I Ching philosophy inspired optimization

I Ching (Chinese characters: $$$) philosophy, stemming from ancient Chinese culture, is Chinese view of empiricism, world outlook and dialectics. Over thousands of years of evolving and interpretation, its cosmological wisdom has broad and profound influences not only on Chinese prevailing philosophy, but also on westerns. I Ching concentrates on the virtue of being moderate and appropriate, representing the balance by which it is contended that power/destiny can be well generated/controlled. Among the whole 64 hexagrams in I Ching, is the QIAN hexagram which is ranked in the first place, standing for the strong action and the everlasting desire for success. Behind I Ching philosophy lie the thinking and action models of optimization, specifically, identification from changing states, embracing vision, and optimal action obeying the balance of moderateness and appropriateness. I Ching philosophy could act as the driving force to establish and develop new optimization scheme. In this regard, enlightened by I Ching philosophy, particularly the QIAN hexagram, we propose I Ching philosophy inspired optimization, labeled as ICO for continuous optimization problems. Characterized by population-based, stochastic, iterative, and empiricism inspired features, the ICO evolves the population of solutions by multiple searching operators derived from underlying mechanism of the QIAN hexagram, as expected that the balance between global exploration and local exploitation can be well achieved. Specifically, the whole population is divided into four subpopulations, each of which corresponds to one solid line (state in the QIAN hexagram), then five search operators are developed to perform the learning, emerging, controlling, chasing and stabilizing operations on each subpopulation. The performances of the proposed ICO are investigated on well-known testing benchmarks and digital IIR filter designing problem which is crucial in control field. Comparisons with several state-of-the-art algorithms show the efficacy of the proposed ICO algorithm.