Robust optimization

area: Optimization and metaheuristics · 8 papers in the last 7 days

← Most-used equations and models · All optimization and metaheuristics equations

\min_{x}\ \max_{u \in U} f(x, u)

Optimises against the worst case within an uncertainty set U; distributionally robust versions use sets of distributions.

LaTeX: \min_{x}\ \max_{u \in U} f(x, u)

Names searched for: robust optimization, robust optimisation, distributionally robust

Variables and notation#

x is the decision, u an uncertain parameter within set U and f(x,u) its objective; the inner maximum represents worst-case cost.

Worked example#

Suppose candidate A costs 2 or 8 across two allowed scenarios and B costs 5 or 6. Worst-case costs are 8 and 6, so the robust choice among these candidates is B.

Expected-cost optimization might prefer A if the cheap scenario is likely; robust optimization does not require those probabilities. Its conservatism depends strongly on the uncertainty set.

Sources and further reading#

The Price of Robustness

Examples use illustrative inputs, not observed research results. Logarithms are natural unless stated otherwise. Guide updated 2026-11-05. Prepared by Scholar4AI. Editorial and verification policy.

Key findings#

Robust optimization was mentioned in 49 papers in the last 30 days (2026-10-07 to 2026-11-05), ranking #23 of the 248 equations and models mentioned.
By journal category: Operations Research (30), AI (13), Economics (5) and Finance (1).
Most of them appeared in Expert Systems with Applications (3), Computers & Operations Research (3) and Operations Research Forum (3).
Often mentioned together with Linear and integer programming (16), Two-stage stochastic programming (7) and Genetic algorithm (5).
Datasets named in the same papers: Facebook (2), Hugging Face Hub (2) and MIMIC (2).
From Nov 2023 to Oct 2026, 2,046 archived papers mentioned Robust optimization in their title, abstract or keywords (the search of earlier months' full texts is still under way), most of them in Jul 2026 (85).
From 2017 to 2026 (so far), Robust optimization was mentioned in 3,169 papers in the tracked journals, most of them in operations research (2,168), AI (780) and economics (78).
671 of them were published in 2025, against 117 in 2017.
Since 2023, the institutions with the most of these papers were Hong Kong Polytechnic University (64), Centre National de la Recherche Scientifique (51) and Tsinghua University (46).
The journals publishing most of them were European Journal of Operational Research (171), Annals of Operations Research (132) and Computers & Industrial Engineering (123).
The most-cited of them is “Unifying Large Language Models and Knowledge Graphs: A Roadmap” (IEEE Transactions on Knowledge and Data Engineering, 2024), with 1,381 citations.

Mentions over 36 months#

Papers mentioning it by publication month, Nov 2023 to Oct 2026 (titles, abstracts and keywords; the full texts of earlier months are still being searched)
Trend	Nov 23–Oct 24	Nov 24–Oct 25	Nov 25–Oct 26	36 months
	588	691	767	2,046

Papers per year#

20172026 (so far)

Papers per publication year and category
Category	2017	2018	2019	2020	2021	2022	2023	2024	2025	2026 (so far)
Operations Research	97	120	119	101	163	184	186	368	388	442
AI	12	11	15	14	21	34	63	219	231	160
Economics	3	3	2	4	3	5	3	12	19	24
Finance	4	1	7	2	4	4	2	17	17	20
Information Systems	1	0	2	1	1	1	1	6	9	8
Management	0	0	0	0	0	0	0	5	7	11
Marketing	0	0	0	0	0	0	1	0	0	4
Statistics	0	1	0	0	0	0	1	1	0	2
Tourism and Hospitality	0	0	0	0	0	0	0	0	0	1
Higher Education and Research	0	0	0	0	0	0	0	0	0	1
All categories	117	136	145	122	192	228	257	628	671	673

Where the papers come from#

Journals with the most papers, since 2023
#	Journal	Papers
1	European Journal of Operational Research	171
2	Annals of Operations Research	132
3	Computers & Industrial Engineering	123
4	Transportation Research Part E Logistics and Transportation Review	121
5	Computers & Operations Research	107
6	Expert Systems with Applications	99
7	Artificial Intelligence Review	65
8	Transportation Research Part C Emerging Technologies	59
9	Omega	58
10	Mathematical Programming	55

