Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

We study distributionally robust chance constrained programs (DRCCPs) with individual chance constraints and random right-hand sides. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. We consider two types of Wasserstein ambiguity sets: one with finite support and one with a continuum of realizations. By exploring the hidden discrete structures, we develop mixed integer programming reformulations under the two types of ambiguity sets to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test instances with transportation problems of diverse sizes and a demand response management problem

Optimisation du développement de nouveaux produits dans l'industrie pharmaceutique par algorithme génétique multicritère

Le développement de nouveaux produits constitue une priorité stratégique de l'industrie pharmaceutique, en raison de la présence d'incertitudes, de la lourdeur des investissements mis en jeu, de l'interdépendance entre projets, de la disponibilité limitée des ressources, du nombre très élevé de décisions impliquées dû à la longueur des processus (de l'ordre d'une dizaine d'années) et de la nature combinatoire du problème. Formellement, le problème se pose ainsi : sélectionner des projets de Ret D parmi des projets candidats pour satisfaire plusieurs critères (rentabilité économique, temps de mise sur le marché) tout en considérant leur nature incertaine. Plus précisément, les points clés récurrents sont relatifs à la détermination des projets à développer une fois que les molécules cibles sont identifiées, leur ordre de traitement et le niveau de ressources à affecter. Dans ce contexte, une approche basée sur le couplage entre un simulateur à événements discrets stochastique (approche Monte Carlo) pour représenter la dynamique du système et un algorithme d'optimisation multicritère (de type NSGA II) pour choisir les produits est proposée. Un modèle par objets développé précédemment pour la conception et l'ordonnancement d'ateliers discontinus, de réutilisation aisée tant par les aspects de structure que de logique de fonctionnement, a été étendu pour intégrer le cas de la gestion de nouveaux produits. Deux cas d'étude illustrent et valident l'approche. Les résultats de simulation ont mis en évidence l'intérêt de trois critères d'évaluation de performance pour l'aide à la décision : le bénéfice actualisé d'une séquence, le risque associé et le temps de mise sur le marché. Ils ont été utilisés dans la formulation multiobjectif du problème d'optimisation. Dans ce contexte, des algorithmes génétiques sont particulièrement intéressants en raison de leur capacité à conduire directement au front de Pareto et à traiter l'aspect combinatoire. La variante NSGA II a été adaptée au problème pour prendre en compte à la fois le nombre et l'ordre de lancement des produits dans une séquence. A partir d'une analyse bicritère réalisée pour un cas d'étude représentatif sur différentes paires de critères pour l'optimisation bi- et tri-critère, la stratégie d'optimisation s'avère efficace et particulièrement élitiste pour détecter les séquences à considérer par le décideur. Seules quelques séquences sont détectées. Parmi elles, les portefeuilles à nombre élevé de produits provoquent des attentes et des retards au lancement ; ils sont éliminés par la stratégie d'optimistaion bicritère. Les petits portefeuilles qui réduisent les files d'attente et le temps de lancement sont ainsi préférés. Le temps se révèle un critère important à optimiser simultanément, mettant en évidence tout l'intérêt d'une optimisation tricritère. Enfin, l'ordre de lancement des produits est une variable majeure comme pour les problèmes d'ordonnancement d'atelier. ABSTRACT : New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline, namely, the presence of uncertainty, the high level of the involved capital costs, the interdependency between projects, the limited availability of resources, the overwhelming number of decisions due to the length of the time horizon (about 10 years) and the combinatorial nature of a portfolio. Formally, the NPD problem can be stated as follows: select a set of R and D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while copying with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGA II type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. An object-oriented model previously developed for batch plant scheduling and design is then extended to embed the case of new product management, which is particularly adequate for reuse of both structure and logic. Two case studies illustrate and validate the approach. From this simulation study, three performance evaluation criteria must be considered for decision making: the Net Present Value (NPV) of a sequence, its associated risk defined as the number of positive occurrences of NPV among the samples and the time to market. Theyv have been used in the multiobjective optimization formulation of the problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. NSGA II has been adapted to the treated case for taking into account both the number of products in a sequence and the drug release order. From an analysis performed for a representative case study on the different pairs of criteria both for the bi- and tricriteria optimization, the optimization strategy turns out to be efficient and particularly elitist to detect the sequences which can be considered by the decision makers. Only a few sequences are detected. Among theses sequences, large portfolios cause resource queues and delays time to launch and are eliminated by the bicriteria optimization strategy. Small portfolio reduces queuing and time to launch appear as good candidates. The optimization strategy is interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multi-Objective Probabilistically Constrained Programming with Variable Risk: New Models and Applications

