# Scenario Generation and Reduction in Stochastic Optimization

I have to generate scenarios for a stochastic optimization program. I want to reduce this number of scenarios but the assignment of a probability to each scenario is my problem. How can I assign a probability to each scenario?

Background

I have historical data for a renewable energy profile such as wind and solar, and I want to formulate a market clearing operation problem using a two-stage stochastic program to minimize the operation cost in the day ahead. I want to have scenarios for each uncertain variable (wind, solar) using a neural network so I don't make fitting to a probability distribution. I then want to assign a probability for each scenario to sum over all scenarios and multiply by its probability to calculate the expected cost. Also I have some confusions about scenarios when I have a lot of uncertain variables like wind, solar and electric load.

• You should provide more context and information. Scenario sampling is usually done for a given fixed number of scenarios (e.g., see the sample average approximation). As the number of scenarios in such methods is large, you might assume equal probability for all the scenarios. Scenario reduction is performed when you are given a large number of scenarios and that makes solving the resulting deterministic equivalent problem hard. In this case, the scenario reduction methods assign probabilities to the remaining scenarios based on the sum of probabilities of omitted scenarions they represent. Dec 7 '19 at 20:44
• Hi Shady, welcome to OR.SE, you can also have a look at the Q/A in the following link: or.stackexchange.com/q/179/39 Dec 7 '19 at 22:36
• @Ehsan I have historical data for renewable energy profile such as wind,solar,I want to make market clearing operation problem using 2 stage stoch program to min the operation cost in the day ahead so I want to have scenarios for each uncertain variable (wind,solar) using nueral network so I don't make fitting to a probability distribution then I want to assign a probability for each scenario to sum over all scenarios and multiply by its probability to calculate the expected cost Also I have confusion about scenarios when I have a lot of uncertain variables like wind, solar and electric load Dec 8 '19 at 10:41
• @OguzToragay Sure Dec 8 '19 at 10:42
• @Ehsan Please may you suggest some papers about the scenario generation that assume equal probabilities and the ways for scenario reduction and assignment of probabilities Dec 11 '19 at 19:34