Institutions with the most papers, since 2023
#	Institution	Papers
1	Hong Kong Polytechnic University	64
2	Centre National de la Recherche Scientifique	51
3	Tsinghua University	46
4	Beijing Jiaotong University	34
5	Beijing Institute of Technology	33
6	Shanghai University	33
7	Chinese Academy of Sciences	32
8	Nanyang Technological University	32
9	University of Chinese Academy of Sciences	32
10	National University of Singapore	31

Countries with the most papers, since 2023
#	Country	Papers
1	China	801
2	United States	342
3	United Kingdom	244
4	Germany	154
5	France	145
6	Hong Kong	138
7	Australia	128
8	Iran	127
9	Canada	124
10	Italy	116

Keywords with the most papers, since 2023
#	Keyword	Papers
1	robust optimization	498
2	distributionally robust optimization	320
3	demand uncertainty	182
4	multi-objective optimization	109
5	mixed-integer linear programming	94
6	column-and-constraint generation	87
7	large language models	73
8	Benders decomposition	71
9	two-stage robust optimization	69
10	facility location	64

Most-cited papers#

Most-cited papers since 2017
#	Citations	Per month	Title	Journal	Published	Authors
1	1,381	40.8	Unifying Large Language Models and Knowledge Graphs: A Roadmap	IEEE Transactions on Knowledge and Data Engineering	2024-01-10	Shirui Pan, Linhao Luo, Yufei Wang et al.
2	710	6.2	Supply chain network design under uncertainty: A comprehensive review and future research directions	European Journal of Operational Research	2017-04-08	Kannan Govindan, Mohammad Fattahi, Esmaeil Keyvanshokooh
3	628	5.4	Data-driven robust optimization	Mathematical Programming	2017-02-25	Dimitris Bertsimas, Vishal Gupta, Nathan Kallus
4	527	4.6	A framework for sensitivity analysis of decision trees	Central European Journal of Operations Research	2017-05-24	Bogumił Kamiński, Michał Jakubczyk, Przemysław Szufel
5	395	14.9	Large language models (LLMs): survey, technical frameworks, and future challenges	Artificial Intelligence Review	2024-08-18	Pranjal Kumar
6	326	3.1	Data-driven risk-averse stochastic optimization with Wasserstein metric	Operations Research Letters	2018-02-09	Chaoyue Zhao, Yongpei Guan
7	322	3.3	A survey of adjustable robust optimization	European Journal of Operational Research	2018-09-06	İhsan Yanıkoğlu, Bram L. Gorissen, Dick den Hertog
8	319	9.6	Advances and Challenges in Meta-Learning: A Technical Review	IEEE Transactions on Pattern Analysis and Machine Intelligence	2024-01-24	Anna Vettoruzzo, Mohamed-Rafik Bouguelia, Joaquin Vanschoren et al.
9	312	9.0	PromptCast: A New Prompt-Based Learning Paradigm for Time Series Forecasting	IEEE Transactions on Knowledge and Data Engineering	2023-12-13	Hao Xue, Flora Dilys Salim
10	264	3.0	The electric vehicle routing problem with energy consumption uncertainty	Transportation Research Part B Methodological	2019-06-25	Samuel Pelletier, Ola Jabali, Gilbert Laporte A

Archive counts by publication year: a paper counts when its title, abstract or keywords name the equation, or when OpenAlex's full-text search finds it there (searched for the last 30 days' papers and, by a pass over the past years, for older ones). Names added to the list later are looked for in older papers as the archive is read again.

