Article
Mathematics, Applied
Gang Ma, Junjun Zheng, Ju Wei, Shilei Wang, Yefan Han
Summary: A study was conducted on the impact of different selling strategies for selling different goods in sequential auctions on price uncertainty and revenue uncertainty, and a robust optimization method was proposed to overcome price uncertainty, extending the traditional maximum revenue model into four robust models of different forms. Numerical examples showed that revenue decreases with higher levels of uncertainty, and not all cases result in revenue increasing with total auction sequence increase.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Management
Vanessa Krebs, Michael Mueller, Martin Schmidt
Summary: The study focuses on uncertain linear complementarity problems (LCPs) with uncertain parameters in the LCP vector q or the LCP matrix M. By applying Gamma-robust optimization to the gap function formulation of the LCP, conditions for tractability of robust counterparts are derived. Existence and uniqueness conditions for these counterparts' solutions are also provided. A case study on an uncertain traffic equilibrium problem illustrates the impact of Gamma values on the feasibility and quality of the robustified solutions.
INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
(2022)
Article
Automation & Control Systems
Monimoy Bujarbaruah, Ugo Rosolia, Yvonne R. Sturz, Xiaojing Zhang, Francesco Borrelli
Summary: We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The approach models the uncertain system as linear parameter varying with an additive disturbance and formulates a constraint tightening strategy based on these bounds. With appropriately designed terminal cost function and constraint set, the resulting MPC satisfies the imposed constraints in closed-loop with the uncertain system and exhibits Input to State Stability of the origin.
Article
Green & Sustainable Science & Technology
Junjie Zhong, Yong Li, Yijia Cao, Yi Tan, Yanjian Peng, Yicheng Zhou, Yosuke Nakanishi, Zhengmao Li
Summary: This paper proposes a distributed scheduling method for the coordination between multi-energy microgrid and distribution network under operational uncertainties. The method combines column and constraint generation algorithm, multi-interval convex hull uncertainty set, and Bregman alternating direction method with multipliers to improve convergence. Simulation tests on IEEE-33 node distribution network and a park-level microgrid demonstrate the effectiveness of the proposed model and method.
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY
(2023)
Article
Engineering, Electrical & Electronic
Shixiong Wang, Zhongming Wu, Andrew Lim
Summary: This paper introduces a new framework for distributionally robust state estimation in linear Markov systems, which efficiently deals with uncertainties in real linear systems and demonstrates advantages over existing methods through intensive experiments.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Mohsen Roytvand Ghiasvand, Donya Rahmani
Summary: This paper proposes a new weighted data-driven robust optimization approach for creating adjustable uncertainty sets, and introduces a multi-stage clustering algorithm and a regularization parameter search algorithm to enhance the model. The numerical results show that adjustable uncertainty sets with the same data coverage can be created by weighting historical data, ensuring the feasibility of the model and reducing extra conservatism.
COMPUTERS & CHEMICAL ENGINEERING
(2023)
Article
Computer Science, Artificial Intelligence
Hashem Omrani, Meisam Shamsi, Ali Emrouznejad, Tamara Teplova
Summary: Conventional Data Envelopment Analysis (DEA) lacks the ability to evaluate Decision-Making Units (DMUs) in vast industries like banks with only one type of efficiency and uncertain data. In this paper, a multi-objective DEA model is proposed to calculate three types of efficiencies for bank branches under uncertain data. The model employs a modified DEA model, a robust approach to handle uncertainty, and a fuzzy programming method to convert the multi-objective model into a single-objective one. The results from a real case study of 45 Agriculture bank branches in Iran validate the accuracy of the proposed model and enable a comparative analysis to identify benchmark and inefficient branches.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Frauke Liers, Lars Schewe, Johannes Thurauf
Summary: This paper studies the radius of robust feasibility (RRF) for mixed-integer linear problems (MIP) and extends its application to various optimization problems and uncertainty sets. The authors provide methods for computing the RRF of MIPs and present a theoretical contribution by generalizing RRF to include safe variables and constraints.
INFORMS JOURNAL ON COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Jose Ramirez-Calderon, V. Jorge Leon, Barry Lawrence
Summary: This article investigates binary linear programming problems in the presence of uncertainties that may hinder the implementation of the computed solution. The study introduces the concept of implementation uncertainty, which affects the decision variables rather than the model parameters. The article proposes a reformulation of the problem as a binary linear program and employs constraint relaxation and cardinality-constrained parameters to control the conservatism of the solutions. A selection approach is used to identify robust solutions with desirable implementation characteristics.
ENGINEERING OPTIMIZATION
(2022)
Article
Operations Research & Management Science
Jia Liu, Abdel Lisser, Zhiping Chen
Summary: This paper discusses distributionally robust geometric programs with individual or joint chance constraints, considering several groups of uncertainty sets. Deterministic reformulations of the programs are found under each group of uncertainty sets. Convexity, solution methods, and relationships of the reformulation programs are discussed. Numerical tests are carried out on a shape optimization problem.
MATHEMATICS OF OPERATIONS RESEARCH
(2022)
Article
Management
Beste Basciftci, Shabbir Ahmed, Siqian Shen
Summary: This paper discusses a distributionally robust facility location problem, highlighting the significant impact of facility location decisions on customer demand. The proposed decision-dependent distributionally robust optimization model demonstrates superior performance in profit and service quality across different scenarios.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)
Article
Automation & Control Systems
Zhuolin Wang, Keyou You, Shiji Song, Yuli Zhan
Summary: This article introduces a second-order conic programming approach to solve distributionally robust two-stage linear programs over 1-Wasserstein balls, addressing distribution uncertainty in both the objective function and constraints. By formulating the problems as tractable SOCP problems and developing a constraint generation algorithm, it provides a solution to NP-hard problems. Additionally, it introduces the concept of the least favorable distribution and demonstrates the model's advantages in terms of out-of-sample performance and computational complexity through experiments.
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
(2022)
Article
Computer Science, Artificial Intelligence
Jie Han, Chunhua Yang, Cheng-Chew Lim, Xiaojun Zhou, Peng Shi
Summary: This article proposes a new robust optimization method that simultaneously considers parametric uncertainties and fuzzy variables to optimize the expectation and variability of system performance. It introduces the expectation-entropy model to transform the fuzzy robust optimization problem into an equivalent biobjective optimization problem. An approximate mapping method is developed to calculate the response of fuzzy variables, improving the computational efficiency of the objective functions. The optimization framework based on the Stackelberg game is established according to the decision makers' preference for objectives, and a leader-follower state transition algorithm is designed to search for equilibrium solutions. Two practical case studies demonstrate the effectiveness of this new optimization approach in both subjective judgment and objective assessment.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Ming Yang, Hongguang Ma, Xiang Li, Changjing Shang, Qiang Shen
Summary: This article studies the bus bridging problem in public transportation systems, where passenger demand is represented as parametric interval-valued fuzzy variables and their associated uncertainty distribution sets. A distributionally robust fuzzy optimization model is proposed to minimize the maximum travel time and find the optimal scheme for vehicle allocation, route selection, and frequency determination. The proposed approach is verified using real-world uncertain parameters and validated to provide a better uncertainty-immunized solution.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Computer Science, Interdisciplinary Applications
Wangshu Mu, Daoqin Tong
Summary: This paper proposes a new model and solution approach for the Continuous Robust Map Classification Problem (CRMCP), allowing mapmakers to customize robustness metrics and using a particle swarm optimization algorithm to solve the problem. Test results suggest that the new approach can find better solutions than the existing algorithm.
COMPUTERS ENVIRONMENT AND URBAN SYSTEMS
(2022)