A scalable parallel Progressive Hedging Algorithm for stochastic cluster-scenario-based mixed-integer models

Abstract

This work presents a general parallelisation of the Progressive Hedging algorithm to coordinate the resolution of two-stage and multi-stage stochastic mixed-integer problems without (binary or integer) variables in the first stage. We report a benchmark study between the computational improvements using our proposal and the parallel version (using pyro) of the Pyomo integrated Progressive Hedging. Moreover, we study the influence of a quadratic term to accelerate the convergence, different scenario-cluster formation and several step update policies by solving different instances using our proposal.