Sample-Based Neural Approximation Approach for Probabilistic Constrained Programs.

Area of Science:

• Optimization
• Machine Learning
• Statistics

Background:

• Continuous optimization problems often involve complex probabilistic constraints.
• Existing methods may struggle with the computational demands of such problems.
• Accurate modeling of uncertainty is crucial in many engineering applications.

Purpose of the Study:

• To introduce a neural approximation-based method for solving continuous optimization problems with probabilistic constraints.
• To develop a robust algorithm for handling uncertainty in optimization.
• To validate the proposed method using a real-world application.

Main Methods:

• Reformulating probabilistic constraints into quantile functions.
• Employing a sample-based neural network to approximate the quantile function.
• Modifying a simulated annealing algorithm with the neural approximation for solving probabilistic constrained programs.

Main Results:

• Demonstrated convergence and feasibility analysis for the neural approximation.
• Successfully applied the revised algorithm to an interval predictor model (IPM) for wind power.
• The neural approximation provides statistical guarantees for the optimization process.

Conclusions:

• The proposed neural approximation method offers an effective approach for continuous optimization under probabilistic constraints.
• The integration with simulated annealing provides a powerful tool for complex, uncertain systems.
• The wind power prediction case study confirms the practical applicability and efficiency of the method.