Adaptive Robust Optimization Research Articles

Nowadays, the use of demand response programs (DRPs) in a variety of long-term and short-term planning problems has been explored. In this paper, a generation and transmission expansion planning (GTEP) model along with FACTS device allocation is presented. Furthermore, demand response programs are taken into account for more load flexibility. The proposed model is presented as a multi-objective minimizing problem considering emission, cost, and voltage security index. Furthermore, the conventional Pareto optimization is adopted using fuzzy weighted sum method (FWSM) to achieve a single-objective model. The final problem is constrained by equations of alternative current power flow, operation and voltage security limits, planning model of shunt FACTS devices, and operation of the DRP. Adaptive robust optimization (ARO) is used to reach suitable models for the active power of renewable resources and power consumption. As a main search algorithm, a hybrid combination of water cycle algorithm (WCA) and ant lion optimization (ALO) is proposed to find the optimum solution with a small standard deviation. The problem is tested on different standard IEEE systems, and the results validate the operation and network security improvement due to optimal location of FACTS devices. According to the results, the economic and environmental status of the network has also improved.

Multistage adaptive robust optimization for the hydrothermal scheduling problem

Adaptive robust optimization for European strategic gas infrastructure planning

An adaptive robust optimization model for parallel machine scheduling

Block-Coordinate-Descent Adaptive Robust Operation of Industrial Multi-layout Energy hubs under Uncertainty

This paper presents a novel methodological approach for the optimal day-ahead energy market bidding behavior of a cascaded hydropower plants (HPPs) portfolio in the sequential electricity markets. The understudy markets are day-ahead energy market and manual frequency restoration reserve (mFRR) markets in both capacity and energy setups. The introduction of the mFRR capacity market ensures transmission system operators (TSOs) about the availability of energy bids in the real-time market, which acts as binding constraints in the mFRR energy markets. As a determining factor, the active-time duration of mFRR energy bids is uncertain at the time of day-ahead bidding, which is modeled as the intervals in our robust optimization, while the electricity prices are considered as the scenarios in the stochastic optimization. Hence, we have proposed a novel stochastic adaptive robust optimization to address the bidding problem in the face of uncertainties accurately. The results show a considerable improvement compared to the conventional fully-stochastic approach in the case study of Swedish cascaded hydropower plants.

This work focuses on a broad class of facility location problems in the context of adaptive robust stochastic optimization under the state-dependent demand uncertainty. The demand is assumed to be significantly affected by related state information, such as the seasonal or socio-economic information. In particular, a state-wise ambiguity set is adopted for modeling the distributional uncertainty associated with the demand in different states. The conditional distributional characteristics in each state are described by a support, as well as by mean and dispersion measures, which are assumed to be conic representable. A robust sensitivity analysis is performed, in which, on the one hand, we analyze the impact of the change in ambiguity-set parameters (e.g., state probabilities, mean value abounds, and dispersion bounds in different states) onto the optimal worst-case expected total cost using the ambiguity dual variables. On the other hand, we analyze the impact of the change in location design onto the worst-case expected second-stage cost and show that the sensitivity bounds are fully described as the worst-case expected shadow-capacity cost. As for the solution approach, we propose a nested Benders decomposition algorithm for solving the model exactly, which leverages the subgradients of the worst-case expected second-stage cost at the location decisions formed insightfully by the associated worst-case distributions. The nested Benders decomposition approach ensures a finite-step convergence, which can also be regarded as an extension of the classic L-shaped algorithm for two-stage stochastic programming to our state-wise, robust stochastic facility location problem with conic representable ambiguity. Finally, the results of a series of numerical experiments are presented that justify the value of the state-wise distributional information incorporated in our robust stochastic facility location model, the robustness of the model, and the performance of the exact solution approach.

