Modeling to Generate Alternatives (MGA)

Modeling to Generate Alternatives (MGA)#

Temoa provides two extensions for Modeling to Generate Alternatives (MGA), an algorithm to explore the near-optimal solution space: hull expansion and single-vector MGA. Both are described in more detail below.

Hull Expansion#

Hull expansion creates the convex hull containing all near-optimal solutions bound by the extreme points along a particular solution axis and then samples the continuum of solutions. The size of the convex hull is determined by the degree of cost relaxation (cost_epsilon). The method is described in Pedersen et al. (2021)

Configuration#

To enable hull expansion, set the scenario_mode to "mga" in your configuration TOML file and provide an [MGA] section:

scenario_mode = "mga"

[MGA]
cost_epsilon = 0.05        # Relax cost by 5%
iteration_limit = 20       # Maximum number of MGA iterations
time_limit_hrs = 12        # Stop after 12 hours
axis = "TECH_CATEGORY_ACTIVITY"
weighting = "HULL_EXPANSION"

Options#

  • cost_epsilon: The fraction by which the optimal cost is allowed to increase (e.g., 0.05 for 5%).

  • iteration_limit: The maximum number of alternative solutions to generate.

  • time_limit_hrs: The maximum wall-clock time for the entire MGA run.

  • axis: The dimension along which to optimize. Supported values:

    • TECH_CAPACITY

    • TECH_CATEGORY_CAPACITY

    • TECH_CATEGORY_ACTIVITY (Default)

    • EMISSION_ACTIVITY

  • weighting: The algorithm used to select the next optimization vector. Currently, only HULL_EXPANSION is supported.

Single-Vector MGA (SVMGA)#

Single-Vector MGA is a simplified, two-stage process. First, it solves the base model to find the minimum cost. Second, it adds a cost relaxation constraint and creates a new objective function that minimizes user-specified quantities, such as technology-specific installed capacity or total carbon dioxide emissions.

Configuration#

To enable SVMGA, set the scenario_mode to "svmga" and provide an [SVMGA] section:

scenario_mode = "svmga"

[SVMGA]
cost_epsilon = 0.05
capacity_labels = ["solar_pv", "wind_onshore"]
# emissions_labels = ["CO2"]
# activity_labels = ["coal_power"]

Options#

  • cost_epsilon: Same as in hull expansion.

  • capacity_labels: A list of technology names whose total capacity should be maximized in the second stage. Matching is exact and case-sensitive against the identifiers in the tech_all set. Example: ["solar_pv", "wind_onshore"].

  • emissions_labels: A list of emission commodities whose total emissions should be minimized. Matching is exact and case-sensitive against identifiers in the commodity_emissions set. Example: ["CO2"].

  • activity_labels: A list of technology names whose total activity (energy flow out) should be maximized. Matching is exact and case-sensitive. Example: ["coal_power"].

Note: SVMGA will construct an unweighted sum of all variables matching these labels as the new objective function. Be careful not to mix different units. In addition, note that the MGA objective function is set to minimize regardless of the label choice.

Parallel Execution and Solver Options#

Standard MGA supports parallel execution of iterative solves to maximize performance. Note: SVMGA executes sequentially and does not utilize parallel workers.

The number of worker processes and solver-specific settings are defined in a MGA_solver_options.toml file. By default, Temoa looks for this file in the same directory as your main configuration file.

# Global setting at the top level of the file
num_workers = 4

[gurobi]
Method = 2
Threads = 4  # Threads per solver instance
BarConvTol = 0.01

Tip

When choosing num_workers, a good rule of thumb is to set it to the number of available CPU cores minus one. This leaves room for the main orchestration process and ensures that the system remains responsive. Also, be mindful of the Threads setting within solver blocks, as the total thread count will be num_workers * Threads.

Outputs#

MGA results are stored in the same output database specified in your configuration. Each iteration is saved as a unique scenario to allow for easy comparison and analysis.

Scenario Naming Convention#

Each run is saved under a unique scenario name in the output tables, following the format: <base_scenario>-<iteration_index>.

  • Iteration 0: The original baseline solve (optimal solution).

  • Iterations 1-N: The alternative solutions generated by the MGA algorithm.

For example, if your base scenario is utopia_mga, the results for the base case will be found under scenario utopia_mga-0, and the first alternative will be under utopia_mga-1.

Key Database Tables#

The results are spread across several tables, consistent with standard Temoa runs:

  • output_objective: Stores the total system cost and MGA optimization objective for each iteration.

  • output_net_capacity: Stores the installed capacity for each technology, period, and iteration.

  • output_flow_out / output_flow_out_summary: Stores energy flows between technologies.

  • output_emission: Stores emission results per commodity and technology.

  • output_cost: Stores detailed cost breakdowns (investment, fixed, variable).

Comparing Iterations#

You can use SQL queries to compare results across different MGA iterations.

Comparing Total System Cost:

SELECT scenario, total_system_cost
FROM output_objective
WHERE scenario LIKE 'utopia_mga-%'
ORDER BY scenario;

Comparing Capacity for a Specific Technology:

SELECT scenario, tech, period, capacity, units
FROM output_net_capacity
WHERE scenario LIKE 'utopia_mga-%'
  AND tech = 'solar_pv'
ORDER BY scenario, period;

Analyzing Diversity (SQL Join Example):

SELECT a.scenario, a.tech, a.capacity as cap_a, b.capacity as cap_b, (a.capacity - b.capacity) as diff
FROM output_net_capacity a
JOIN output_net_capacity b ON a.tech = b.tech AND a.period = b.period
WHERE a.scenario = 'utopia_mga-1'
  AND b.scenario = 'utopia_mga-0'
  AND a.tech = 'solar_pv';