Generating hard instances for robust combinatorial optimization |
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| Affiliation: | 1. Network and Data Science Management, University of Siegen, Unteres Schloß 3, 57072 Siegen, Germany;2. Department of Management Science, Lancaster University, Lancaster LA1 4YX, United Kingdom;1. Carey Business School, Johns Hopkins University, 100 International Drive, Baltimore, MD 21202, United States;2. Department of Information Systems and Business Analytics, Florida International University, Miami, FL 33199, United States;1. Leiden University Mathematical Institute, Niels Bohrweg 1, 2333 CA, Leiden, NL, UK;2. Department of Management Science, Center for Transportation and Logistics, Lancaster University Management School, Bailrigg, Lancaster LA1 4YX, UK;1. School of Business, Stevens Institute of Technology, 1 Castle Point Terrace, Hoboken, NJ 07030, USA;2. Lally School of Management, Rensselaer Polytechnic Institute, 110 8th Street, Pittsburgh Building, Troy, NY 12180, USA;3. Division of Economic and Risk Analysis, US Securities and Exchange Commission, 100 F St NE, Washington DC 20549, USA;4. Department of Electrical, Computer & Systems Engineering, Rensselaer Polytechnic Institute, Jonsson Engineering Center 6048, Troy, NY 12180, USA;1. Department of Finance, National Central University, Taiwan;2. Department of Finance, National Taiwan University, Taiwan;3. Department of International Business, National Taiwan University, Taiwan;4. Chinese Academy of Mathematics and Systems Science, China;1. College of Auditing and Evaluation, Nanjing Audit University, Nanjing, Jiangsu Province, 211815, China;2. Schulich School of Business, York University, Toronto, Ontario M3J 1P3, Canada;3. Foisie Business School, Worcester Polytechnic Institute, Worcester, MA 01609, USA |
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| Abstract: | While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm performance better comparable, and makes reproducing instances unnecessary. Such a benchmark set should contain hard instances in particular, but so far, the standard approach to produce instances has been to sample values randomly from a uniform distribution.In this paper we introduce a new method to produce hard instances for min-max combinatorial optimization problems, which is based on an optimization model itself. Our approach does not make any assumptions on the problem structure and can thus be applied to any combinatorial problem. Using the Selection and Traveling Salesman problems as examples, we show that it is possible to produce instances which are up to 500 times harder to solve for a mixed-integer programming solver than the current state-of-the-art instances. |
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