not available. The results from both simulations and experiments show disturbance rejection in the steady state. Copyright / Dissertation (MSc)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n _> 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.

In den vergangenen Jahrzehnten konzentrierte sich das Operations Management auf Optimierungsstrategien, insbesondere wurden Meta-Heuristiken für das komplexe, kombinatorische Problem der ressourcenbegrenzten Ablaufplanung erforscht. In einfachen Worten gehört dieses Problem zu den NP-schweren Problemen, die einen derart großen Lösungsraum besitzen, der mittels Enumerationverfahren rechnerisch unlösbar ist. Daher erfordert die Exploration von optimalen Lösungen andere Methoden als Zufallssuchverfahren. Solche Suchalgorithmen in Meta-Heuristik starten mit einer oder mehreren Ausgangslösung und erkunden den Suchraum nach optimalen Lösungen. Jedoch stellen die existierenden Forschungsansätze zur Lösungssuche nur diejenigen Lösungen bereit, die ausschließlich unter den gegebenen Eingangsbedingungen optimal sind. Diese Eingabebedingungen definieren einen Lösungsraum, in dem alles nach Plan geht. Jedoch ist das in der Praxis sicherlich nicht der Fall. Wie wir sagen, der Wandel ist die einzige Konstante in dieser Welt. Risiken und Unsicherheiten begegnen stets im täglichen Leben. Die vorliegende Dissertation untersucht Optimierungsansätze unter Unsicherheit. Der Forschungsbeitrag ist zweigeteilt. Wie bereits gesagt, wurden Optimierungsstrategien zum Durchsuchen des Lösungsraums in den letzten Jahren stark erforscht. Obwohl es eine anerkannte Tatsache ist, dass die Verbesserung und die Leistung von Optimierungsstrategien stark mit den Initiallösungen korreliert, scheint die Literatur diesbezüglich inexistent, während zumeist auf die Entwicklung von meta-heuristischen Algorithmen wie Genetische Algorithmen und Particle-Swarm-Optimierung fokussiert wird. Die Initiallösungen werden durch simulationsbasierte Strategien entwickelt, die typischerweise gierige Regeln und ereignisbasierte Simulation nutzen. Allerdings verhalten sich kommerzielle Basis-Softwareprodukte meist als Black-Box und stellen keine Informationen über das interne Verhalten bereit. Außerdem erfordern derartige Softwareprodukte meist spezielle Architekturen und missachten Ressourcenbeschränkungen. Die vorliegende Studie diskutiert die ressourcenbeschränkte Projektplanung mit alternativen Modi und schlägt ein simulationsbasiertes Rahmenwerk vor, mit dem ein heuristisches Multi-Pass-Verfahren zur Verfügung gestellt wird. Das erweiterte Multi-Modus-Problem ist in der Lage, den Produktionsbereich in einer besseren Art und Weise nachzubilden, bei dem eine Aktivität von mehreren Ressourcen unterschiedlicher Qualifikation ausgeführt werden kann. Der vorgeschlagene Rahmen diskutiert die Leistung von Algorithmen und verwendet hierfür Benchmark-Instanzen. Das Verhalten verschiedener Projektnetze und deren Eigenschaften werden auch innerhalb des vorgeschlagenen Rahmenwerks bewertet. Darüber hinaus hilft das offene Rahmenwerk, besondere Eigenschaften von Aktivitäten zu analysieren, um deren Verhalten im Fall von Störungen zu prognostizieren. Die traditionellen Methoden der Risikoanalyse schlagen Slack-basierte Maßzahlen vor, um die Effizienz von Basisplänen zu bestimmen. Das Rahmenwerk wird weiter entwickelt, um mit diesem einen Prüfstand zu gestalten, mit dem nicht-reguläre Maßzahlen bestimmt werden können. Diese Maßnahmen werden als Robustheitsindikatoren bezeichnet und korrelieren mit der Verzögerung derartiger Multi-Modus-Probleme. Solche Leistungsmaße können genutzt werden, um die Wirksamkeit von Basisplänen zu bewerten und ihr Verhalten unter Unsicherheiten zu prognostizieren. Die Ergebnisse dieser Tests werden als modifizierte Zielfunktion verwendet, in der ein bi-objektives Leistungsmaß aus Durchlaufzeit und Robustheit eingesetzt wird, um die Effizienz der vorgeschlagenen Heuristiken zu testen. Da diese Leistungsmaße das Verhalten