A survey of adjustable robust optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions.

Algorithm engineering in robust optimization

Smart microgrids are experiencing an increasing growth due to their economic, social, and environmental benefits. However, the inherent intermittency of renewable energy sources (RESs) and users’ behavior lead to significant uncertainty, which implies important challenges on the system design. Facing this issue, this article proposes a novel robust framework for the day-ahead energy scheduling of a residential microgrid comprising interconnected smart users, each owning individual RESs, noncontrollable loads (NCLs), energy- and comfort-based CLs, and individual plug-in electric vehicles (PEVs). Moreover, users share a number of RESs and an energy storage system (ESS). We assume that the microgrid can buy/sell energy from/to the grid subject to quadratic/linear dynamic pricing functions. The objective of scheduling is minimizing the expected energy cost while satisfying device/comfort/contractual constraints, including feasibility constraints on energy transfer between users and the grid under RES generation and users’ demand uncertainties. To this aim, first, we formulate a min–max robust problem to obtain the optimal CLs scheduling and charging/discharging strategies of the ESS and PEVs. Then, based on the duality theory for multi-objective optimization, we transform the min–max problem into a mixed-integer quadratic programming problem to solve the equivalent robust counterpart of the scheduling problem effectively. We deal with the conservativeness of the proposed approach for different scenarios and quantify the effects of the budget of uncertainty on the cost saving, the peak-to-average ratio, and the constraints’ violation rate. We validate the effectiveness of the method on a simulated case study and we compare the results with a related robust approach. Note to Practitioners —This article is motivated by the emerging need for intelligent demand-side management (DSM) approaches in smart microgrids in the presence of both power generation and demand uncertainties. The proposed robust energy scheduling strategy allows the decision maker (i.e., the energy manager of the microgrid) to make a satisfactory tradeoff between the users’ payment and constraints’ violation rate considering the energy cost saving, the system technical limitations and the users’ comfort by adjusting the values of the budget of uncertainty. The proposed framework is generic and flexible as it can be applied to different structures of microgrids considering various types of uncertainties in energy generation or demand.

Robust Optimal Energy Management of a Residential Microgrid Under Uncertainties on Demand and Renewable Power Generation

The assignment of tasks to teams is a challenging combinatorial optimisation problem. The uncertainty in the tasks’ execution processes further complicates the assignment decisions. This study investigates a variant of the typical assignment problem, in which each task can be divided into two parts, one is deterministic and the other is uncertain with respect to their workloads. From the stochastic perspective, this paper proposes both a stochastic programming model that can cope with arbitrary probability distributions of tasks’ random workload requirements, and a robust optimisation model that is applicable to situations in which limited information about probability distributions is available. An example of its application in the software project management is given. Some numerical experiments are also performed to validate the effectiveness of the proposed models and the relationships between the two models.

Adam Ouorou

Papers

Tractable approximations to a robust capacity assignment model in telecommunications under demand uncertainty