Papers mentioning Robust optimization, newest first.
Date	Title	Journal	Authors	Affiliations
2026-11-04	Distributionally robust operational planning for mixed charging and decentralized swapping	Transportation Research Part E Logistics and Transportation Review	Jianzhi Leng, Lun Ran, Chi Xie et al.
2026-11-02	Square-root loss optimization for robust sparse precision matrix estimation: A Wasserstein distributionally robust perspective	Expert Systems with Applications	Ning Zhang, Jia-Nan Liu, Yi Zhang	East China University of Science and Technology; Dongguan University of Technology
2026-11-01	A distributionally robust optimization model for road–rail intermodal transportation of hazardous materials with product-code conversion under demand uncertainty	Transportation Research Part E Logistics and Transportation Review	Xunqing Wang, Jiaping Li, Mingliang Ma et al.	Shandong Institute of Business and Technology
2026-10-31	Robust mask-based appointment scheduling in primary care practices	Health Care Management Science	Sabrina Schmitz, Martin Comis, Christina Büsing	RWTH Aachen University
2026-10-31	Solving 0–1 integer programs with unknown knapsack constraints using membership oracles	Computational Optimization and Applications	Rosario Messana, Rui Chen, Andrea Lodi et al.	Cornell Tech; Chinese University of Hong Kong, Shenzhen; Technion – Israel Institute of Technology; …
2026-10-30	Chance constrained optimization of hub transport systems	Computers & Operations Research	Max Bourgeat, Öykü Naz Attila, Rémy Chevrier et al.	Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport; Polytechnique Montréal; Société Nationale des Chemins de Fer Français (France); …
2026-10-30	Factors influencing aircraft ground delays in passenger air transport: Evidence from China	Transportation Research Part A Policy and Practice	Yuwei Zhou, Lei Bian, Hanjun Wu	Beihang University; Massey University
2026-10-30	Optimal reserve prices under seller uncertainty	Economic Theory	Allan Hernandez-Chanto, Dong‐Hyuk Kim	The University of Queensland
2026-10-29	Extending PPCEF: probabilistically plausible counterfactual explanations for regression and heterogeneous tabular data	Data Mining and Knowledge Discovery	Oleksii Furman, Ł.ukasz Lenkiewicz, Jerzy Stefanowski et al.	Wrocław University of Science and Technology; Poznań University of Technology
2026-10-29	A chance-constrained robust model for the multi-mode resource-constrained project scheduling problem with uncertain activity durations	Computers & Industrial Engineering	Changchun Liu	Xi'an Jiaotong University
2026-10-29	Robust deterministic policies for Markov decision processes under budgeted uncertainty	Discrete Optimization	Fei Wu, Erik L. Demeulemeester, Jannik Matuschke	Tsinghua University; KU Leuven
2026-10-28	Validating Worst-Case System Performance Under Multi-State System Disruptions: Evidence from Supply Chain Networks	Operations Research Forum	Ashish Chandra	Illinois State University
2026-10-27	On Convexity and Optimization Approaches for Electric Vehicle Charging Scheduling Under Time-of-Use Pricing	Operations Research Forum	Heena Jain, Churlzu Lim	University of North Carolina at Charlotte
2026-10-24	A Stackelberg game analytics model for pricing and integration in a three-channel renewable microgrid supply chain	Supply Chain Analytics	Mohammad Amin Maftoon, Razieh Keshavarzfard, Narges Norouzi	Islamic Azad University, Tehran
2026-10-24	Optimal Portfolio Allocation with Gromov-Wasserstein Barycenter	Computational Economics	Alessandro Spelta, Nicoló Pecora, Mario Maggi	University of Pavia; Università Cattolica del Sacro Cuore
2026-10-23	The paradox of standardization: A game-theoretic analysis of EV charging station compatibility policy	Energy Policy	Mingqing Ma, Lei Chen, Chaocheng Gu	Nanjing University of Finance and Economics; Jinan University
2026-10-23	Truck appointment quota optimization for an inland logistics port: Balancing port operational efficiency and planning stability for trucking companies	Computers & Industrial Engineering	Yating Li, Yongman Zhao, Shi Qiang Liu et al.	Shihezi University; Xinjiang Production and Construction Corps; Ministry of Agriculture and Rural Affairs; …
