Benders algorithm for bi-objective two-stage stochastic optimization problems with multiple scenarios

We present a Benders algorithm for bi-objective optimization problems. In this algorithm, a sequence of weighted-sum problems is solved with Benders decomposition to find a complete set of extreme efficient solutions. Rather than using pre-determined weights or a dichotomic weighting approach, we present a procedure to identify the next weight to consider based on information obtained from the decomposed problem to obtain a complete set of extreme efficient solutions. This is applied to solve bi-objective two-stage multi-scenario stochastic linear optimization problems, in particular a capacity expansion network problem with multiple scenarios. Some numerical results will be presented.