von Aktivitäten unter Störungen zeigen, werden diese auch genutzt, um die Formfaktoren und Puffergrößen für die Entwicklung eines stochastischen Modells zu bestimmen. Die Analyse der Projektergebnisse, durchgeführt mittels Monte-Carlo-Simulationen, unterstützt das Argument von Teilpuffern für die Modellierung von Aktivitätsdauern anstatt Ansätze mit Extrempuffern und PERT-beta-Schätzungen. / Over the past decades, researches in the field of operations management have focused on optimization strategies based on meta-heuristics for the complex-combinatorial problem of resource constrained scheduling. In simple terms, the solution for this particular problem categorized as NP-hard problem, exhibits a large search space, is computationally intractable, and requires techniques other than random search. Meta-heuristic algorithms start with a single or multiple solutions to explore and optimize using deterministic data and retrieve a valid optimum only under specified input conditions. These input conditions define a solution search space for a theoretical world undergoing no disturbance. But change is inherent to the real world; one is faced with risks and uncertainties in everyday life. The present study explores solution methodologies in the face of uncertainties. The contributions of this thesis are two-fold. As mentioned earlier, existing optimization strategies have been vigorously investigated in the past decade with respect to exploring large solution search space. Although, it is an established fact that the improvement and performance of optimization strategies is highly correlated with the initial solutions, existing literature regarding this area is not exhaustive and mostly focuses on the development of meta-heuristic algorithms such as genetic algorithms and particle swarm optimization. The initial solutions are developed through simulation based strategies mainly based on greedy rules and event based simulation. However, the available commercial softwares are primarily modeled as a black box and provide little information as to internal processing. Additionally, such planners require special architecture and disregard resource constraints. The present study discusses the multi-mode resource constrained scheduling problem and proposes a simulation-based framework to provide a multi-pass heuristic method. The extended version of multi-mode problem is able to imitate production floor in an improved manner where a task can be performed with multiple resources with certain qualifications. The performance of the proposed framework was analyzed using benchmark instances. The behavior of different project networks and their characteristics is also evaluated within the proposed framework. In addition, the open framework aids in determining the particular characteristic of tasks in order to analyze and forecast their behavior in case of disruptions. The traditional risk analysis techniques suggest slack-based measures in order to determine the efficiency of baseline schedules. The framework is further developed to design a test bench in order to determine non-regular performance measures named as robustness indicators which correlate with the delay of such cases as multi-mode problem. Such performance measures can be used to indicate the effectiveness of baseline schedules and forecast their behavior. The outputs of these tests are used to modify the objective function which uses makespan and robustness indicators as a bi-objective performance measure in order to test the efficiency of proposed heuristics. Furthermore, since these measures indicate the behavior of tasks under disruptions, they are utilized in order to determine the shape factors and buffers for the development of a stochastic model. The analysis of project outcomes performed through Monte-Carlo simulations supports the argument of partial buffer sizing for modeling activity duration estimates rather than extreme buffer approaches proposed via PERT-beta estimates.

