Off-Line and On-Line Optimization Under Uncertainty: A Case Study on Energy Management

Optimization problems under uncertainty arise in many application areas and their solution is very challenging. We propose here methods that merge off-line and on-line decision stages: we start with a two stage off-line approach coupled with an on-line heuristic. We improve this baseline in two directions: (1) by replacing the on-line heuristics with a simple anticipatory method; (2) by making the off-line component aware of the on-line heuristic. Our approach is grounded on a virtual power plant management system, where the load shifts can be planned off-line and the energy balance should be maintained on-line. The overall goal is to find the minimum cost energy flows at each point in time considering (partially shiftable) electric loads, renewable and non-renewable energy generators, and electric storages. We compare our models with an oracle operating under perfect information and we show that both our improved models achieve a high solution quality, while striking different trade-offs in terms of computation time and complexity of the off-line and on-line optimization techniques.