Robust optimization of EMU brake module based on interval analysis

Under intense industry competition, decision makers must ensure that products demanded by consumers can be quickly produced with minimum production cost. However, because uncertainties are unavoidable and inevitably affect decision makers, numerous studies have discussed how to control uncertainties or minimize their effects. Multiple uncertainties that interact simultaneously may cause a combined effect in actual systems. Therefore, this study presents a robust optimization model with two uncertainties, extending the method of robust optimization with one uncertainty. To demonstrate the applicability of the proposed model with two uncertainties, this study uses the supplier selection problem with component purchase quantity allocation in supply chain management as an analysis case. This considers the reliability of production and transportation and develops a multi-objective robust optimization model with two uncertainties. In addition, a nondominated sorting genetic algorithm is proposed for solving the proposed multi-objective robust optimization model. The relationship between price of robustness and budget parameters is explored by considering the robust optimization model with production and transportation uncertainties proposed in this study. Finally, there is a comparative analysis between the results for price of robustness in the proposed two-uncertainty model and in the one-uncertainty model.

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

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.

The hazardous hospital waste (HHW) is one of the main problems in urban waste management, which requires the design and implementation of a special collection and disposal system. Hospital wastes were known as important hazardous waste to be efficiently disposed within a short operational time in order to prevent the spread of infections and diseases. In this research, a multi-objective robust optimization model was developed to design a collection and disposal network of HHW under uncertain condition. The objectives are to concurrently minimize the total cost including transportation and operations costs, and the total risk of transportation and operations. To solve the proposed bi-objective model, the augmented e-constraint method was employed. Moreover, the model validation is achieved using and solving several test problems in different sizes, and the analysis of the robust model was performed compared to the deterministic model. Finally, a real case study was conducted to demonstrate the applicability of the research’s methodology, which was done by determining Pareto front and performing a sensitivity analysis to evolve the managerial insights.

Designing a production process normally is involved with some important constraints such as uncertainty, trade-off between production costs and quality, customer’s expectations and production tolerances. In this paper, a novel multi-objective robust optimization model is introduced to investigate the best levels of design variables. The primary objective is to minimize the production cost while increasing robustness and performance. The response surface methodology is utilized as a common approximation model to fit the relationship between responses and design variables in the worst-case scenario of uncertainties. The target mean ratio α is applied to ensure the quality of the process by providing the robustness for all types of quality characteristics and with a trade-off between variability and deviance from the ideal point. The Lp metric method is used to integrate all objectives in one overall function. In order to estimate target value of the quality loss by considering production tolerances, the process capability ratio (Cpm) is applied. At the end, a numerical chemical mixture problem is served to show the applicability of the proposed method.

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

Multi-objective distributionally robust approach for optimal location of renewable energy sources

Robust multi-objective optimization for islanded data center microgrid operations

A multi-objective robust grey wolf optimization model for the study of concrete mix using copper slag and glass powder

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

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.

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.

Optimal Robust Insurance with a Finite Uncertainty Set

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.

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