Optimization in multi-modal continuous space with little globally convex using differential evolution on scattered parents

Differential Evolution (DE) is a powerful stochastic algorithm for real-coded optimization. However, DE has a problem as well as other traditional stochastic optimization algorithms: difficult to optimize search spaces that are little globally convex. Thus, it is difficult for DE and traditional algorithms to optimize some practical problems where globally convex cannot be assumed. As one of the solution for this problem, we propose Differential Evolution on Scattered Parents (DE-SP) that re-selects the individuals on each dimension when the mutant individual is calculated and some children individuals´ candidates unconditionally become the children individuals. We have implemented 2 types of optimization experiment to verify the performance of DE-SP: Noisy Function 1 (NF1), that is a benchmark problem with little globally convex, Noisy Function 2 (NF2), that is the one with globally convex. And we compared the performance of DE-SP with those of 15 types of algorithms. Thereby, it is confirmed that DE-SP was the most stable algorithm to optimize little globally convex spaces among 15 comparative algorithms from the experiment of optimizing NF1. And it is comfirmed that DE-SP can optimize globally convex spaces as well as DE from the experiment of optimizing NF2.