Controlled Source Audio Magnetotellurics (CSAMT) is a geophysical method for characterizing the resistivity of the subsurface with the help of electromagnetic waves. The method is used for various purposes, such as geothermal- and hydrocarbon exploration, mineral prospecting and for investigation of groundwater resources. Electromagnetic fields are created by running an alternating current in a grounded electric dipole and by varying the frequency, different depths can be targeted. Orthogonal components of the electromagnetic fields are measured at receiver stations a few kilometers away from the source. From these field components, so called magnetotellurics transfer functions are estimated, which can be used to invert for the resistivity of the subsurface. The data used in this project is from a survey conducted in 2014 and 2016 in Kiruna by Uppsala University and the mining company LKAB. Measurements were made at 31 stations along two orthogonal profiles. The data have been processed earlier, but due to noise, especially in the lower frequencies, a significant part of the data set could not be inverted. The aim of this project was to improve the results by analyzing the data and testing different methods to remove noise. First, robust regression was used to account for possible non-Gaussian noise in the estimation of the magnetotelluric transfer functions. Except for one station on profile 1, the robust method did not improve the results, which suggests that the noise is mostly Gaussian. Then modified versions of least squares, each affected by a different bias, were used to estimate the transfer functions. Where there is more noise, the estimates should differ more due to their different biases. The estimates differed most for low frequencies and especially on the part of profile 2 that was measured in 2014. It was investigated whether the railway network could explain part of the low frequency noise. Measures were taken to reduce spectral leakage from the railway signal at 16 ⅔ Hz to the closest transmitter frequencies 14 Hz and 20 Hz, but no clear improvement was seen and more detailed studies need to be conducted to determine this matter. Finally, a method based on comparing the ratio of short-term and long-term averages was tested to remove transients in the measured time series of the electromagnetic field components. This proved difficult to implement due to the variability of the time series’ behavior between different stations, frequencies and field components. However, the method showed some potential for stations 9 and 10 on profile 1, and could probably be developed further to remove transients more efficiently and thus improve the data. / Magnetotellurik med kontrollerad källa (förkortat CSAMT på engelska) är en metod där elektromagnetiska fält används för att undersöka markens resistivitet. Resisitivitet är ett mått på hur bra eller dåligt marken leder elektriska strömmar. Metoden används till exempel för att mäta djupet till berggrunden, som oftast har högre resistivitet (sämre ledningsförmåga) än marken ovanför. Man kan också hitta metaller, så som guld och koppar, vilka har väldigt låg resistivitet (bra ledningsförmåga). Elektromagnetiska vågor skapas genom att man låter en växelström gå igenom en lång ledning. Vågorna färdas först genom luften och sen ner i marken. Hur djupt ner de når beror på växelströmmens frekvens; med låga frekvenser når vågorna djupare ner i marken än med höga. Under markytan inducerar de elektromagnetiska vågorna elektriska strömmar, så kallade telluriska strömmar (dvs. jordströmmar). Strömmarna blir svagare ju längre de färdas och hur snabbt de avtar i styrka beror på jordens resistivitet. Strömmarna skapar också nya elektriska och magnetiska fält som färdas tillbaka mot ytan. Vid markytan mäter man fältens styrka för olika frekveser, vilket då ger information om resistiviteten på olika djup. Från mätningarna tar man ofta fram så kallade magnetotelluriska överföringsfunktioner. Dessa överföringsfunktioner gör det lättare att tolka datan och ta reda på resistiviteten hos marken. I detta projekt har CSAMT-data använts från en undersökning i Kiruna som genomfördes av Uppsala Universitet och gruvföretaget LKAB. Datan har bearbetats tidigare, men på grund av mycket brus i mätningarna blev inte resultatet så bra som väntat. Brus kan komma från allt som genererar elektromagnetiska fält, till exempel elledningar, tågledningar eller naturliga variationer i jordens