Partial Sampling Operator and Structural Distance Ranking for Multi-Objective GP

摘要

This paper describes a technique on an optimization of tree-structure data, or genetic programming (GP), by means of a multi-objective optimization technique. NSGA-II is applied as a frame work of the multi-objective optimization. GP induces bloat of the tree structure as one of the major problem. The cause of bloat is that the tree structure obtained by the crossover operator grows bigger and bigger but its evaluation does not improve. To avoid the risk of bloat, a partial sampling (PS) operator is proposed instead to the crossover operator. Repeating processes of proliferation and metastasis in PS operator, new tree structure is generated as a new individual. Moreover, the size of the tree and a structural distance (SD) are additionally introduced into the measure of the tree-structure data as the objective functions. And then, the optimization problem of the tree-structure data is defined as a three-objective optimization problem. SD is also applied to the selection of parent individuals instead to the crowding distance of the conventional NSGA-II. The effectiveness of the proposed techniques is verified by applying to the double spiral problem.