Mathematical Analysis of Evolutionary Algorithms for Optimization

Simulating evolution as seen in nature has been identified as one of the key computing paradigms for the new decade. Today evolutionary algorithms have been successfully used in a number of applications. These include discrete and continuous optimization problems, synthesis of neural networks, synthesis of computer programs from examples (also called genetic programming) and even evolvable hardware. But in all application areas problems have been encountered where evolutionary algorithms performed badly. In this survey we concentrate on the analysis of evolutionary algorithms for optimization. We present a mathematical theory based on probability distributions. It gives the reasons why evolutionary algorithms can solve many difficult multi-modal functions and why they fail on seemingly simple ones. The theory also leads to new sophisticated algorithms for which convergence is shown.