L-Shaped BONUS Algorithm: An algorithm to solve stochastic nonlinear programming problems computationally efficiently

The L-shaped BONUS algorithm is proposed to solve the stochastic nonlinear programming (SNLP) problems in a computationally efficient manner. It derives its computational advantage by integrating the standard L-shaped method with BONUS algorithm, which has been proposed to solve SNLP problems by avoiding repeated model simulations. The details of various aspects of the L-shaped BONUS algorithm and their advantages are given below:

Sampling Based L-Shaped Method:

• Use of statistical approximations to solve two or multiple stage stochastic programming problems
• Internal sampling at each iteration to approximate uncertain space
• Decomposition of the problem to improve computational efficiency
• Requirement of repeated model simulations for each sample and each iteration
• Computationally demanding for complex (nonlinear/high-dimensional models)

BONUS (Better Optimization of Nonlinear Uncertain Systems):

• New algorithm to solve stochastic nonlinear problems efficiently
• Use of reweighting to bypass repeated model simulations
• Reweighting concept based on the reweighting scheme proposed by Hesterberg
• Uses model output distribution for one sample set to compute output distribution for another sample set when both the sample sets are known

Hammersley Sequence Sampling:

• New sampling technique based on the inversion of Hammersley sequence points
• Sampling technique with k dimensional uniformity property
• Improved sampling efficiency results in better convergence of the algorithm