Optimal scheduling of a hybrid AC/DC multi-energy microgrid considering uncertainties and Stackelberg game-based integrated demand response

The rapid growth of microgrids with various distributed energy resources (DERs) brings new opportunities for local energy sharing in the microgrids. However, the uncertainties of renewable distributed generation and loads pose a great technical challenge for a microgrid operator (MGO). Thus, this paper proposes a transactive energy sharing (TES) approach for the MGO and DER aggregators to minimize the total social cost, considering network operating constraints. Accordingly, a two-settlement transactive energy (TE) market with an incentive energy pricing scheme is developed to encourage the participation in the energy sharing. Besides, the real-time energy transactions of the aggregators are considered in a day-ahead optimization stage to address their negative impacts on microgrid operation. To solve the proposed TES problem, an alternating direction method of multipliers (ADMM) is applied. The uncertainties in each ADMM local problem are further addressed by an adaptive robust optimization (ARO) method solved by a column-and-constraint generation (C&CG) algorithm. The updated dual and coupling variables at each ADMM iteration could interact with the C&CG algorithm, impairing ADMM convergence. To solve this issue, an alternating uncertainty-update procedure is developed. The simulation results verify the high efficiency and solution robustness of the proposed TES method.

Reliable planning of electricity networks is a crucial challenge to maintain the continuous power supply. This can be ensured through careful planning which requires a number of parameters as inputs such as electricity demand, generation capacity, fuel price, renewable intermittent generation, among others. The uncertain behaviors of such parameters have been well studied in literature. Another important parameter which is a vital requirement for reliable planning is the resistance of overhead transmission lines. Traditionally, the current models ignore to consider the resistance variations due to Joule heating and ambient temperature changes in transmission expansion planning (TEP) problem. In this sense, this paper presents an adaptive robust optimization (ARO) framework for TEP to model the uncertain resistance through ellipsoidal uncertainty set. Moreover, a data-driven selection of the ellipsoidal uncertainty set is proposed. In this regard, Khachiyans algorithm (KA) is used to identify the minimum-volume covering ellipsoid (MVCE) that contains all uncertain parameters. A case study based on IEEE 118-bus power system is presented to demonstrate the effectiveness of the proposed method. Simulation results show that resistance uncertainty is of serious concern in the TEP problem since the solutions are highly sensitive to fluctuations in the line resistances.

The benefits of networked microgrids in terms of economics and resilience are investigated and validated in this work. Considering the stochastic unintentional islanding conditions and conventional forecast errors of both renewable generation and loads, a two-stage adaptive robust optimization is proposed to minimize the total operating cost of networked microgrids in the worst scenario of the modeled uncertainties. By coordinating the dispatch of distributed energy resources (DERs) and responsive demand among networked microgrids, the total operating cost is minimized, which includes the start-up and shut-down cost of distributed generators (DGs), the operation and maintenance (O&M) cost of DGs, the cost of buying/selling power from/to the utility grid, the degradation cost of energy storage systems (ESSs), and the cost associated with load shedding. The proposed optimization is solved with the column and constraint generation (C&CG) algorithm. The results of case studies demonstrate the advantages of networked microgrids over independent microgrids in terms of reducing total operating cost and improving the resilience of power supply.

In this paper, we consider a variant of adaptive robust combinatorial optimization problems where the decision maker can prepare K solutions and choose the best among them upon knowledge of the true data realizations. We suppose that the uncertainty may affect the objective and the constraints through functions that are not necessarily linear. We propose a new exact algorithm for solving these problems when the feasible set of the nominal optimization problem does not contain too many good solutions. Our algorithm enumerates these good solutions, generates dynamically a set of scenarios from the uncertainty set, and assigns the solutions to the generated scenarios using a vertex p-center formulation, solved by a binary search algorithm. Our numerical results on adaptive shortest path and knapsack with conflicts problems show that our algorithm compares favorably with the methods proposed in the literature. We additionally propose a heuristic extension of our method to handle problems where it is prohibitive to enumerate all good solutions. This heuristic is shown to provide good solutions within a reasonable solution time limit on the adaptive knapsack with conflicts problem. Finally, we illustrate how our approach handles nonlinear functions on an all-or-nothing subset problem taken from the literature. Summary of Contribution: Our paper describes a new exact algorithm for solving adaptive robust combinatorial optimization problems when the feasible set of the nominal optimization problems does not contain too many good solutions. Its development relies on a progressive relaxation of the problem augmented with a row-and-column generation technique. Its efficient execution requires a reformulation of this progressive relaxation, coupled with dominance rules and a binary search algorithm. The proposed algorithm is amenable to exploiting the special structures of the problems considered as illustrated with various applications throughout the paper. A practical view is provided by the proposition of a heuristic variant. Our computational experiments show that our proposed exact solution method outperforms the existing methodologies and therefore pushes the computational envelope for the class of problems considered.

Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel stochastic adaptive robust optimization (SARO) model for determining the optimal self-scheduling plan for VPP’s participation in the day-ahead energy-reserve market. We consider exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind generation, as well as endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution methodology based on modified Benders dual decomposition is developed to effectively solve the proposed SARO model with both DIUs and DDUs. Case studies are conducted to verify the efficiency and applicability of the proposed approach. Comparative results show that the proposed method can mitigate the conservatism of robust strategy by capturing a satisfactory trade-off between profitability and real-time operation feasibility.

This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done . A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization.

With the increasing penetration of distributed renewable generations (DRGs), microgrids will play an important role in the future power system. This paper studies the coordinated scheduling strategy of networked microgrids with private data exchange limitations and local management independence. Based on an adaptive robust optimization method, a coordinated scheduling model of networked systems considering the uncertainty of renewable generations is established. Then distributed algorithms are developed to meet the needs of data privacy protection of individual microgrids. The Augmented Lagrangian (AL) decomposition method decomposes the model into several sub-problems, and an alternate optimization method is developed to speed up the solution. Case studies demonstrate the effectiveness of the proposed model and the solution methods.

Edge computing has emerged as a key technology to reduce network traffic, improve user experience, and enable numerous Internet of Things applications. In this article, we study an optimal resource procurement problem for a service provider (SP), who can purchase resources from various edge nodes in the edge computing market to serve its users’ requests. How to jointly optimize the service placement, resource sizing, and workload allocation decisions is a challenging problem, which becomes even more complicated when considering demand uncertainty. To this end, we propose a novel two-stage adaptive robust optimization framework to help the SP optimally determine the locations for installing its service (i.e., placement) and the amount of computing resource to purchase from each location (i.e., sizing). The proposed placement and sizing solution can hedge against any possible realization within a predefined demand uncertainty set. Given the first-stage robust solution, the optimal resource and workload allocation decisions are computed in the second stage after the uncertainty is revealed. To solve the two-stage model, this article presents an iterative solution approach by employing the column-and-constraint generation method that decomposes the underlying problem into a master problem and a max–min subproblem associated with the second stage. Extensive numerical results are shown to illustrate the efficacy of the proposed model.

A two-stage adaptive robust optimization is developed for pre-disturbance scheduling in microgrids (MGs) for handling uncertainties associated with electricity market prices, renewable generation, demand forecasts, and islanding events. The objective is to produce a reliable and optimal solution for MG operation that minimizes operational costs and the risk/failure in islanding events. In the literature, the uncertainty sets associated with islanding events cover a full scheduling period which results in a sub-optimal solution. In this paper, uncertainty sets corresponding to islanding events are modeled based on reliability/resiliency-oriented indexes of the MG/grid to achieve a more accurate/reliable solution. Besides, the Benders decomposition algorithm which is used to handle uncertainties in solving the optimization problem is time-consuming. Therefore, the column-and-constraint generation (C&CG) decomposition strategy is adopted to make the problem computationally tractable. Further, the uncertainty budget parameters are clarified to balance the conservatism and optimality (cost minimization) of the robust solution in uncertainty sets. The effectiveness of the proposed framework is evaluated and discussed by using a set of numerical studies with different scenarios in an MG. The simulations show that the proposed framework reduces operational costs by using the precise analysis of uncertainty budgets and a change in scheduling periods.

This work presents a novel microgrid scheduling model considering the stochastic unintentional islanding conditions as well as forecast errors of both renewable generation and loads. By optimizing the dispatch of distributed energy resources (DERs), utility grid, and demand, the proposed model is targeted to minimize total operating cost of the microgrid, including start-up and shut-down cost of distributed generators (DGs), operation and maintenance (O&M) cost of DGs, cost of buying/selling power from/to utility grid, degradation cost of energy storage systems (ESSs) and cost associated with load shedding. To capture the stochastic unintentional islanding conditions and conventional forecast errors of renewable generation and loads, a two-stage adaptive robust optimization is proposed to optimize the objective function in the worst case scenario of the modeled uncertainties. The proposed optimization is solved with the column and constraint generation (C&CG) algorithm. The result obtained ensures robust microgrid operation in consideration of all possible realization of renewable generation, demand and unintentional islanding condition. The proposed model is validated with results of case studies on a microgrid consisting of various DGs and ESSs.

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the epsilon -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.

Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty