EURO 2024 Copenhagen
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1922. Mixed-integer reformulations for influence diagrams with conditional information structures

Invited abstract in session WA-34: Decision problems represented as influence diagrams, stream Stochastic, Robust and Distributionally Robust Optimization.

Wednesday, 8:30-10:00
Room: 43 (building: 303A)

Authors (first author is the speaker)

1. Olli Herrala
Systems Analysis Laboratory, Aalto University
2. Fabricio Oliveira
Mathematics and Systems Analysis, Aalto University
3. Tommi Ekholm
P.O. Box 503, Finnish Meteorological Institute

Abstract

Endogenous, or decision-dependent, uncertainties pose significant challenges for decision making under uncertainty. Various methods have been developed for different types of endogenous uncertainty, including influence diagrams (ID) for intuitively representing decision-dependent probability distributions. If the problem instead has a decision-dependent information structure, that is, some of the information is revealed conditionally, conditional non-anticipativity constraints can be added to a stochastic programming model representing the problem. However, combining these two types of uncertainty has proven challenging, and no framework existed for such problems until recently.
This presentation aims to shed light on two approaches for reformulating an influence diagram as a mixed-integer linear problem (MILP), enabling us to simultaneously consider different types of endogenous uncertainty and risk measures. A framework called Decision Programming directly reformulates the ID into a MILP, but it has been shown that first reformulating the ID into a rooted junction tree can greatly enhance computational performance and result in asymptotically smaller MILPs. Our discussion is focused on a Julia package implementing the framework along with possible improvements, and an illustrative climate change mitigation case study. Additionally, we mention some other application areas where the methods have been applied to give the audience an overview of the possibilities.

Keywords

Status: accepted

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