Invited Session Tue.3.MA 141

Tuesday, 15:15 - 16:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Advances in stochastic programming


Chair: Daniel Kuhn



Tuesday, 15:15 - 15:40 h, Room: MA 141, Talk 1

Angelos Georghiou
A stochastic capacity expansion model for the UK energy system

Coauthors: Daniel Kuhn, Wolfram Wiesemann


Energy markets are currently undergoing one of their most radical changes in history. Both market liberalisation and the increasing penetration of renewable energy sources highlight the need to accommodate uncertainty in the design and management of future energy systems. This work aims to identify the most cost-efficient expansion of the UK energy grid, given a growing future demand for energy and the target to move towards a more sustainable energy system. To this end, we develop a multi-stage stochastic program where the investment decisions (generation capacity that should be built) are taken here-and-now, whereas the operating decisions are taken in hourly time stages over a horizon of 30 years. The resulting problem contains several thousand time stages and is therefore severely intractable. We develop a novel problem reformulation, based on the concept of time randomisation, that allows us to equivalently reformulate the problem as a two-stage stochastic program. By taking advantage of the simple structure of the decision rule approximation scheme, we can model and solve a problem that optimises over the whole generation capacity of the UK energy system.



Tuesday, 15:45 - 16:10 h, Room: MA 141, Talk 2

Panos Parpas
Dimensionality reduction and a maximum principle for multiscale stochastic processes


Weakly connected Markov Processes are often used to capture stochastic dynamics that evolve along different time scales. We show that if the system has sufficient scale separation then a Maximum Principle of reduced order holds. The reduced order Maximum Principle is used to develop a solution algorithm for the optimisation of multiscale processes.



Tuesday, 16:15 - 16:40 h, Room: MA 141, Talk 3

Daniel Kuhn
Polyhedrality in distributionally robust optimization

Coauthors: Melvyn Sim, Wolfram Wiesemann


Distributionally robust optimization studies stochastic programs whose uncertain parameters follow a distribution that is itself uncertain. The distribution is only known to belong to an ambiguity set defined in terms of certain statistical or structural properties, and the decision-maker is assumed to hedge against the worst-case distribution within the ambiguity set. Most distributionally robust optimization problems studied to date rely on mean, covariance and support information about the uncertain parameters. These problems can often be reformulated as semidefinite programs, which are computationally tractable in theory but suffer from limited scalability in practice. In this talk we propose new uncertainty models specified in terms of maximum variability bounds with polyhedral integrands, minimum variability bounds with polyhedral integrands and polyhedral confidence sets, respectively. We employ these ambiguity sets in the context of standard and risk-averse stochastic programming as well as chance constrained programming, and we show that the resulting distributionally robust optimization problems admit highly scalable reformulations or approximations as linear programs.


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