On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints

We present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.

On a method of solving of possibilistic-probabilistic programming problems

В статье исследуется задача возможностно-вероятностной оптимизации, основанная на принципе ожидаемой возможности, и метод решения ее стохастического аналога в случае слабейшей t-нормы, описывающей взаимодействие нечетких параметров. Получены более простые для проверки условия, обеспечивающие сходимость метода стохастических квазиградиентов решения эквивалентного стохастического аналога. The paper studies possibilistic-probabilistic optimization problems, based on the principle of expected possibility, and a method for solving its stochastic analogue in the case of the weakest t-norm describing the interaction of fuzzy parameters. The conditions that are easier to verify and ensure the convergence of the method of stochastic quasigradients of the solution of an equivalent stochastic analog are obtained.

Probabilistic Optimization of Networked Multi-Carrier Microgrids to Enhance Resilience Leveraging Demand Response Programs

Microgrids have emerged as a practical solution to improve the power system resilience against unpredicted failures and power outages. Microgrids offer substantial benefits for customers through the local supply of domestic demands as well as reducing curtailment during possible disruptions. Furthermore, the interdependency of natural gas and power networks is a key factor in energy systems’ resilience during critical hours. This paper suggests a probabilistic optimization of networked multi-carrier microgrids (NMCMG), addressing the uncertainties associated with thermal and electrical demands, renewable power generation, and the electricity market. The approach aims to minimize the NMCMG costs associated with the operation, maintenance, CO2e emission, startup and shutdown cost of units, incentive and penalty payments, as well as load curtailment during unpredicted failures. Moreover, two types of demand response programs (DRPs), including time-based and incentive-based DRPs, are addressed. The DRPs unlock the flexibility potentials of domestic demands to compensate for the power shortage during critical hours. The heat-power dual dependency characteristic of combined heat and power systems as a substantial technology in microgrids is considered in the model. The simulation results confirm that the suggested NMCMG not only integrates the flexibility potentials into the microgrids but also enhances the resilience of the energy systems.

Optimal Booking Control for Physical Examination considering Late Cancellation and Overbooking

Background: Late cancellation of physical examination has a severe impact on the profit of a healthcare center since it is often too late to ll the vacancy. A booking control policy that considers overbooking is then one natural solution.Case presentation: In this study, we consider a healthcare center providing different examination sets using dierent resources. As each resource has its unique cost, revenue, and capacity, the optimal booking limits of all examination sets are hard to be calculated. We propose a probabilistic optimization model that maximizes the expected prot given the late cancellation probability of each type of customer, where the probabilities are estimated through logistic regression and customer grouping using historical booking and cancellation records. To test the performance of our proposed solution, we collaborate with a leading healthcare center. We simulate the presence and absence of customers generated by historical records and compare different strategies of overbooking.Conclusions: Through the experiment, we show that our method can significantly increase the expected profit of the healthcare center by around 11%.