Approximate Uncertain Program

TL;DR

This paper introduces an approximate method using neural networks and a randomized algorithm to efficiently solve chance constrained programs, which are otherwise computationally intractable, especially for non-convex problems.

Contribution

It proposes a novel neural network-based approximation combined with a sequential extreme learning machine and a randomized sampling approach for chance constrained optimization.

Findings

The method outperforms scenario approach and parallel randomized algorithms.

Numerical simulations validate improved performance on non-convex problems.

The approach effectively approximates violation probabilities and converges to optimal feasible decisions.

Abstract

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address chance constrained program. Firstly, a single layer neural-network is used to approximate the function from decision domain to violation probability domain. The algorithm for updating parameters in single layer neural-network adopts sequential extreme learning machine. Based on the neural violation probability approximate model, a randomized algorithm is then proposed to approach the optimizer in the probabilistic feasible domain of decision. In the randomized algorithm, samples are extracted from decision domain uniformly at first. Then, violation probabilities of all samples are calculated according to neural violation probability approximate model. The ones with violation probability higher than the required level are discarded. The minimizer in the remained feasible decision samples is used to update sampling policy. The policy converges to the optimal feasible decision. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach and parallel randomized algorithm. The result shows that proposed method have improved performance.