EURO 2024 Copenhagen
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1882. Risk averse mixed-integer linear programming models for influence diagrams

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. Topias Terho
Department of mathemathics and systems analysis, Aalto University
2. Olli Herrala
Systems Analysis Laboratory, Aalto University
3. Fabricio Oliveira
Mathematics and Systems Analysis, Aalto University

Abstract

Influence diagrams are an intuitive representation of decision problems with dependencies between uncertain events, decisions, and consequences. Recently, two frameworks that transform influence diagrams into mixed-integer-linear programs (MILP) have been developed. Decision Programming (Salo et al., EJOR 299/2, 2022) enforces constraints on different possible realizations of the whole problem. This exposes the full probability distribution of consequences to be used in the optimization model, which in turn allows risk to be explicitly constrained or optimized. Rooted junction tree approach (Parmentier et al., Informs Journal on Optimization, 2/3, 2020) decomposes an influence diagram into clusters, that are subsets of nodes, and finds the probability distributions of these clusters with a MILP. Compared to decision programming, the rooted junction tree model offers better computational performance, but risk cannot be straightforwardly represented in the optimization model. We present approaches and conditions that combine the computational efficiency of rooted junction trees and the modeling flexibility of decision programming. More specifically, we highlight how risk can be directly represented in rooted junction tree models with examples.

Keywords

Status: accepted

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