A new evolution strategy and its application to solving optimal control problems

Abstract

Evolution strategies (ESs) are search algorithms which imitate the principles of natural evolution as a method to solve parameter optimization problems numerically. The effectiveness and simplicity of ES algorithms have lead many people to believe that they are the methods of choice for difficult, real-life problems superseding traditional search techniques. However, the inherent strength of the ES algorithms largely depends upon the choice of a suitable crossover and mutation technique in their application domains. This paper discusses a new ES in which both a subpopulation-based arithmetical crossover (SBAC) and a time-variant mutation (TVM) operator are used. The SBAC operator explores promising areas in the search space with different directivity while the TVM operator exploits fast (but not premature) convergence with high precision results. Thus, a balance between exploration and exploitation is achieved in the evolutionary process with these combined efforts. The TVM also acts as a fine local tuner at the converging stages for high precision solutions. Its action depends upon the age of the populations, and its performance is quite different from the Uniform Mutation (UM) operation. The efficacy of the proposed methods is illustrated by solving discrete-time optimal control models which are frequently used in the applications.