Optimal Robust Insurance with a Finite Uncertainty Set

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

Reservoir development optimization under uncertainty for infill well placement in brownfield redevelopment

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.

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.

Robust multi-objective optimization for islanded data center microgrid 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.

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.

Recent advances in robust optimization: An overview

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.

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

A proposed practical fuel budget problem aims to determine a group of bunker fuel budget values for a liner container ship over a round-trip voyage under uncertainties caused by severe weather conditions. According to research collaboration with a global container shipping line in Singapore, the proposed problem holds a kernel position in the ship fuel efficiency management programs advocated by container shipping lines because of the downward pressure of soaring bunker prices. The synergetic influence of sailing speed and weather conditions on ship fuel consumption rate was considered when the bunker fuel budget of a ship over a round-trip voyage was estimated. To address the adverse random perturbation of fuel consumption rate under severe weather conditions, state-of-the-art robust optimization techniques were employed, and a robust optimization model for the fuel budget problem was developed. The developed model can be dualized into a mixed-integer linear programming model that may be solved by commercial optimization solvers. However, algorithmic findings in the field of robust optimization provided a polynomial time solution algorithm, and it was retrofitted to accommodate the proposed ship fuel budget problem. The case study of an Asia–Europe service demonstrates the computational performance of the proposed solution algorithm and the competence of the proposed robust optimization model to produce fuel budget values at different levels of conservatism possessed by the fuel efficiency specialists in container shipping lines.

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this paper, we propose a new type of distributionally robust optimization model called the likelihood robust optimization (LRO) model for this class of problems. In contrast to previous work on distributionally robust optimization that focuses on certain parameters (e.g., mean, variance, etc.) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of optimizing the expected value of the objective function under the worst-case distribution in that set. Our model avoids the over-conservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present statistical analyses of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance.

A robust optimization approach to the integrated berth allocation and quay crane assignment problem

This study presents a parameter coordination and robust optimization approach based on knowledge network modeling. The method allows multidisciplinary designer to synthetically coordinate and optimize parameter considering multidisciplinary knowledge. First, a knowledge network model is established, including design knowledge from assembly, manufacture, performance, and simulation. Second, the parameter coordination method is presented to solve the knowledge network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given knowledge. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. A design instance is introduced to show the validity of this method.