Bi-objective multistage stochastic linear programming

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.

Automated summary

We propose an algorithm for solving a class of bi-objective multistage stochastic linear programs and develop a new variant of the stochastic dual dynamic programming algorithm by exploiting the structure of the cost-to-go functions as saddle functions. We apply our algorithm to a hydro-thermal scheduling problem using data from the Brazilian Interconnected Power System and propose a computationally tractable heuristic for bi-objective stochastic convex programs.