Since its introduction, Geometric Semantic Genetic Programming (GSGP) has been the inspiration to ideas on how to reach optimal solutions efficiently. Among these, in 2016 Pawlak has shown how to analytically construct optimal programs by means of a linear combination of a set of random programs. Given the simplicity and excellent results of this method (LC) when compared to GSGP, the author concluded that GSGP is "overkill". However, LC has limitations, and it was tested only on simple benchmarks. In this paper, we introduce a new method, Population-Wide Semantic Crossover (PSXO), also based on linear combinations of random programs, that overcomes these limitations. We test the first variant (Inv) on a diverse set of complex real-life problems, comparing it to LC, GSGP and standard GP. We realize that, on the studied problems, both LC and Inv are outperformed by GSGP, and sometimes also by standard GP. This leads us to the conclusion that GSGP is not overkill. We also introduce a second variant (GPinv) that integrates evolution with the approximation of optimal programs by means of linear combinations. GPinv outperforms both LC and Inv on unseen test data for the studied problems.