egna magnetfält. Målet med projektet var att förbättra resultatet genom att analysera datan och testa olika metoder för att ta bort brus. Den vanligaste metoden för att beräkna överföringsfunktionerna antar att det magnetiska fältet är fritt från brus. Detta är inte nödvändigtvis sant och kan leda till bias, alltså ett snedvridet resultat. Andra sätt att beräkna överföringsfunktionerna på ger olika bias. Det här kan man utnyttja för att se hur mycket brus som finns i datan. Om det inte finns något brus alls så blir alla överföringsfunktioner lika, medan om det finns mycket brus så skiljer de sig mer åt. På detta sätt upptäcktes att det var mer brus för frekvenserna 14 och 20 Hz (där 1 Hz är 1 svängning per sekund). En förklaring till det kan vara att tågledningar, som genererar elektromagnetiska fält med 16.67 Hz, ligger nära i frekvens och stör dessa signaler. För att minska brusets påverkan testades så kallad robust processering. Det innebär att man lägger mindre vikt vid de mätningar som tycks vara mycket annorlunda (alltså innehåller mer brus) från andra mätningar. Tyvärr så hjälpte inte denna strategi nämnvärt för att förbättra resultatet. Till sist tog vi fram en metod för att ta bort transienter, vilket är kortvarigt brus med hög intensitet. Transienter kan till exempel komma från åskblixtar, som ju är kortvariga elektriska urladdningar. Det visade sig dock att detta inte var helt enkelt, då det var svårt att se vad som var brus och vad som bara var naturliga variationer hos de elektromagnetiska fälten. Men i några fall kunde bruset urskiljas och därför verkar det troligt att fortsatt arbete med denna metod skulle kunna ge ännu bättre resultat.

Mountain biking is a sport where riders bike on trails, varying in slope and difficulty. Mountain bikes are generally equipped with suspension on the front wheel and often also on the rear. Some types of rear shocks use pressurized air for a spring action instead of the traditional metal coil. Air is sealed inside the shock’s air can by means of X-ring seals, providing a spring force on the wheel. It is of great importance that the sealing system performs as intended so the air spring does not quickly lose pressure during use. An experimental plan is conducted in an attempt to estimate the effects of seal dimension, lubrication and surface roughness on air leakage for more robust shocks. Accelerated tests were performed in a dynamometer, believed to repeatedly cause significant wear on the shock’s air seal within 24 hours. Nineteen tests were carried out, for a duration up to 72 hours, with variations to test parameters such as stroke length and frequency. The expected failure modes did not occur in any of them. Eleven tests showed no signs of failure while the other eight failed due to unexpected components breaking or wearing out. The shock’s main seal was found to wear out faster than the air seal, causing leakage within the air spring, between its positive and negative air chambers. This unforeseen failure needs further examination with tests conducted on more shock types. / Mountainbike är en sport där utövare åker på stigar med varierande lutning och svårighet. Terrängcyklar är generellt utrustade med stötdämpare eller fjädrar på framhjulet och ofta också på bakhjulet. Vissa terrängcyklar har stötdämpare bak som använder trycksatt luft för att dämpa istället för att använda traditionella stålfjädrar. Luften är sluten inuti stötdämparen med hjälp av X-rings tätningar, vilket ger en fjäderkraft på hjulet. Det är viktigt att tätningen fungerar så att luftfjädern inte snabbt tappar trycket när den används. En experimentplan skapades i ett försök att uppskatta effekten av tätningsdimension, smörjning och ytjämnhet på luftläckage för mer robusta stötdämpare. Accelererade tester gjordes i en dynamometer, som troddes kunna skapa signifikant slitage på en stötdämpares tätning inom 24 timmar upprepade gånger. 19 test gjordes med en körtid på upp till 72 timmar med variation av testparametrar som slaglängd och frekvens. De förväntade felkällorna uppstod inte i något av testerna. 11 tester visade inga tecken på fel medan 8 tester misslyckades på grund av att oväntade komponenter slets ut eller gick sönder. Stötdämparens huvudtätning visade sig slitas fortare än lufttätningen, vilket resulterade i läckage inuti luftfjädern mellan dess positiva och negativa kammare. Detta oförutsedda fel behöver vidare undersökning med tester på fler olika typer av stötdämpare.

