Optimizing genetic programming by exploiting semantic impact of sub trees

Abstract

Abstract Now-a-days researchers have diverted their attentions towards making stochastic algorithms deterministic. This is to reduce the fruitless exploration during the search process and to give direction to the search process. Lack of locality in the algorithms is the biggest hindrance in achieving this goal. Locality in GP is described as the correlation between the change in genotype and the semantics of its phenotype (solution). In strong locality, neighboring genotype and phenotype correspond to each other in a search space. It is believed that search algorithms exhibiting strong locality perform better than the algorithms with weak locality. Genetic Programming is among the best performing stochastic algorithms for solving challenging problems and is cursed with the same problem. This means, a small change in GP tree may result in a huge change in the behavior of the solution and vice versa. Unfortunately, this stochastic behavior stops GP from achieving its true potential. 30 years of research since GP’s inception has not solved this problem and even today it is among the biggest challenges faced by the GP community. In this paper we propose a partial derivative based technique for calculating impact of a sub tree on the output of a GP tree. This information is then used to define an impact aware crossover operator. This operator reduces semantic error of a GP tree by intelligently picking crossover points in the tree. Performance of the GP augmented with the new proposed crossover operator is compared with the state of the art techniques. The proposed technique is found efficient, reliable and outperforms the state of the art algorithms on all the tested problems.