An Extension of the Multicut L-Shaped Method INEN 698 - Large-Scale Stochastic Optimization Semester project

The L-shaped method allows to solve large scale stochastic problems that cannot be solved directly. Each major iteration method solves all scenario subproblems and generate a single optimality or feasibility cut to the master problem by aggregating all the cuts obtained from the subproblems. This causes an ”information loss” and results in a large number of major iterations. The multicut L-shaped method of Birge and Louveaux (1988) allows to add all cuts at once to the master problem. This potentially reduces the number of major iterations but increase the number of decision variables in the master problem drastically (each cut requires one new variable). Also the number of constraints added each iteration is huge. These facts make multicut method useless for practical application. This project involves making an extension to make partial aggregation of the cuts instead of full aggregation (as in original L-shaped) or no aggregation (as multicut L-shaped does). The main idea is to find a compromise between the master problem size and the number of major iteration that minimizes total runtime.