Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization

References

• Ben-Hur A, Horn D, Siegelmann H, Vapnik V (2001) Support vector clustering. J. Machine Learn. Res. 2:125–137.Google Scholar
• Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.Link, Google Scholar
• Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming, Ser. B 88(3):411–424.Crossref, Google Scholar
• Ben-Tal A, Nemirovski A (2008) Selected topics in robust convex optimization. Math. Programming 112(1):125–158.Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski AS (2009) Robust Optimization. Princeton Series in Applied Mathematics (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Program. 99(2):351–376.Crossref, Google Scholar
• Bertsimas D, Brown DB (2009) Constructing uncertainty sets for robust linear optimization. Oper. Res. 57(6):1483–1495.Link, Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Bertsimas D, Thiele A (2006) A robust optimization approach to inventory theory. Oper. Res. 54(1):150–168.Link, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Data-driven robust optimization. Math. Programming 167(2):235–292.Crossref, Google Scholar
• Campi MC, Garatti S (2008) The exact feasibility of randomized solutions of uncertain convex programs. SIAM J. Optim. 19(3):1211–1230.Crossref, Google Scholar
• Chassein A, Dokka T, Goerigk M (2019) Algorithms and uncertainty sets for data-driven robust shortest path problems. Eur. J. Oper. Res. 274(2):671–686.Crossref, Google Scholar
• Cheramin M, Chen RLY, Cheng J, Pinar A (2021) Data-driven robust optimization using scenario-induced uncertainty sets. Preprint, submitted July 11, https://arxiv.org/abs/2107.04977.Google Scholar
• Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: An overview. Eur. J. Oper. Res. 235(3):471–483.Crossref, Google Scholar
• Goerigk M, Kurtz J (2021) Data-driven robust optimization using unsupervised deep learning. Preprint, submitted November 19, https://arxiv.org/abs/2011.09769.Google Scholar
• Han B, Shang C, Huang D (2021) Multiple kernel learning-aided robust optimization: Learning algorithm, computational tractability, and usage in multi-stage decision-making. Eur. J. Oper. Res. 292(3):1004–1018.Crossref, Google Scholar
• Kaufman L, Rousseeuw PJ (1990) Partitioning around medoids (program PAM). Finding Groups in Data (John Wiley & Sons, Hoboken, NJ), 68–125.Crossref, Google Scholar
• Keogh E, Mueen A (2017) Curse of dimensionality. Sammut C, Webb GI, eds. Encyclopedia of Machine Learning and Data Mining (Springer, Boston), 314–315.Crossref, Google Scholar
• Loger B, Dolgui A, Lehuédé F, Massonnet G (2022) Improving the tractability of SVC-based robust optimization. IFAC-PapersOnLine 55(10):719–724.Crossref, Google Scholar
• Mohseni S, Pishvaee MS (2020) Data-driven robust optimization for wastewater sludge-to-biodiesel supply chain design. Comput. Indust. Engrg. 139:105944.Crossref, Google Scholar
• Ning C, You F (2018) Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods. Comput. Chemical Engrg. 112:190–210.Crossref, Google Scholar
• Ning C, You F (2019) Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming. Comput. Chemical Engrg. 125:434–448.Crossref, Google Scholar
• Qiu R, Sun Y, Shu P, Sun M (2019) Robust multi-product inventory optimization under support vector clustering-based data-driven demand uncertainty set. Soft Comput. 24:6259–6275.Crossref, Google Scholar
• Schubert E, Rousseeuw PJ (2019) Faster k-medoids clustering: Improving the PAM, CLARA, and CLARANS algorithms. Amato G, Gennaro C, Oria V, Radovanović M, eds. Similarity Search and Applications (Springer International Publishing, Cham, Switzerland), 171–187.Crossref, Google Scholar
• Shang C, You F (2019) A data-driven robust optimization approach to scenario-based stochastic model predictive control. J. Process Control 75(March):24–39.Crossref, Google Scholar
• Shang C, Huang X, You F (2017) Data-driven robust optimization based on kernel learning. Comput. Chemical Engrg. 106:464–479.Crossref, Google Scholar
• Shang C, Chen WH, Stroock AD, You F (2020) Robust model predictive control of irrigation systems with active uncertainty learning and data analytics. IEEE Trans. Control Systems Tech. 28(4):1493–1504.Crossref, Google Scholar
• Shen F, Zhao L, Du W, Zhong W, Qian F (2020) Large-scale industrial energy systems optimization under uncertainty: A data-driven robust optimization approach. Appl. Energy 259:114199.Crossref, Google Scholar
• Soyster AL (1973) Technical note-convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.Link, Google Scholar
• Sözüer S, Thiele AC (2016) The state of robust optimization. Doumpos M, Zopounidis C, Grigoroudis E, eds. Robustness Analysis in Decision Aiding, Optimization, and Analytics. International Series in Operations Research & Management Science (Springer International Publishing, Cham, Switzerland), 89–112.Crossref, Google Scholar
• Wu W, Liu R, Yang Q, Quek TQS (2021) Learning-based robust resource allocation for D2D underlaying cellular network. Preprint, submitted May 18, https://arxiv.org/abs/2105.08324.Google Scholar
• Zhang Y, Jin X, Feng Y, Rong G (2018) Data-driven robust optimization under correlated uncertainty: A case study of production scheduling in ethylene plant. Comput. Chemical Engrg. 109:48–67.Crossref, Google Scholar