Robust portfolio optimization model for electronic coupon allocation

A robust optimization framework for energy management of CCHP users with integrated demand response in electricity market

The economic and low‐carbon operation strategy of multi‐energy microgrids (MEM) has become an important research topic in smart grids. The operation of MEM is affected by uncertain factors from renewable energy and internal load. To handle uncertainties from both source and load sides, the authors propose a novel worst‐case‐and‐probability uncertainty sets and a novel worst‐expectation min‐max‐max‐min two‐stage four‐level robust optimisation (RO) model considering stepped carbon trading for MEM. This four‐level RO model is a more generalised model compared with the traditional two‐stage RO and distributionally robust optimisation based models. First, the unsolvable original four‐level model is decoupled into a master problem and a sub‐problem (SP). Second, Karush–Kuhn–Tucker condition is applied to convert SP into a solvable problem. Third, column and constraint generation (C&CG) algorithm is employed to solve the reformulated four‐level RO. Finally, the effectiveness of the proposed model and solution method is verified by case studies. The results indicate that the convergence behaviour of this solution method is excellent. The MEM operator can select appropriate robustness factors and comprehensive norms to control its conservatism level. Besides, MEM could reduce carbon emissions by participating in carbon trading and installing carbon capture devices.

A robust optimization model for green supplier selection and order allocation in a closed-loop supply chain considering cap-and-trade mechanism

As the proportion of new energy continues to increase, the safety and stability of the new power system are challenged, urgently requiring the allocation of new flexible resources. This paper proposes a two-stage robust capacity optimization model considering flexibility demand constraints. Firstly, the uncertain characteristics of new energy are described, and a model of flexible resource adjustment capacity is established. Then, uncertain parameters are introduced to construct a robust capacity optimization model considering supply-demand balance, solved by column constraint generation algorithm and KKT theorem. Finally, a power system in a certain region of China is selected as the simulation object for empirical analysis to verify the effectiveness of the constructed model. The results show that the two-stage robust configuration optimization model constructed in this paper can address the uncertainty of power system and the flexibility demand brought by new energy, and the planning results can achieve a balance between the safety and economy of the new power system.

Chapter 4 - Data-driven robust stochastic optimization for power systems operations

Tremendous number of renewable energy sources (RES) and distributed generators integrated into distribution system, power generation uncertainty and massive decision variables bring about significant challenges to distribution system operator (DSO). Benefiting from advanced information technologies, distribution system evolves into cyber-physical distribution system (CPDS), and effective countermeasures can be made under distributed control framework to achieve optimality and resiliency of CPDS. For this purpose, fully distributed robust control strategy is specifically explored in this paper. Firstly, a two-stage robust optimization (RO) model is developed for each sub-area in CPDS, which takes uncertainty of wind power into consideration. After that, based on Consensus-ADMM algorithm, a fully distributed solution strategy of combined Consensus-ADMM and RO model is proposed. Results of study case verify that by adopting our method, accurate robust solution under different uncertainty budge can be obtained adaptively under diverse cyber or physical topologies, which guarantees optimality and resiliency of CPDS.

Active power dispatch and reactive power optimization problems are usually handled separately in active distribution systems, aiming at minimizing the total generation cost or transmission losses. However, the separate optimization cannot achieve a global optimum scheme in distribution system operations. Moreover, the significant relationship between the active power and reactive power may pose great challenges to distribution system operations due to the uncertain nature of load demands and intermittent renewable energy resources. In this paper, using the branch flow model-based relaxed optimal power flow, we formulate a robust coordinated optimization problem for active and reactive powers as a mixed integer second-order cone (SOC) programming problem. Furthermore, in order to address the uncertainties, a two-stage robust optimization model is proposed to coordinate the on load tap changer ratios, reactive power compensators, and charge–discharge power of energy storage system to find a robust optimal solution. Then the column-and-constraint generation algorithm is applied to solve the proposed robust two-stage optimization model. In the relaxed optimal power flow, a stricter cut is added to speed up the computation process of the SOC relaxation in order to guarantee the exactness for representative cases, such as those with high penetration of distributed energy resources. Numerical results based on the 33-bus and 69-bus systems verify the effectiveness of the proposed method.

Optimal Robust Insurance with a Finite Uncertainty Set

Nonoperating room anesthesia (NORA) refers to the practice and administration of anesthesia or sedation outside the operating room (OR), which has been increasingly implemented in practice. The novelty of NORA is to separate the anesthesia preoperative stage from an OR for the sake of saving OR time and improving its efficiency. In this article, we study the scheduling problem for NORA considering both anesthetic rooms (ARs) and operating rooms (ORs) based on ambiguous information about surgical durations. Our goal is to devise a robust and efficient scheduling mechanism for NORA. To address this problem, we develop a two‐stage mixed‐integer Robust Optimization (RO) model that minimizes the total costs, including the sum of operating costs of opened ORs and ARs, delay cost of surgeries, and overtime cost of ORs. Decisions include the number of ARs and ORs to open, the allocation of patients to ARs and ORs, the sequence of surgeries, and the planned starting time for each surgery. Accordingly, a heuristic algorithm, so‐called column‐and‐constraint generation (C&CG), is developed that renders a desirable performance. Some salient properties of the problem are also discussed. In addition, by leveraging practical data in conjunction with data reported in the extant research, the computational efficacy of the proposed algorithm is verified under various sets of parameters. Our numerical experiments reveal that (1) the implementation of NORA can reduce the OR overtime cost and the waiting time of patients; (2) our proposed Robust Optimization (RO) model possesses stronger robustness and computational efficiency than the distributionally robust model (DRO); and (3) while considering surgical duration uncertainty, the developed scheduling approach outperforms the corresponding deterministic setting in terms of decreasing the total cost and alleviating the surgery delay. Generally, the proposed approach is more adaptive to take the advantage of the surgical duration uncertainty to enhance its efficacy.

