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Scenario Reduction

scenario reduction

backward reduction

delete least important scenarios one by one

  • step 1: select scenario with smallest distance to other scenario

  • step 2: merge and update scenario weights

  • step i: go to step 1 again

fast forward selection

keep most important scenarios one by one

  • step 1:

    • determine the scenario that can represent all scenarios with the min probability distance
    • keep that scenario

  • step i:

    • for each remaining scenarios, calculate the min probability distance to other remaining scenarios
    • keep that scenario as well

  • do util the number of scenarios to keep reached the provided number

scenario tree

2003: https://www.wias-berlin.de/people/heitsch/ieee03ghr.pdf

  • relative accuracy: eq. (1)

    • when only one scenario is kept, the loss is 100%
    • so use that scenario with the minimum sum prob distance as a base reference
    • when a scenario linked to a deleted scenario is to be deleted, we must update the distance of the deleted scenario to new preserved scenario set
    • as the distance increases so the total loss

  • optimal reduction problem:

    • minimize the total min distance between all deleted scenarios to the remaining scenarios
    • each deleted scenario will be merged to one of the remaining scenarios with the shortest distance
    • the sum(p_j * d_ji) is the information loss

  • probability redistribution: eq.(2)

    • all deleted scenarios will be merged to one of the scenarios in the remaining set with the shortest distance

code

c++ version

  • https://github.com/Jonas-eng/scenred/issues/1

  • https://github.com/Jonas-eng/scenred/blob/master/scenario_reduction_c.pyx

python version (fast forward selection):

  • https://github.com/DanieleGioia/ScenarioReducer/blob/main/main_example.py

scenario tree

  • https://gitlab.com/supsi-dacd-isaac/scenred

papaers

  • 2000: Scenario reduction in stochastic programming: An approach using probability metrics https://edoc.hu-berlin.de/bitstream/handle/18452/8896/20.pdf?sequence=1

  • 2003: Scenario Reduction and Scenario Tree Construction for Power Management Problems https://www.wias-berlin.de/people/heitsch/ieee03ghr.pdf

  • 2003: Scenario reduction algorithms in stochastic programming

  • https://edoc.hu-berlin.de/server/api/core/bitstreams/ed72ccea-3fd6-4e4b-8975-53a27184c758/content
  • backward reduction: eq.(12)

  • forward reduction: eq.(13)

  • 2008: Scenario tree modelling for multistage stochastic programs https://edoc.hu-berlin.de/server/api/core/bitstreams/7f0e1eb1-ca9b-42d5-a213-97b1c0b71764/content

  • 2009: Scenario reduction for futures market trading in electricity markets https://pdfs.semanticscholar.org/6b05/95e54011b6925647adbf837ebb30f77f29d9.pdf