Improving solution times of Capacity Expansion Energy System Models using aggregated problem solution as warm start

Energy System Models are complex MIPs that frequently need substantial CPU time to be solved. We study Capacity Expansion Models which are used for finding an optimal mix of technologies to secure stability in future energy systems. The need of model detail for this purpose tends to increase. Firstly, due to the many possible alternatives to fossil fuel, the solution space grows.

Secondly, a detailed modelling including e.g. unit commitment makes the models NP-hard to solve. Consequently, simplification methods are needed. Promising results have been reported using aggregation, where the reduced models capture most of the needed investments while being much faster to solve. However, the solutions typically are sub-optimal, and a too aggressive aggregation may lead to infeasible solutions for the original problem.

We analyze the potential of achieving optimal solutions using less computational time. By warm-starting the solution process of the original problem using solutions of aggregated problems, we help the MIP solver in finding good search directions. Moreover, we suggest to exploit the high quality of aggregated solutions by reducing the solution space according to the aggregated investment strategy to reduce solution times even further.

Results show that the gains of using warm starts depend on both warm starting solution and problem instance. Still, using the reduction span on investments, solution time reductions for most warm starts are seen with reductions up to 75%.