Applications of evolutionary algorithms (EAs) to real-world problems are usually hindered due to the parameterisation issues and computational efficiency. This paper shows how the combinatorial effects related to the parameterisation issues of EAs can be visualised and extracted by the so-called compass plot. This new plot is inspired by the traditional Chinese compass used for navigation and geomantic detection. We demonstrate the value of the proposed compass plot in two scenarios with the application to the optimal design of the Hanoi water distribution system. One is to identify the dominant parameters in the well-known NSGA-II. The other is to seek the efficient combinations of search operators embedded in Borg, which uses an ensemble of search operators by auto-adapting their use at runtime to fit an optimisation problem. As such, the implicit and vital interdependency among parameters and search operators can be intuitively demonstrated and identified. In particular, the compass plot revealed some counter-intuitive relationships among the algorithm parameters that led to a considerable change in performance. The information extracted, in turn, facilitates a deeper understanding of EAs and better practices for real-world cases, which eventually leads to more cost-effective decision-making.