Mathematical Analysis of the Heuristic Optimisation Mechanism of Evolutionary Programming

Evolutionary algorithms are robust and adaptive. They have found a wide variety of applications solving optimisation and search problems. As one of the main stream algorithms in evolutionary computation evolutionary programming (EP) mainly uses real values of parameters. This makes it very attractive for many engineering optimisation applications. In addition to the evolutionary characteristics more in depth dynamic optimisation mechanisms of EP is investigated in this paper. An optimisation model based on differential equations is developed to explore and exploit the inherent optimal operation process of EP. The proposed model is based on the characteristics of population evolution and uses two performance measures, (i) Population On-line Performance measure and (ii) Population Off-line Performance measure. These two measures are used to quantify the dynamic population optimisation of EP and to form the foundation for the construction of the differential equation based optimisation model. The model is proposed with strict theoretical and numerical analysis. A number of important conclusions and observations are presented in accordance with the analytical results.