Context: Software model optimization is a process that automatically generates design alternatives, typically to enhance quantifiable non-functional properties of software systems, such as performance and reliability. Multi-objective evolutionary algorithms have shown to be effective in this context for assisting the designer in identifying trade-offs between the desired non-functional properties. Objective: In this work, we investigate the effects of imposing a time budget to limit the search for design alternatives, which inevitably affects the quality of the resulting alternatives. Method: The effects of time budgets are analyzed by investigating both the quality of the generated design alternatives and their structural features when varying the budget and the genetic algorithm (NSGA-II, PESA2, SPEA2). This is achieved by employing multi-objective quality indicators and a tree-based representation of the search space. Results: The study reveals that the time budget significantly affects the quality of Pareto fronts, especially for performance and reliability. NSGA-II is the fastest algorithm, while PESA2 generates the highest-quality solutions. The imposition of a time budget results in structurally distinct models compared to those obtained without a budget, indicating that the search process is influenced by both the budget and algorithm selection. Conclusions: In software model optimization, imposing a time budget can be effective in saving optimization time, but designers should carefully consider the trade-off between time and solution quality in the Pareto front, along with the structural characteristics of the generated models. By making informed choices about the specific genetic algorithm, designers can achieve different trade-offs.

翻译：摘要：背景：软件模型优化是一个自动生成设计备选方案的过程，通常旨在提升软件系统的可量化非功能属性（如性能和可靠性）。多目标进化算法在此背景下已被证明能有效协助设计者识别所需非功能属性间的权衡。目标：本文研究施加时间预算限制设计备选方案搜索所带来的影响，这种限制不可避免地影响最终备选方案的质量。方法：通过研究不同时间预算和遗传算法（NSGA-II、PESA2、SPEA2）下生成的设计备选方案质量及其结构特征，分析时间预算的影响。采用多目标质量指标和基于树的搜索空间表示实现这一分析。结果：研究表明时间预算显著影响帕累托前沿的质量，尤其对性能和可靠性影响明显。NSGA-II是最快的算法，而PESA2能生成最高质量的解。施加时间预算会导致生成模型在结构上与无预算情况存在显著差异，表明搜索过程同时受预算和算法选择的影响。结论：在软件模型优化中，施加时间预算能有效节省优化时间，但设计者需谨慎权衡帕累托前沿中时间与解的质量，以及生成模型的结构特征。通过明智选择特定的遗传算法，设计者可实现不同的权衡方案。