We consider a class of multi-objective probabilistically constrained problems MOPCP with a joint chance constraint, a multi-row random technology matrix, and a risk parameter (i.e., the reliability level) defined as a decision variable. We propose a Boolean modeling framework and derive a series of new equivalent mixed-integer programming formulations. We demonstrate the computational efficiency of the formulations that contain a small number of binary variables. We provide modeling insights pertaining to the most suitable reformulation, to the trade-off between the conflicting cost/revenue and reliability objectives, and to the scalarization parameter determining the relative importance of the objectives. Finally, we propose several MOPCP variants of multi-portfolio financial optimization models that implement a downside risk measure and can be used in a centralized or decentralized investment context. We study the impact of the model parameters on the portfolios, show, via a cross-validation study, the robustness of the proposed models, and perform a comparative analysis of the optimal investment decisions

Multiobjective optimization of New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline, namely, the presence of uncertainty, the high level of the involved capital costs, the interdependency between projects, the limited availability of resources, the overwhelming number of decisions due to the length of the time horizon (about 10 years) and the combinatorial nature of a portfolio. Formally, the NPD problem can be stated as follows: select a set of R and D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while copying with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGA II type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. An object-oriented model previously developed for batch plant scheduling and design is then extended to embed the case of new product management, which is particularly adequate for reuse of both structure and logic. Two case studies illustrate and validate the approach. From this simulation study, three performance evaluation criteria must be considered for decision making: the Net Present Value (NPV) of a sequence, its associated risk defined as the number of positive occurrences of NPV among the samples and the time to market. Theyv have been used in the multiobjective optimization formulation of the problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. NSGA II has been adapted to the treated case for taking into account both the number of products in a sequence and the drug release order. From an analysis performed for a representative case study on the different pairs of criteria both for the bi- and tricriteria optimization, the optimization strategy turns out to be efficient and particularly elitist to detect the sequences which can be considered by the decision makers. Only a few sequences are detected. Among theses sequences, large portfolios cause resource queues and delays time to launch and are eliminated by the bicriteria optimization strategy. Small portfolio reduces queuing and time to launch appear as good candidates. The optimization strategy is interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

Heuristic algorithms for solving a class of multiobjective zero-one programming problems

