On the Global Optimization of a Short Term Hydro Scheduling Problem. Relaxations by Generalized Disjunctive Programming and Mixed Integer Linear Programming Reformulations
R. Lima, On the Global Optimization of a Short Term Hydro Scheduling Problem. Relaxations by Generalized Disjunctive Programming and Mixed Integer Linear Programming Reformulations, European Journal of Operational Research, Submitted (2015).
This paper addresses the derivation of efficient over-estimator problems for a non-convex Mixed Integer Non-Linear Programming (MINLP) problem describing the short term scheduling of a cascade of hydro plants to generate electricity. Good formulations for over-estimator prob- lems are paramount for the implementation of global optimization strategies to solve MINLP problems, and useful to calculate rigorous bounds within decomposition methods applied to non- convex problems. The MINLP problem studied involves several bilinear and power terms defined over each time period, leading to a large number of nonlinear terms to handle. The relaxation of the bilinear terms is made by using convex McCormick and Piecewise McCormick envelopes. The over-estimator problems are built with a special emphasis in Generalized Disjunctive Program- ming (GDP) formulations, which are then reformulated using Big-M or Convex-Hull methods as Mixed Integer Linear Programming (MILP) problems. A new GDP formulation is proposed in order to improve the computational performance of Piecewise McCormick envelopes. The computational results show that the compact formulations using McCormick envelopes provide fast bounds for the objective function of the original MINLP problem, while the new proposed GDP formulation provides a tighter bound, and for some problems has a superior computational performance when compared with other Piecewise McCormick-based formulations.
OR in EnergyShort-Term Hydro SchedulingMINLPGDPGlobal Optimization