We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple bound constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours in terms of performance, disruptiveness, and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants, on a special test function and the BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem dimensionality. Differential Evolution is not at all special in this regard—there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the heuristic optimisation community to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we refer to as the strategy of dealing with infeasible solutions. This component needs to be consistently: (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on an algorithm's performance in a wider sense (i.e., convergence time, robustness, etc.), and (c) included in the (automatic) design of algorithms. All of these should be done even for problems with bound constraints.

我们认为，启发式优化算法产生的结果不能被认为是可重现的，除非该算法完全指定了应该如何处理域外生成的解决方案，即使在简单的边界约束的情况下也是如此。目前，在启发式优化领域，由于假设这个问题的琐碎或无关紧要，因此很少提及或研究这种规范。在这里，我们证明，至少在基于差异进化的算法中，这种选择会在性能、破坏性和群体多样性方面引起显着不同的行为。这在没有选择压力的情况下对标准差分进化在理论上（如果可能）得到了证明，并且在特殊测试函数和 BBOB 基准测试套件上分别对标准和最先进的差分进化变体进行了实验。此外，我们证明这种选择的重要性随着问题维度的增加而迅速增长。差分进化在这方面一点也不特殊——没有理由假设其他启发式优化器不会同样受到上述算法选择的影响。因此，我们敦促启发式优化社区在启发式优化器中形式化并采用新算法组件的想法，我们将其称为处理不可行解决方案的策略。该组件需要一致：(a) 在算法描述中指定，以保证结果的可重复性，(b) 研究以更好地理解其对更广泛意义上的算法性能的影响（即收敛时间、鲁棒性等），以及(c) 包含在算法的（自动）设计中。即使对于有边界约束的问题也应该完成所有这些操作。