Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Exploiting Structure In Combinatorial Problems With Applications In Computational Sustainability

Combinatorial decision and optimization problems are at the core of many tasks with practical importance in areas as diverse as planning and scheduling, supply chain management, hardware and software verification, electronic commerce, and computational biology. Another important source of combinatorial problems is the newly emerging field of computational sustainability, which addresses decision-making aimed at balancing social, economic and environmental needs to guarantee the long-term prosperity of life on our planet. This dissertation studies different forms of problem structure that can be exploited in developing scalable algorithmic techniques capable of addressing large real-world combinatorial problems. There are three major contributions in this work: 1) We study a form of hidden problem structure called a backdoor, a set of key decision variables that captures the combinatorics of the problem, and reveal that many real-world problems encoded as Boolean satisfiability or mixed-integer linear programs contain small backdoors. We study backdoors both theoretically and empirically and characterize important tradeoffs between the computational complexity of finding backdoors and their effectiveness in capturing problem structure succinctly. 2) We contribute several domain-specific mathematical formulations and algorithmic techniques that exploit specific aspects of problem structure arising in budget-constrained conservation planning for wildlife habitat connectivity. Our solution approaches scale to real-world conservation settings and provide important decision-support tools for cost-benefit analysis. 3) We propose a new survey-planning methodology to assist in the construction of accurate predictive models, which are especially relevant in sustainability areas such as species- distribution prediction and climate-change impact studies. In particular, we design a technique that takes advantage of submodularity, a structural property of the function to be optimized, and results in a polynomial-time procedure with approximation guarantees

Robust Placement of Sensors in Dynamic Water Distribution Systems

Designing a robust sensor network to detect accidental contaminants in water distribution systems is a challenge given the uncertain nature of the contamination events (what, how much, when, where and for how long) and the dynamic nature of water distribution systems (driven by the random consumption of consumers). We formulate a set of scenario-based minimax and minimax regret models in order to provide robust sensor-placement schemes that perform well under all realizable contamination scenarios, and thus protect water consumers. Single-and multi objective versions of these models are then applied to a real water distribution system. A heuristic solution method is applied to solve the robust models. The concept of ‘‘sensitivity region” is used to visualize trade-offs between multiple objectives

Robust placement of sensors in dynamic water distribution systems

Designing a robust sensor network to detect accidental contaminants in water distribution systems is a challenge given the uncertain nature of the contamination events (what, how much, when, where and for how long) and the dynamic nature of water distribution systems (driven by the random consumption of consumers). We formulate a set of scenario-based minimax and minimax regret models in order to provide robust sensor-placement schemes that perform well under all realizable contamination scenarios, and thus protect water consumers. Single-and multi-objective versions of these models are then applied to a real water distribution system. A heuristic solution method is applied to solve the robust models. The concept of "sensitivity region" is used to visualize trade-offs between multiple objectives.Facilities planning and design Robust optimization Scenarios Water distribution systems