Hyperparameter optimisation in differential evolution using summed local difference strings, a rugged but easily calculated landscape for combinatorial search problems

We analyse the effectiveness of differential evolution hyperparameters in large-scale search problems, i.e. those with very many variables or vector elements, using a novel objective function that is easily calculated from the vector/string itself. The objective function is simply the sum of the differences between adjacent elements. For both binary and real-valued elements whose smallest and largest values are min and max in a vector of length N, the value of the objective function ranges between 0 and (N-1) ? (max-min) and can thus easily be normalised if desired. String length, population size and generations for computational iterations have been studied. Finally, a neural network is trained by systematically varying three hyper-parameters, viz population (NP), mutation factor (F) and crossover rate (CR), and two output target variables are collected (a) median (b) maximum cost function values from 10-trial experiments and compared with SMAC3 and OPTUNA against grid and random search.