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This study presents an extensive account of Locally Geometric Semantic Crossover (LGX), a semantically-aware recombination operator for genetic programming (GP). LGX is designed to exploit the semantic properties of programs and subprograms, in particular the geometry of semantic space that results from distance-based fitness functions used predominantly in GP. When applied to a pair of parents, LGX picks in them at random a structurally common (homologous) locus, calculates the semantics of subprograms located at that locus, finds a procedure that is semantically medial with respect to these subprograms, and replaces them with that procedure. The library of procedures is prepared prior to the evolutionary run and indexed by a multidimensional structure (kd-tree) allowing for efficient search. The paper presents the rationale for LGX design and an extensive computational experiment concerning performance, computational cost, impact on program size, and capability of generalization. LGX is compared with six other operators, including conventional tree-swapping crossover, semantic-aware operators proposed in previous studies, and control methods designed to verify the importance of homology and geometry of the semantic space. The overall conclusion is that LGX, thanks to combination of the semantically medial operation with homology, improves the efficiency of evolutionary search, lowers the variance of performance, and tends to be more resistant to overfitting.

Locally geometric semantic crossover: a study on the roles of semantics and homology in recombination operators