Kilian Schindler | EPFL Graph Search

Daniel Kuhn is Professor of Operations Research at the College of Management of Technology at EPFL, where he holds the Chair of Risk Analytics and Optimization (RAO). His current research interests are focused on data-driven optimization, the development of efficient computational methods for the solution of stochastic and robust optimization problems and the design of approximation schemes that ensure their computational tractability. This work is primarily application-driven, the main application areas being engineered systems, machine learning, business analytics and finance.

Before joining EPFL, Daniel Kuhn was a faculty member in the Department of Computing at Imperial College London (2007-2013) and a postdoctoral research associate in the Department of Management Science and Engineering at Stanford University (2005-2006). He holds a PhD degree in Economics from University of St. Gallen and an MSc degree in Theoretical Physics from ETH Zurich. He is the editor-in-chief of Mathematical Programming and the area editor for continuous optimization for Operations Research.

A Planner-Trader Decomposition for Multi-Market Hydro Scheduling

Daniel Kuhn, Napat Rujeerapaiboon, Kilian Schindler, Wolfram Wiesemann

Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout and the steady growth in photovoltaic capacity. The reduced profitability of peak/off- peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bi-layer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner’s problem) optimizes end-of-day reservoir filling levels over one year, whereas the inner layer (the trader’s problem) selects optimal hourly market bids within each day. Using an information restriction whereby the planner prescribes the end-of-day reservoir targets one day in advance, we prove that the trader’s problem simplifies from an infinite-dimensional stochastic program with 25 stages to a finite two- stage stochastic program with only two scenarios. Substituting this reformulation back into the outer layer and approximating the reservoir targets by affine decision rules allows us to simplify the planner’s problem from an infinite-dimensional stochastic program with 365 stages to a two-stage stochastic program that can conveniently be solved via the sample average approximation. Numerical experiments based on a cascade in the Salzburg region of Austria demonstrate the effectiveness of the suggested framework.

2021

Paradoxical simulation results of chaos-like chattering in the bouncing ball system

Kilian Schindler

This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value. (C) 2021 Elsevier B.V. All rights reserved.

ELSEVIER2021

Scalable Stochastic Optimization: Scenario Reduction with Guarantees

Kilian Schindler

Stochastic optimization is a popular modeling paradigm for decision-making under uncertainty and has a wide spectrum of applications in management science, economics and engineering. However, the stochastic optimization models one faces in practice are intractable, and numerical solutions necessitate approximations. The mainstream approach for making a stochastic optimization model amenable to numerical solution is to discretize the probability distribution of the uncertain problem parameters. However, both the accuracy of the approximation as well as the computational burden of solving the approximate problem scale with the number of scenarios of the approximate distribution. An effective means to ease the computational burden is to use scenario reduction, which replaces an accurate initial distribution accommodating many scenarios with a simpler distribution supported on only few scenarios that is close to the initial distribution with respect to a probability metric. Using the Wasserstein distance as measure of proximity between distributions, we provide new insights into the fundamental limitations of scenario reduction, and we propose the first polynomial-time constant-factor approximations for a popular scenario reduction problem from the literature. As scenario reduction is equivalent to clustering, it suffers from two well-known shortcomings. Namely, it suffers from outlier sensitivity and may produce highly unbalanced clusters. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, where the clusters must satisfy certain cardinality constraints. We cast this problem as a mixed-integer linear program (MILP) that admits tractable semidefinite and linear programming relaxations. We propose deterministic rounding schemes that transform the relaxed solutions to feasible solutions for the MILP. We also prove that these solutions are optimal in the MILP if a cluster separation condition holds. Finally, we develop a highly efficient scenario reduction method for a large-scale hydro scheduling problem. Specifically, we study the optimal operation of a fleet of interconnected hydropower plants that sell energy on both the spot and the reserve markets, and we propose a two-layer stochastic programming framework for its solution. The outer layer problem (the planner's problem) optimizes the end-of-day reservoir filling levels over one year, whereas the inner layer problem (the trader's problem) selects optimal hourly market bids within each day. We prove that the trader's problem admits a scenario reduction that dramatically reduces its complexity without loss of optimality, which in turn facilitates an efficient approximation of the planner's problem.

EPFL2020

Scalable Stochastic Optimization: Scenario Reduction with Guarantees

Kilian Schindler

EPFL2020