Adaptive Racing Sampling Based Immune Optimization Approach for Nonlinear Multi-Objective Chance Constrained Programming

Abstract

This work investigates a multi-objective immune optimization approach to solve the general type of nonlinear multi-objective chance constrained programming without prior noise information. One such kind of model is first converted into a sample-dependent approximation one, while a sample bound estimate model is theoretically acquired based on the empirical Bernstein bound, in order to control the sampling size of random variable. Secondly, a feasibility detection approach with adaptive sampling is designed to quickly justify whether an individual is empirically feasible. Inspired by the danger theory, an artificial immune optimization model is drawn in terms of immune response mechanisms in the immune system, which derives out a multi-objective chance constrained optimizer with small populations and multiple evolutionary strategies. The computational complexity of the optimizer depends mainly on the sample bound and the size of memory pool. Comparative experiments have validated that it is a robust, stable, and effective optimizer with high efficiency while helping for solving complex chance constrained problems.

Keywords

• Multi-objective chance constrained programming
• immune optimization
• adaptive sampling
• danger theory
• sample-dependent approximation