LOTUS: A Warm-Start Framework for Powering Dual Decomposition in Large-Scale Two-Stage Stochastic Programs

TL;DR

LOTUS is a warm-start framework that improves dual decomposition efficiency in large two-stage stochastic programs by using informed initial multipliers, leading to faster convergence and better solutions within fixed time limits.

Contribution

This paper introduces LOTUS, a novel subset-based warm-start method that enhances dual decomposition for large-scale stochastic programs, addressing computational challenges.

Findings

LOTUS improves primal solutions in 45.83% of cases within two hours.

It outperforms traditional dual decomposition in only 4.17% of cases.

LOTUS accelerates convergence and mitigates weak LP relaxation effects.

Abstract

Solving large two-stage stochastic mixed-integer programs is computationally challenging. We propose LOTUS, a subset-based warm-start framework that enhances Dual Decomposition under fixed time budgets. By initializing the dual search with informed multipliers, LOTUS accelerates primal convergence and partially alleviates the impact of weak LP relaxations. Through an extensive computational study on production planning instances, we show that, within two hours, LOTUS yields significantly better primal solutions in 45.83% of cases, while being outperformed by Dual Decomposition in only 4.17%.