A naive approach to filtering for feedback control of dynamic systems that is robust and stable is proposed. Simulations are run on the filters presented to investigate the robustness properties of each filter. Each simulation with the comparison of the filters is carried out using the usual mean squared error. The filters to be included are the classic Kalman filter, Krein space Kalman, two adjustments to the Krein filter with input modeling and a second uncertainty parameter, a newly developed filter called the Naive filter, bias corrected Naive, exponentially weighted moving average (EWMA) Naive, and bias corrected EWMA Naive filter.

In order to be able to perform many tasks, autonomous devices need to understand their environment and know where they are in this environment. Simultaneous Localisation and Mapping (SLAM) is a solution to this problem. When several devices attempt to jointly solve this problem they use Collaborative SLAM (C-SLAM), but this is a very resource-demanding process. In order to enable resource-constrained devices, like small mobile robots or eXtended Reality (XR) devices, to run C-SLAM we look towards a Server-Assisted C-SLAM architecture to lift the computational burden from these devices. In a real-world scenario, sensors might fail, the devices might process sensor data wrongly or a malicious actor might inject wrong data into the system. In order for these solutions to be reliable, they must be able to deal with these \emph{outliers}. This thesis looks into the impact of outliers in Server-Assisted C-SLAM algorithms and presents two novel solutions for a robust algorithm, based on robust estimation of the initial device poses. We show the novel solutions outperform the state of the art both in estimation accuracy, yielding better estimates of the real device trajectories, and computational performance, making it suitable for device-constrained devices. / För att kunna utföra flertalet uppgifter måste autonoma enheter förstå sin miljö och veta var de befinner sig i den här miljön. Simultaneous Localization and Mapping (SLAM) är en lösning på detta problem. När flera enheter försöker lösa detta problem tillsammans använder de Samarbetande SLAM (C-SLAM), men detta är en mycket resurskrävande process. För att möjliggöra att resursbegränsade enheter, så som exempelvis små mobila robotar eller eXtended Reality (XR)-enheter, ska kunna köra C-SLAM föreslås en serverassisterar C-SLAM-arkitektur beräkningsbördan kan lyftas från dessa enheter till servern. I ett verkligt scenario kan sensorer vara felaktiga, enheter behandla sensordata felaktigt eller illvilliga aktörer injicera felaktig data i systemet. Därför undersöker detta arbete effekten av \emph{outliers} i Serverassisterade C-SLAM-algoritmer och presenterar två nya lösningar för en robust algoritm, baserad på robusta uppskattningar av enhetens initiala positioner. Denna lösning visar sig överträffa likartade lösningar i litteraturen både vad gäller uppskattningsnoggrannhet, vilket ger bättre uppskattningar av den verkliga enhetsbanor och beräkningsprestanda, vilket gör den lämplig för enheter med begränsade resurser.

