Solving influence diagrams via efficient mixed-integer programming formulations and heuristics

TL;DR

This paper introduces new mixed-integer programming formulations and heuristics for solving influence diagrams, demonstrating improved computational performance and showcasing decision programming as an alternative approach for multi-stage stochastic problems.

Contribution

It presents novel MIP formulations and heuristics for influence diagrams, along with a case study on decision programming as an alternative modeling framework.

Findings

Improved MIP formulations outperform existing methods.

Heuristic methods effectively warm start MIP solvers.

Decision programming offers a viable alternative for complex stochastic problems.

Abstract

In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as provide heuristic solutions to more computationally challenging problems. We provide computational results showcasing the superior performance of these improved formulations as well as the performance of the proposed heuristic. Lastly, we describe a novel case study showcasing decision programming as an alternative framework for modelling multi-stage stochastic dynamic programming problems.