Logical Stochastic Optimization

TL;DR

This paper introduces a logical framework using probability answer set programming to model and solve stochastic optimization problems with probabilistic criteria, demonstrated on two-stage stochastic problems with recourse.

Contribution

It extends probability answer set programming with optimization aggregates to handle stochastic optimization problems, including two-stage cases with recourse.

Findings

Framework effectively models stochastic optimization problems.

Application to two-stage stochastic problems demonstrates practical utility.

Enables minimization and maximization under probabilistic environments.

Abstract

We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the language of probability answer set programming to allow minimization or maximization of some desired criteria under the probabilistic environments. We show the application of the proposed logical stochastic optimization framework under the probability answer set programming to two stages stochastic optimization problems with recourse.