The hop-like problem nature -- unveiling and modelling new features of real-world problems

Benchmarks are essential tools for the optimizer's development. Using them, we can check for what kind of problems a given optimizer is effective or not. Since the objective of the Evolutionary Computation field is to support the tools to solve hard, real-world problems, the benchmarks that resemble their features seem particularly valuable. Therefore, we propose a hop-based analysis of the optimization process. We apply this analysis to the NP-hard, large-scale real-world problem. Its results indicate the existence of some of the features of the well-known Leading Ones problem. To model these features well, we propose the Leading Blocks Problem (LBP), which is more general than Leading Ones and some of the benchmarks inspired by this problem. LBP allows for the assembly of new types of hard optimization problems that are not handled well by the considered state-of-the-art genetic algorithm (GA). Finally, the experiments reveal what kind of mechanisms must be proposed to improve GAs' effectiveness while solving LBP and the considered real-world problem.