This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.
This work investigates one immune optimization algorithm in uncertain environments, solving linear or nonlinear joint chance-constrained programming with a general distribution of the random vector. In this algorithm, an a priori lower bound estimate is developed to deal with one joint chance constraint, while the scheme of adaptive sampling is designed to make empirically better antibodies in the current population acquire larger sample sizes in terms of our sample-allocation rule. Relying upon several simplified immune metaphors in the immune system, we design two immune operators of dynamic proliferation and adaptive mutation. The first picks up those diverse antibodies to achieve proliferation according to a dynamical suppression radius index, which can ensure empirically potential antibodies more clones, and reduce noisy influence to the optimized quality, and the second is a module of genetic diversity, which exploits those valuable regions and finds those diverse and excellent antibodies. Theoretically, the proposed approach is demonstrated to be convergent. Experimentally, the statistical results show that the approach can obtain satisfactory performances including the optimized quality, noisy suppression and efficiency.
