Parallel Randomized Algorithm for Chance Constrained Program

TL;DR

This paper introduces a parallel randomized algorithm for solving chance constrained programs, improving robustness and efficiency by iteratively sampling and discarding infeasible solutions based on violation probabilities.

Contribution

It presents a novel two-layer randomized parallel algorithm that effectively handles chance constraints in non-convex optimization problems.

Findings

Better robustness in finding probabilistic feasible solutions.

Outperforms scenario approach in numerical simulations.

Applicable to non-convex problems with chance constraints.

Abstract

Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address chance constrained program. Randomized optimization is applied to search the optimizer which satisfies chance constraints in a framework of parallel algorithm. Firstly, multiple decision samples are extracted uniformly in the decision domain without considering the chance constraints. Then, in the second sampling layer, violation probabilities of all the extracted decision samples are checked by extracting the disturbance samples and calculating the corresponding violation probabilities. The decision samples with violation probabilities higher than the required level are discarded. The minimizer of the cost function among the remained feasible decision samples are used to update optimizer iteratively. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach. The proposed method exhibits better robustness in finding probabilistic feasible optimizer.