Function optimization using differential evolution without explicit parameter tuning

This thesis investigated the possibility of developing a new version of the Differential Evolution (DE) algorithm that does not require explicit tuning of any of its evolutionary parameters. Similar to other types of canonical evolutionary algorithms, DE requires the user to manually hand-tune the Crossover Rate (Cr), Scaling Factor (F) and Number of Population (NP) using preliminary test runs prior to conducting the actual evolutionary optimization process. The main objective of this thesis is thus to design, implement and test different versions of DE which either uses a self-adaptive or fixed approach to determining these evolutionary parameters. To achieve this main objective, firstly, a standardized 3-Parents DE (3PDE) algorithm is implemented and tested against the original 4-Parents DE (4PDE). Next, the thesis investigates the removal of the first two evolutionary parameters, Cr and F, from the explicit hand-tuning requirement. A series of experiments are conducted involving self-adaptive Cr and F individually and in combination. Lastly, the thesis investigates the self-adaptation of NP using two different methodologies, which are absolute and relative encodings, to determine which is favorable. To analyze and compare the performances of the proposed algorithms, a suite of 20 well-known numerical optimization benchmark test functions were used. Each experimental setup for each test function was repeated for 50 times using different seeds for statistical significance. A total of 7000 evolutionary runs were conducted in this thesis. The results are compared based firstly on the average solution quality in terms of optimization precision and secondly its convergence properties. In addition, statistical testing using two-tailed t-tests are performed at the end of each experimental phase to ascertain the significance of the findings. From the empirical investigations and statistical analysis conducted. a new DE algorithm employing self-adaptation of F and relative self-adaptation of NP with a fixed Cr (3PDE-SAF-Rel) yielded the best outcome in terms of removing the explicit hand-tuning of evolutionary parameters in DE. Moreover, this new DE algorithm not only performed comparably against the original DE but in fact outperformed DE very significantly in 7 of the 20 test functions in terms of average solution quality and 8 of the 20 test functions in terms of convergence as explained in last objective in this thesis