2026-10-23	Robust queueing for single-server queues with abandonment	Queueing Systems	Wei You
2026-10-23	Retrieval-augmented generation in biomedicine: a survey of technologies, datasets, and clinical applications	Artificial Intelligence Review	Jiawei He, Boya Zhang, Hossein Rouhizadeh et al.	University of Geneva; Hunan City University; Henan University; …
2026-10-21	Pricing over a bundle network	Computers & Operations Research	Trivikram Dokka, Sonali Sen Gupta	Air Products (United Kingdom); Queen's University Belfast
2026-10-20	A Distributionally Robust Framework for Sustainable Freight Transportation	Operations Research Forum	Thiziri Sifaoui, Méziane Aı̈der	University of Tamanghasset; Mouloud Mammeri University of Tizi-Ouzou; University of Sciences and Technology Houari Boumediene; …
2026-10-20	Social distancing under strategic uncertainty: The role of strategic sophistication in the COVID-19 pandemic	Journal of Risk and Uncertainty	Mimi Jeon, Seonghoon Kim, Kanghyock Koh et al.	Korea Fair Trade Commission; Singapore Management University; Korea University; …
2026-10-20	A carbon-sensitive heterogeneous fleet framework for time-critical urban quick-commerce delivery with synchronised drone integration	Research in Transportation Business & Management	Gülseli İşler, Harun Reşit Yazg̈an, Muhammed Sever	Sakarya University
2026-10-20	Weighted UnLearning from Experience for Improved Spurious Correlation Robustness	Machine Learning	Jeff Mitchell, Jesus Martinez-del-Rincon, Niall McLaughlin	Queen's University Belfast
2026-10-19	A dual-perspective two-stage robust minimum cost consensus modeling for trust-based large-scale group decision making	Information Fusion	Yiran Wang, Yanjing Guo, Zhongming Wu et al.	Southeast University; Nanjing University of Information Science and Technology
2026-10-19	Solutions of two-stage stochastic minimax problems	Mathematical Programming	Hailin Sun, Xiaojun Chen	Nanjing Normal University; Hong Kong Polytechnic University
2026-10-18	Robust vertiport location planning under operational disruptions: A two-stage optimization framework integrating UAM-HSR demand shifts	Transport Policy	Gege Jiang, Wu Hui, Shengjie Ma et al.	Sun Yat-sen University; Central South University
2026-10-18	Design of hybrid multi-energy systems under uncertainty: An adjustable robust optimization approach	Computers & Operations Research	Patrizia Beraldi, Derya Dinler	University of Calabria; Hacettepe University
2026-10-17	Language modeling on tabular data: a survey of foundations, techniques and evolution	Artificial Intelligence Review	Yucheng Ruan, Xiang Lan, Jingying Ma et al.	National University of Singapore; Institute of Data Science
2026-10-16	Scenario-based robust optimization for the design of a resilient and sustainable power supply chain network using energy storage system	Operational Research	Elyas Nemati	University of Tehran
2026-10-16	ITEACH-Net: Inverted teacher-student search network for emotion recognition in conversation	Artificial Intelligence	Haiyang Sun, Zheng Lian, Chenglong Wang et al.	Chinese Academy of Sciences; Institute of Automation; University of Chinese Academy of Sciences; …
2026-10-15	Uncertainty-aware stock selection and portfolio optimization with deep learning-based return prediction	Annals of Operations Research	Mustafa Etcil, Burak Kolukısa, Burcu Bakır Güngör	Abdullah Gül University; Kayseri Üniversitesi
2026-10-14	Robust Data-Driven CARA Optimization	Mathematical Programming	Li Chen, Arjun Ramachandra, Napat Rujeerapaiboon	The University of Sydney; Indian Institute of Management Bangalore; National University of Singapore
2026-10-14	Demand-driven urban rail transit timetabling: Research perspectives	Transportation Research Part C Emerging Technologies	Tommaso Schettini, Ola Jabali, Gilbert Laporte et al.	Concordia University; HEC Montréal; Politecnico di Milano; …
