Evolutionary algorithms (EAs), inspired by the principles of natural evolution, have demonstrated strong performance across a wide range of practical optimization problems. However, their behavior is not yet fully explained by existing theoretical frameworks. Much of the current theoretical research in evolutionary computation remains limited, focusing either on worst-case scenarios or on highly simplified mathematical models that rely on asymptotic analysis under narrowly defined conditions. As a result, important questions remain about how and why evolutionary algorithms behave as they do in practice. This thesis aims to address this gap through an empirical study of EAs across three domains: binary, integer, and continuous. By designing experiments that serve not only as benchmarks but also as explanatory tools, this work provides insights that complement theoretical analysis, raise new research questions, and demonstrate how concepts developed in discrete settings can inform algorithm design in more complex, real-world applications. In the binary space, we focus on problems that are theoretically well-studied but still leave room for unanswered questions. When purely mathematical proofs cannot establish certain properties or intuitions, we turn to experiments designed with theoretical purposes in mind. These experiments reveal patterns that support or refine existing analyses, making theoretical ideas visible and offering a way to test assumptions that are otherwise inaccessible. In this way, experiments are used not as a substitute for proofs but as an additional instrument for theoretical investigation. Building on this foundation, the integer space serves as a bridge toward more complex optimization problems. Mixed-Integer Black-Box Optimization (MI-BBO) combines discrete and continuous challenges and is increasingly important in practical applications. Here, we design theoretically inspired test problems that extend the discrete perspective, and we analyze how algorithms adapt when moving into more complicated, mixed settings. This stage highlights how ideas from the binary space, such as analytical approaches and mutator designs, can be extended to problems with richer structure, identifying both the strengths and limitations of EAs in this transition. Finally, in the continuous space, we examine whether the lessons learned in the discrete settings can be transferred to problems that dominate practical applications. We adapt methods from binary analysis and mutators studied in the integer setting, testing whether these strategies can improve algorithm performance on continuous landscapes. Continuous optimization offers broader applicability but also greater complexity. Here, experiments allow us to evaluate how far discrete-inspired approaches can be generalized. This part of the thesis demonstrates the potential of cross-domain transfer, showing that theoretical insights gained from simpler domains can inform algorithm design in more realistic contexts. Adopting a methodological perspective, this thesis treats experiments not only as performance comparisons but also as instruments of explanation. They provide insight where theoretical analysis becomes too complicated, reveal structural reasons for algorithmic behavior, and highlight patterns that are valuable in their own right as well as suggestive for further theoretical study. By moving systematically from binary to integer to continuous domains, the thesis demonstrates how empirical analysis can complement proofs, how discrete insights can inform real-world optimization, and how evolutionary algorithms can be more clearly understood through an integrated view of theory, practice, and experimentation.
Xiaoyue Li (Thu,) studied this question.