Master'sMASTER OF ENGINEERIN

Query processing in complex modern traffic networks

The transport sector generates about one quarter of all greenhouse gas emissions worldwide. In the European Union (EU), passenger cars and light-duty trucks make up for over half of these traffic-related emissions. It is evident that everyday traffic is a serious environmental threat. At the same time, transport is a key factor for the ambitious EU climate goals; among them, for instance, the reduction of greenhouse gas emissions by 85 to 90 percent in the next 35 years. This thesis investigates complex traffic networks and their requirements from a computer science perspective. Modeling of and query processing in modern traffic networks are pivotal topics. Challenging theoretical problems are examined from different perspectives, novel algorithmic solutions are provided. Practical problems are investigated and solved, for instance, employing qualitative crowdsourced information and sensor data of various sources. Modern traffic networks are often modeled as graphs, i.e., defined by sets of nodes and edges. In conventional graphs, the edges are assigned numerical weights, for instance, reflecting cost criteria like distance or travel time. In multicriteria networks, the edges reflect multiple, possibly dynamically changing cost criteria. While these networks allow for diverse queries and meaningful insight, query processing usually is significantly more complex. Novel means for computation are required to keep query processing efficient. The crucial task of computing optimal paths is particularly expensive under multiple criteria. The most established set of optimal paths in multicriteria networks is referred to as path skyline (or set of pareto-optimal paths). Until now, computing the path skyline either required extensive precomputation or networks of minor size or complexity. Neither of these demands can be made on modern traffic networks. This thesis presents a novel method which makes on-the-fly computation of path skylines possible, even in dynamic networks with three or more cost criteria. Another problem examined is the exponentially growth of path skylines. The number of elements in a path skyline is potentially exponential in the number of cost criteria and the number of edges between start and target. This often produces less meaningful results, sometimes hindering usability. These drawbacks emphasize the importance of the linear path skyline which is investigated in this thesis. The linear path skyline is based on a different notion of optimality. By the notion of optimality, the linear path skyline is a subset of the conventional path skyline but in general contains less and more diverse elements. Thus, the linear path skyline facilitates interpretation while in general reducing computational effort. This topic is first studied in networks with two cost criteria and subsequently extended to more cost criteria. These cost criteria are not limited to purely quantitative measures like distance and travel time. This thesis examines the integration of qualitative information into abstractly modeled road networks. It is proposed to mine crowdsourced data for qualitative information and use this information to enrich road network graphs. These enriched networks may in turn be used to produce routing suggestions which reflect an opinion of the crowd. From data processing to knowledge extracting, network enrichment and route computation, the possibilities and challenges of crowdsourced data as a source for information are surveyed. Additionally, this thesis substantiates the practicability of network enrichment in real-world experiments. The description of a demonstration framework which applies some of the presented methods to the use case of tourist route recommendation serves as an example. The methods may also be applied to a novel graph-based routing problem proposed in this thesis. The problem extends the family of Orienteering Problems which find frequent application in tourist routing and other tasks. An approximate solution to this NP-hard problem is presented and evaluated on a large scale, real-world, time-dependent road network. Another central aspect of modern traffic networks is the integration of sensor data, often referred to as telematics. Nowadays, manifold sensors provide a plethora of data. Using this data to optimize traffic is and will continue to be a challenging task for research and industry. Some of the applications which qualify for the integration of modern telematics are surveyed in this thesis. For instance, the abstract problem of consumable and reoccurring resources in road networks is studied. An application of this problem is the search for a vacant parking space. Taking statistical and real-time sensor information into account, a stochastic routing algorithm which maximizes the probability of finding a vacant space is proposed. Furthermore, the thesis presents means for the extraction of driving preferences, helping to better understand user behavior in traffic. The theoretical concepts partially find application in a demonstration framework described in this thesis. This framework provides features which were developed for a real-world pilot project on the topics of electric and shared mobility. Actual sensor car data collected in the project, gives insight to the challenges of managing a fleet of electric vehicles.Verkehrsmittel erzeugen rund ein Viertel aller Treibhausgas-Emissionen weltweit. Für über die Hälfte der verkehrsbedingten Emissionen in der Europäischen Union (EU) zeichnen PKW und Kleinlaster verantwortlich. Die Tragweite ökologischer Konsequenzen durch alltäglichen Verkehr ist enorm. Zugleich ist ein Umdenken im Bezug auf Verkehr entscheidend, um die ehrgeizigen klimapolitischen Ziele der EU zu erfüllen. Dazu gehört unter anderem, Treibhausgas-Emissionen bis 2050 um 85 bis 90 Prozent zu verringern. Die vorliegende Arbeit widmet sich den komplexen Anforderungen an Verkehr und Verkehrsnetzwerke aus der Sicht der Informatik. Dabei spielen sowohl die Modellierung von als auch die Anfragebearbeitung in modernen Verkehrsnetzwerken eine entscheidende Rolle. Theoretische Fragestellungen werden aus unterschiedlichen Persepektiven beleuchtet, neue Algorithmen werden vorgestellt. Ebenso werden praktische Fragestellungen untersucht und gelöst, etwa durch die