The authors propose a multi-point combinatorial optimization method based on the hierarchical structure of the solutionspace as a meta-heuristic. This method leverages the novel concept of the ”hierarchical structure of solutionspace” to perform intensive searches within current basins of attraction and diverse searches into unexplored basinsof attraction. Furthermore, during the transition to unexplored basins of attraction, interactions between search pointsare introduced based on the principle of proximity optimality. The population size, a critical parameter in this method,significantly influences search performance. A small population size weakens diversity and increases the likelihood ofconverging to a locally optimal solution. Conversely, a large population size can enhance diversity but may lead to decreasedsearch efficiency, potentially resulting in wasted search resources. Therefore, this study aims to fundamentallyinvestigate the population size in this method and analyze its impact on search performance and interaction.
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