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Bi-objective multistage stochastic linear programming

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Abstract

We propose an algorithm for solving a class of bi-objective multistage stochastic linear programs. We show that the cost-to-go functions are saddle functions, and we exploit this structure, developing a new variant of the stochastic dual dynamic programming algorithm. Our algorithm is implemented in the open-source stochastic programming solver SDDP.jl. We apply our algorithm to a hydro-thermal scheduling problem using data from the Brazilian Interconnected Power System. We also propose and implement a computationally tractable heuristic for bi-objective stochastic convex programs.

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Acknowledgements

This research was supported, in part, by Northwestern University’s Center for Optimization & Statistical Learning (OSL).

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA

    O. Dowson & D. P. Morton

  2. Department of Engineering Science, University of Auckland, Auckland, New Zealand

    A. Downward

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Dowson, O., Morton, D.P. & Downward, A. Bi-objective multistage stochastic linear programming. Math. Program. 196, 907–933 (2022). https://doi.org/10.1007/s10107-022-01872-x

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