Automated Software Test Case Generation (ATCG) is one of the most active research topics in Software Engineering, with a wide range of techniques and tools being used in academia and industry. While their usefulness is widely recognized, due to the labour-intensive nature of the task, the suitability of the different techniques in automatically generating test cases for different software systems is not thoroughly understood. Some methods use search methods, such as evolutionary algorithms, while others perform random testing. The No Free Lunch of Optimization (NFLT) states that a universal strategy of optimization is impossible, and the only way one strategy can outperform another is if it is specialized to the structure of the specific problem under consideration. Thus, the characteristics of the software systems have an important role when analyzing ATCG techniques performance. Therefore, we propose a new methodology to evaluate and select the most effective ATCG technique using structure-based complexity measures. Empirical tests are going to be performed using two different techniques: Search-based Software Testing and Random Testing.