Convergence Analysis on Immune Optimization Solving CCP Problems

Abstract

This work concentrates on studying the property of convergence of a sample allocation-based immune optimization approach used in solving linear or nonlinear chance-constrained programming (CCP) with general random variables. First, we make some theoretical studies about existence of optimal reliable solutions and give an approximate relation between the true CCP and the sample average approximation problem, depending on some statistic and analysis theory. Second, a bio-inspired immune optimization approach is developed to assume solving CCP problems. Our theoretical analysis shows that such approach, which is capable of being formulated by a non-homogeneous Markov model, is convergent. Experimentally, performance searching curves reveal that the approach can obtain valuable performances including the optimized quality, noisy suppression and convergence.