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

Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty

Ph.DDOCTOR OF PHILOSOPH

Generalizing the Min-Max Regret Criterion using Ordered Weighted Averaging

In decision making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios, including the ordered weighted averaging (OWA) criterion and min-max regret. This paper introduces a novel generalization of min-max regret, leveraging the modeling power of OWA to enable a more nuanced expression of preferences in handling regret values. This new OWA regret approach is studied both theoretically and numerically. We derive several properties, including polynomially solvable and hard cases, and introduce an approximation algorithm. Through computational experiments using artificial and real-world data, we demonstrate the advantages of our OWAR method over the conventional min-max regret approach, alongside the effectiveness of the proposed clustering heuristics

Pilot3 D2.1 - Trade-off report on multi criteria decision making techniques

This deliverable describes the decision making approach that will be followed in Pilot3. It presents a domain-driven analysis of the characteristics of Pilot3 objective function and optimisation framework. This has been done considering inputs from deliverable D1.1 - Technical Resources and Problem definition, from interaction with the Topic Manager, but most importantly from a dedicated Advisory Board workshop and follow-up consultation. The Advisory Board is formed by relevant stakeholders including airlines, flight operation experts, pilots, and other relevant ATM experts. A review of the different multi-criteria decision making techniques available in the literature is presented. Considering the domain-driven characteristics of Pilot3 and inputs on how the tool could be used by airlines and crew. Then, the most suitable methods for multi-criteria optimisation are selected for each of the phases of the optimisation framework

Models and algorithms for deterministic and robust discrete time/cost trade-off problems

Ankara : The Department of Management, Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 136-145Projects are subject to various sources of uncertainties that often negatively impact activity durations and costs. Therefore, it is of crucial importance to develop effective approaches to generate robust project schedules that are less vulnerable to disruptions caused by uncontrollable factors. This dissertation concentrates on robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). Firstly, Benders Decomposition based exact algorithms to solve the deadline and the budget versions of the deterministic DTCTP of realistic sizes are proposed. We have included several features to accelerate the convergence and solve large instances to optimality. Secondly, we incorporate uncertainty in activity costs. We formulate robust DTCTP using three alternative models. We develop exact and heuristic algorithms to solve the robust models in which uncertainty is modeled via interval costs. The main contribution is the incorporation of uncertainty into a practically relevant project scheduling problem and developing problem specific solution approaches. To the best of our knowledge, this research is the first application of robust optimization to DTCTP. Finally, we introduce some surrogate measures that aim at providing an accurate estimate of the schedule robustness. The pertinence of proposed measures is assessed through computational experiments. Using the insight revealed by the computational study, we propose a two-stage robust scheduling algorithm. Furthermore, we provide evidence that the proposed approach can be extended to solve a scheduling problem with tardiness penalties and earliness rewards.Hazır, ÖncüPh.D

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm

A review of network location theory and models

Cataloged from PDF version of article.In this study, we review the existing literature on network location problems. The study has a broad scope that includes problems featuring desirable and undesirable facilities, point facilities and extensive facilities, monopolistic and competitive markets, and single or multiple objectives. Deterministic and stochastic models as well as robust models are covered. Demand data aggregation is also discussed. More than 500 papers in this area are reviewed and critical issues, research directions, and problem extensions are emphasized.Erdoğan, Damla SelinM.S