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Modelling to generate alternatives

Through modelling to generate alternatives (short MGA), near-optimal solutions can be explored under certain conditions. Currently, SpineOpt supports two methods for MGA are available.

Modelling to generate alternative: Maximally different portfolios

The idea is that an orginal problem is solved, and subsequently solved again under the condition that the realization of variables should be maximally different from the previous iteration(s), while keeping the objective function within a certain threshold (defined by max_mga_slack).

In SpineOpt, we choose units_invested_available, connections_invested_available, and storages_invested_available as variables that can be considered for the maximum-difference-problem. The implementation is based on Modelling to generate alternatives: A technique to explore uncertainty in energy-environment-economy models.

How to set up an MGA problem

  • model: In order to explore an MGA model, you will need one model of type spineopt_mga. You should also define the number of iterations (max_mga_iterations, and the maximum allowed deviation from the original objective function (max_mga_slack).
  • at least one investment candidate of type unit, connection, or node. For more details on how to set up an investment problem please see: Investment Optimization.
  • To include the investment decisions in the MGA difference maximization, the parameter units_invested_mga, connections_invested_mga, or storages_invested_mga need to be set to true, respectively.
  • The original MGA formulation is non-convex (maximization problem of an absolute function), but has been linearized through big M method. For this purpose, one should always make sure that units_invested_big_m_mga, connections_invested_big_m_mga, or storages_invested_big_m_mga, respectively, is sufficently large to always be larger the the maximum possible difference per MGA iteration. (Typically the number of candidates could suffice.)
  • As outputs are used to intermediately store solutions from different MGA runs, it is important that units_invested, connections_invested, or storages_invested, respectively, are defined as output objects in your database.

Modelling to generate alternative: Trade-offs between technology investments

The idea of this approach is to explore near-optimal solutions that maximize/minimize investment in a certain technology (or multiple technologies simultanesously).

How to set up an MGA problem

  • model: In order to explore an MGA model, you will need one model of type spineopt_mga. The maximum allowed deviation from the original objective function should be defined via max_mga_slack. Note that for this method, we don't define an explicit number of iteration via the max_mga_iterations parameter (see also below)
  • at least one investment candidate of type unit, connection, or node. For more details on how to set up an investment problem please see: Investment Optimization.
  • To include the investment decisions in the MGA min/maximization, the parameter units_invested_mga, connections_invested_mga, or storages_invested_mga need to be set to true, respectively.
  • To explore near-optimal solutions using this methodology, the units_invested_mga_weight, connections_invested_mga_weight, and storages_invested_mga_weight parameters are used to define near-optimal solutions. For this purpose, these parameters are defined as Arrays, defining the weight of the technology per iterations. Note that the length of these Arrays should be the same for all technologies, as this will correspond to the number of MGA iterations, i.e., the number of near-optimal solutions. To analyze the trade-off between two technology types, we can, e.g., define units_invested_mga_weight for unit group 1 as [-1,-0.5,0], whereas the use the weights [0,-0.5,-1] for the other technology storage group 1 in question. Note that a negative sign will correspond to a minimization of investments in the corresponding technology type, while positive signs correspond to a maximization of the respective technology. In the given example, we would hence first minimize the investments in unit group 1, then minimize the two technologies simultaneuously, and finally only minimize investments in storage group 2.
  • As outputs are used to intermediately store solutions from different MGA runs, it is important that units_invested, connections_invested, or storages_invested, respectively, are defined as output objects in your database.