A Parallelized Cutting-Plane Algorithm for Computationally Efficient Modelling to Generate Alternatives

Abstract: Contemporary macro energy systems modelling is characterized by the need to represent strategic and operational decisions with high temporal and spatial resolution and represent discrete investment and retirement decisions. This drive towards greater fidelity, however, conflicts with a simultaneous push towards greater model representation of inherent complexity in decision making, including methods like Modelling to Generate Alternatives (MGA). MGA aims to map the feasible space of a model within a cost slack by varying investment parameters without changing the operational constraints, a process which frequently requires hundreds of solutions. For large, detailed energy system models this is impossible with traditional methods, leading researchers to reduce complexity with linearized investments and zonal or temporal aggregation. This research presents a new solution method for MGA type problems using cutting-plane methods based on a tailored reformulation of Benders Decomposition. We accelerate the algorithm by sharing cuts between MGA master problems and grouping MGA objectives. We find that our new solution method consistently solves MGA problems times faster and requires less memory than existing monolithic Modelling to Generate Alternatives solution methods on linear problems, enabling rapid computation of a greater number of solutions to highly resolved models. We also show that our novel cutting-plane algorithm enables the solution of very large MGA problems with integer investment decisions.