Profile monitoring is a relatively new approach in quality control best used where the process data follow a profile (or curve) at each time period. The essential idea for profile monitoring is to model the profile via some parametric, nonparametric, and semiparametric methods and then monitor the fitted profiles or the estimated random effects over time to determine if there have been changes in the profiles. The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or at least uncertain. Consequently, we consider monitoring profiles via two techniques, a nonparametric technique and a semiparametric procedure that combines both parametric and nonparametric profile fits, a procedure we refer to as model robust profile monitoring (MRPM). Also, we incorporate a mixed model approach to both the parametric and nonparametric model fits. For the mixed effects models, the MMRPM method is an extension of the MRPM method which incorporates a mixed model approach to both parametric and nonparametric model fits to account for the correlation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we formulated two Hotelling's T 2 statistics, one based on the estimated random effects and one based on the fitted values, and obtained the corresponding control limits. In addition,we used two different formulas for the estimated variancecovariance matrix: one based on the pooled sample variance-covariance matrix estimator and a second one based on the estimated variance-covariance matrix based on successive differences. A Monte Carlo study was performed to compare the integrated mean square errors (IMSE) and the probability of signal of the parametric, nonparametric, and semiparametric approaches. Both correlated and uncorrelated errors structure scenarios were evaluated for varying amounts of model misspecification, number of profiles, number of observations per profile, shift location, and in- and out-of-control situations. The semiparametric (MMRPM) method for uncorrelated and correlated scenarios was competitive and, often, clearly superior with the parametric and nonparametric over all levels of misspecification. For a correctly specified model, the IMSE and the simulated probability of signal for the parametric and theMMRPM methods were identical (or nearly so). For the severe modelmisspecification case, the nonparametric andMMRPM methods were identical (or nearly so). For the mild model misspecification case, the MMRPM method was superior to the parametric and nonparametric methods. Therefore, this simulation supports the claim that the MMRPM method is robust to model misspecification. In addition, the MMRPM method performed better for data sets with correlated error structure. Also, the performances of the nonparametric and MMRPM methods improved as the number of observations per profile increases since more observations over the same range of X generally enables more knots to be used by the penalized spline method, resulting in greater flexibility and improved fits in the nonparametric curves and consequently, the semiparametric curves. The parametric, nonparametric and semiparametric approaches were utilized for fitting the relationship between torque produced by an engine and engine speed in the automotive industry. Then, we used a Hotelling's T 2 statistic based on the estimated random effects to conduct Phase I studies to determine the outlying profiles. The parametric, nonparametric and seminonparametric methods showed that the process was stable. Despite the fact that all three methods reach the same conclusion regarding the –in-control– status of each profile, the nonparametric and MMRPM results provide a better description of the actual behavior of each profile. Thus, the nonparametric and MMRPM methods give the user greater ability to properly interpret the true relationship between engine speed and torque for this type of engine and an increased likelihood of detecting unusual engines in future production. Finally, we conclude that the nonparametric and semiparametric approaches performed better than the parametric approach when the user's model is misspecified. The case study demonstrates that, the proposed nonparametric and semiparametric methods are shown to be more efficient, flexible and robust to model misspecification for Phase I profile monitoring in a practical application. Thus, our methods are robust to the common problem of model misspecification. We also found that both the nonparametric and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency than current parametric methods used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications. / Ph. D.

Le domaine de recherche de cette thèse est l'optimisation linéaire robuste en deux étapes. Nous sommes intéressés par des algorithmes d'exploration de sa structure et aussi pour ajouter des alternatives afin d'atténuer le conservatisme inhérent à une solution robuste. Nous développons des algorithmes qui incorporent ces alternatives et sont personnalisés pour fonctionner avec des exemples de problèmes à moyenne ou grande échelle. En faisant cela, nous expérimentons une approche holistique du conservatisme en optimisation linéaire robuste et nous rassemblons les dernières avancées dans des domaines tels que l'optimisation robuste basée sur les données, optimisation robuste par distribution et optimisation robuste adaptative. Nous appliquons ces algorithmes dans des applications définies du problème de conception / chargement du réseau, problème de planification, problème combinatoire min-max-min et problème d'affectation de la flotte aérienne. Nous montrons comment les algorithmes développés améliorent les performances par rapport aux implémentations précédentes. / The research scope of this thesis is two-stage robust linear optimization. We are interested in investigating algorithms that can explore its structure and also on adding alternatives to mitigate conservatism inherent to a robust solution. We develop algorithms that incorporate these alternatives and are customized to work with rather medium or large scale instances of problems. By doing this we experiment a holistic approach to conservatism in robust linear optimization and bring together the most recent advances in areas such as data-driven robust optimization, distributionally robust optimization and adaptive robust optimization. We apply these algorithms in defined applications of the network design/loading problem, the scheduling problem, a min-max-min combinatorial problem and the airline fleet assignment problem. We show how the algorithms developed improve performance when compared to previous implementations.