Einbindung nutzergenerierten Inhalts oder die Verwendung von Sensordaten aus unterschiedlichen Quellen. Moderne Verkehrsnetzwerke werden häufig als Graphen modelliert, d.h., durch Knoten und Kanten dargestellt. Man unterscheidet zwischen konventionellen Graphen und sogenannten Multiattributs-Graphen. Während die Kanten konventioneller Graphen numerische Gewichte tragen, die statische Kostenkriterien wie Distanz oder Reisezeit modellieren, beschreiben die Kantengewichte in Multiattributs-Graphen mehrere, möglicherweise dynamisch veränderliche Kostenkriterien. Das erlaubt einerseits vielseitige Anfragen und aussagekräftige Erkenntnisse, macht die Anfragebearbeitung jedoch ungleich komplexer und verlangt deshalb nach neuen Berechnungsmethoden. Eine besonders aufwendige Anfrage ist die Berechnung optimaler Pfade, zugleich eine der zentralsten Fragestellungen. Die gängigste Menge optimaler Pfade wird als Pfad-Skyline (auch: Menge der pareto-optimalen Pfade) bezeichnet. Die effiziente Berechnung der Pfad-Skyline setzte bisher überschaubare Netzwerke oder beträchtliche Vorberechnungen voraus. Keine der beiden Bedingung kann in modernen Verkehrsnetzwerken erfüllt werden. Diese Arbeit stellt deshalb eine Methode vor, die die Berechnung der Pfad-Skyline erheblich beschleunigt, selbst in dynamischen Netzwerken mit drei oder mehr Kostenkriterien. Außerdem wird das Problem des exponentiellen Wachstums der Pfad-Skyline betrachtet. Die Anzahl der Elemente der Pfad-Skyline wächst im schlechtesten Fall exponentiell in der Anzahl der Kostenkriterien sowie in der Entfernung zwischen Start und Ziel. Dies kann zu unübersichtlichen und wenig aussagekräftigen Resultatmengen führen. Diese Nachteile unterstreichen die Bedeutung der linearen Pfad-Skyline, die auch im Rahmen diese Arbeit untersucht wird. Die lineare Pfad-Skyline folgt einer anderen Definition von Optimalität. Stets ist die lineare Pfad-Skyline eine Teilmenge der konventionellen Pfad-Skyline, meist enthält sie deutlich weniger, unterschiedlichere Resultate. Dadurch lässt sich die lineare Pfad-Skyline im Allgemeinen schneller berechnen und erleichtert die Interpretation der Resultate. Die Berechnung der linearen Pfad-Skyline wird erst für Netzwerke mit zwei Kostenkriterien, anschließend für Netzwerke mit beliebig vielen Kostenkriterien untersucht. Kostenkriterien sind nicht notwendigerweise auf rein quantitative Maße wie Distanz oder Reisezeit beschränkt. Diese Arbeit widmet sich auch der Integration qualitativer Informationen, mit dem Ziel, intuitivere und greifbarere Routingergebnisse zu erzeugen. Dazu wird die Möglichkeit untersucht, abstrakte Straßennetzwerke mit qualitativen Informationen anzureichern, wobei die Informationen aus nutzergenerierten Daten geschöpft werden. Solche sogenannten Enriched Networks ermöglichen die Berechnung von Pfaden, die in gewisser Weise das Wissen der Nutzer reflektieren. Von der Datenverarbeitung, über die Extraktion von Wissen, bis hin zum Network-Enrichment und der Pfadberechnung, gibt diese Arbeit einen überblick zum Thema. Weiterhin wird die Praktikabilität dieses Vorgehens mit Experimenten auf Realdaten untermauert. Die Beschreibung eines Demonstrationstools für den Anwendungsfall der Navigation von Touristen dient als anschauliches Beispiel. Die vorgestellten Methoden sind darüber hinaus auch anwendbar auf ein neues, graphentheoretisches Routingproblem, das in dieser Arbeit vorgestellt wird. Es handelt sich dabei um eine zeitabängige Erweiterung der Familie der Orienteering Probleme, die häufig Anwendung finden, etwa auch im der Bereich der Touristennavigation. Das vorgestellte Problem ist NP-schwer lässt sich jedoch dank eines hier vorgestellten Algorithmus effizient approximieren. Die Evaluation untermauert die Effizienz des vorgestellten Lösungsansatzes und ist zugleich die erste Auswertung eines zeitabhängigen Orienteering Problems auf einem großformatigen Netzwerk. Ein weiterer zentraler Aspekt moderner Verkehrsnetzwerke ist die Integration von Sensordaten, oft unter dem Begriff Telematik zusammengefasst. Heutzutage generiert eine Vielzahl von Sensoren Unmengen an Daten. Diese Daten zur Verkehrsoptimierung einzusetzen ist und bleibt eine wichtige Aufgabe für Wissenschaft und Industrie. Einige der Anwendungen, die sich für den Einsatz von Telematik anbieten, werden in dieser Arbeit untersucht. So wird etwa das abstrakte Problem konsumierbarer und wiederkehrender Ressourcen im Straßennetzwerk untersucht. Ein alltägliches Beispiel für dieses Problem ist die Parkplatzsuche. Der vorgeschlagene Algorithmus, der die Wahrscheinlichkeit maximiert, einen freien Parkplatz zu finden, baut auf die Verwendung statistischer sowie aktueller Sensordaten. Weiterhin werden Methoden zur Ableitung von Fahrerpräferenzen entwickelt. Die theoretischen Fundamente finden zum Teil in einem hier beschriebenen Demonstrationstool Anwendung. Das Tool veranschaulicht Features, die für ein Pilotprojekt zu den Themen Elektromobilität und Fahrzeugflotten entwickelt wurden. Im Rahmen eines Pilotversuchs wurden Sensordaten von Elektrofahrzeugen erhoben, die Einblick in die Herausforderungen beim Management von Elektrofahrzeugflotten geben

Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design

We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A recently introduced class of such models treats the reliability levels / risk tolerances associated with the chance constraints as decision variables and trades off the actual cost / return against the cost of the selected reliability levels in the objective function. Leveraging recent methodological advances for modeling and solving chance-constrained linear programs with fixed reliability levels, we develop strong mixed-integer programming formulations for this new variant with variable reliability levels. In addition, we introduce an alternate cost function type associated with the risk tolerances which requires capturing the value-at-risk (VaR) associated with a variable reliability level. We accomplish this task via a new integer linear programming representation of VaR. Our computational study illustrates the effectiveness of our mathematical programming formulations. We also apply the proposed modeling approach to a new stochastic last mile relief network design problem and provide numerical results for a case study based on the real-world data from the 2011 Van earthquake in Turkey