2026-10-14	Modeling and simulating human behavior in large-scale emergency evacuations: A comprehensive review	Transportation Research Part B Methodological	Shiva Moslemi, Ada Arıkanoğlu, Vedat Bayram et al.	Koç University; University of Kent; TED University
2026-10-13	Hierarchical facility location-inventory-routing problem for maximal joint and gradual coverage	Operational Research	Büşra Sultan Bayat, Ertan Yakıcı, Levent Erişkin et al.	Milli Savunma Üniversitesi; Çankaya University; Piri Reis University; …
2026-10-13	Monte Carlo tree search for the multi-crane scheduling problem with temporal constraints	Flexible Services and Manufacturing Journal	Woo-Jin Shin, Seungkyu Yoon, Hyun-Jung Kim	Gyeongsang National University; Korea Advanced Institute of Science and Technology
2026-10-13	The Implementation Gap in Portfolio Optimisation	Financial Innovation	Mohamad Hassan
2026-10-13	Distributionally robust elective surgery scheduling for day-ahead capacity assessment of the post-anesthesia care unit	Omega	Jianfeng Ren, Haodong Wu, Jiguang Chen et al.	Qufu Normal University; Xiamen University
2026-10-12	Transit lines structures when users’ costs are dismissed: Lessons from stylized networks	Transportation Research Part A Policy and Practice	Sergio R. Jara-Diaz, Diego de Amesti, Antonio Gschwender	University of Chile
2026-10-12	Distributionally robust optimization with integer recourse: Convex reformulations and critical recourse decisions	Operations Research Letters	Yiling Zhang, Zhe Li, Eojin Han	University of Minnesota; University of Notre Dame
2026-10-12	CIPHER-Fed: An inference-resistant federated learning framework via structural gradient obfuscation	Information Sciences	Waheeb Algethami, Guowei Wu, Faisal Alshami	Dalian University of Technology
2026-10-10	Hyperspectral image restoration via spatial-spectral continuous priors and subspace convolution	Expert Systems with Applications	Yilun Lou, Yanping Luo, Jiangjun Peng et al.	Southern University of Science and Technology; Xi'an Jiaotong University; Northwestern Polytechnical University
2026-10-08	Personalized assignment of UAV rescue tasks: an integrated framework of content-based filtering and two-stage robust optimization	Expert Systems with Applications	Yin Xiang, Xinlong Zheng	Suzhou University of Science and Technology
2026-10-08	JTCSE: Joint tensor-modulus constraints and cross-attention for unsupervised contrastive learning of sentence embeddings	Neural Networks	Tianyu Zong, Bingkang Shi, Hongzhu Yi et al.	University of Chinese Academy of Sciences
2026-10-07	Stakeholder interactions in Mobility as a Service (MaaS): A unified bi-level optimization framework	Research in Transportation Business & Management	Rihab Amghar, Nadir Farhi, S. M. Hassan Mahdavi Moghaddam et al.	VeDeCoM Institute; Université Gustave Eiffel
2026-10-07	Mind the Gap: A survey of chronic wound datasets, methods, and clinical translation	Medical Image Analysis	Anum Fatima, Moi Hoon Yap, Neil D. Reeves et al.	Manchester Metropolitan University; Lancaster University
2026-10-07	Distributionally-robust heterogeneous graph neural networks via relation-aware grouping	Information Processing & Management	Yunfei Wang, Yanghui Fu, Shixuan Liu et al.	National University of Defense Technology; Renmin University of China
2026-10-07	A multi-stage optimization framework for battery electric bus deployment and renewable energy hubs with stochastic energy management and resilience analysis	Transportation Research Part C Emerging Technologies	Shouzheng Pan, Xiaohan Liu, Liu Xiaoyue Cathy et al.	University of Utah; Beihang University; University of California, Riverside

Cite this page

Scholar4AI. (2026). Robust optimization. Journal and Conference Research Rankings. Retrieved November 5, 2026, from https://scholar4ai.com/equations/robust-optimization

@misc{scholar4ai-equations-robust-optimization,
  author = {{Scholar4AI}},
  title = {Robust optimization},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/robust-optimization}},
  urldate = {2026-11-05},
  note = {Journal and Conference Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}

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