Experiments have been conducted from five protruding rectangular discrete heat sources (aluminum) of non-identical sizes arranged at different positions on a substrate board (Bakelite), under natural convection, to determine their optimal configuration. A substrate board is designed for conducting experiments on multiple configurations of heat sources using the same board. A heuristic non-dimensional geometric parameter, lambda, is defined for the purpose of identifying the optimal configuration for which the maximum temperature excess among the five heat sources of a configuration is the minimum, among all possible configurations. The maximum temperature excess is found to decrease with lambda, so the configuration with highest lambda is deemed to be the optimal one. The effect of surface radiation on the heat transfer rate from the heat sources is studied by painting their surfaces with black paint of high emissivity, which reduces their temperature by as much as 15%. An empirical correlation is developed for the non-dimensional maximum temperature excess (theta) in terms of lambda, taking into account the effect of radiation. To minimize the error between the temperatures obtained by prediction (correlation) and experiment, and to determine the global optimal configuration of heat sources more rigorously, an artificial neural network (ANN) is trained using the experimental data, which then powers the genetic algorithm (GA) code.