In order to overcome the drawback of the conventional signal timing optimization, a robust optimization algorithm for signal control parameters based on Tabu search-artificial bee colony algorithm is proposed under unsaturated flow condition. Based on the analysis of the characteristics of traffic signal control, a robust optimization model of signal control parameters is constructed by considering the minimum the average delay and the mean square error of average delay. As a consequence, the formation process of the initial solution to the bee colony is improved and the robust optimization model is solved by using the Tabu search-artificial bee colony algorithm. The proposed robust optimization model is validated by using an intersection in Zhangye City of China. The simulation results have shown that the robust optimization model and the algorithm are feasible and practicable. This robust model and algorithm can effectively deal with the volatility of traffic flow and reduce traffic delays.

PurposeThis study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.Design/methodology/approachA robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.FindingsCompared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.Originality/valueThis study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

Due to its unique uncertainty and volatility, wind power is increasingly penetrating various levels of power grids, and its impact on the stability of power grid operations is gradually increasing. In order to cope with the uncertainty of wind power output and to improve the stability of system operation, a robust optimization and scheduling model for the integrated electricity-gas-heat system (IEGHS), and heat considering the DC power flow security domain is proposed. Firstly, based on the traditional DC power flow security domain model, a DC power flow security domain model based on wind power uncertainty is established and the operating safety boundary of nodes is established. Secondly, considering the security domain and wind power uncertainty, a robust budget parameter is introduced, and a controllable robust optimization and scheduling model for IEGHS is proposed. Finally, the effectiveness and practicality of the proposed model are demonstrated through numerical simulation. In summary, the proposed model takes into account the uncertainty of wind power and the safety domain of the DC power flow, and introduces robust budget parameters to achieve a controllable robust optimization and scheduling for IEGHS. The simulation results demonstrate the effectiveness and practicality of the proposed model.

Purpose: To test the feasibility of a robust direct aperture optimization (DAO) model for cardiac sparing IMRT planning of left‐sided breast cancer patients. Methods: We extended a previously developed robust optimization method to obtain a DAO approach for tangential breast IMRT that is robust against uncertainty in the patient's breathing pattern. The robust DAO model contains additional constraints on the segment shapes and weights in order to reduce the complexity of delivery and ensure that high weight segments cover the whole breast volume. A 4DCT dataset was used to test the model, and 100 simulated breathing patterns were generated. Results were compared with the previously developed robust fluence map optimization (FMO) model as well as the clinical treatment methods for breast cancer (inhale breath‐hold with active breathing control (ABC) and free breathing). Results: On average, the robust DAO approach reduced the mean heart dose by 15.1% compared to the conventional IMRT method for breast cancer (with free breathing) using an equal number of segments. The maximum dose to 10cc of the heart was reduced by 19.7%. Compared to the previous robust FMO method, the robust DAO method delivered less than 1% higher dose to the heart and 1% lower dose to the CTV on average. The dose‐volume criteria for the heart and CTV were met in all of the breathing scenarios. The robust DAO approach resulted in a 20.8% reduction in the number of cases that would have required ABC treatment in comparison with the clinical method with free breathing. Conclusions: The proposed DAO approach results in lower heart dose compared to the conventional method with free breathing and shows low sensitivity to breathing pattern uncertainty. The robust DAO method is able to derive simpler IMRT segments during free breathing and can potentially reduce the need for breath‐hold techniques. This research was supported in part by the Ontario Ministry of Economic Development and Innovation, the Canadian Breast Cancer Foundation ‐ Ontario Region, and the Ontario Consortium for Adaptive Interventions in Radiation Oncology (OCAIRO) funded by the Ontario Research Fund (ORF).

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Quay cranes are among the most important resources in port terminals, and their efficient use is crucial for port terminals to remain competitive in the market. The problem of determining the sequence of tasks performed by the quay cranes that minimizes the turnaround time of a vessel is an NP‐hard problem known as the quay crane scheduling problem (QCSP).In this paper, we consider the unidirectional QCSP under uncertain processing times, where the cranes are only allowed to move in a specific direction. We start by presenting the first distributionally robust optimization (DRO) model for this problem and an exact decomposition algorithm to solve it. The proposed DRO model makes it possible to derive a stochastic programming model and a robust optimization model for the unidirectional QCSP by an appropriate choice of the risk‐averse parameter of the model. Through extensive numerical results, we compare these three approaches—stochastic programming, robust optimization, and DRO—to investigate whether significant differences among the solutions obtained exist. Finally, we propose a new method for helping practitioners to determine a representative set of different DRO solutions.