Advances in robust and adaptive optimization : algorithms, software, and insights

Optimization in the presence of uncertainty is at the heart of operations research. There are many approaches to modeling the nature of this uncertainty, but this thesis focuses on developing new algorithms, software, and insights for an approach that has risen in popularity over the last 15 years: robust optimization (RO), and its extension to decision making across time, adaptive optimization (AO). In the first chapter, we perform a computational study of two approaches for solving RO problems: "reformulation" and "cutting planes". Our results provide useful evidence for what types of problems each method excels in. In the second chapter, we present and analyze a new algorithm for multistage AO problems with both integer and continuous recourse decisions. The algorithm operates by iteratively partitioning the problem's uncertainty set, using the approximate solution at each iteration. We show that it quickly produces high-quality solutions. In the third chapter, we propose an AO approach to a general version of the process flexibility design problem, whereby we must decide which factories produce which products. We demonstrate significant savings for the price of flexibility versus simple but popular designs in the literature. In the fourth chapter, we describe computationally practical methods for solving problems with "relative" RO objective functions. We use combinations of absolute and relative worst-case objective functions to find "Pareto-efficient" solutions that combine aspects of both. We demonstrate through three in-depth case studies that these solutions are intuitive and perform well in simulation. In the fifth chapter, we describe JuMPeR, a software package for modeling RO and AO problems that builds on the JuMP modeling language. It supports many features including automatic reformulation, cutting plane generation, linear decision rules, and general data-driven uncertainty sets.

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2016

Author dc:creator

• Dunning, Iain Robert

Advisor dc:contributor.advisor

• Dimitris Bertsimas.

• Operations Research Center.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/105004

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/105004