受约束的重要性:处理微分进化论中的不可行解及其他问题

IF 4.6 2区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Anna V Kononova, Diederick Vermetten, Fabio Caraffini, Madalina-A Mitran, Daniela Zaharie
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引用次数: 0

摘要

我们认为,启发式优化算法产生的结果不能被认为是可重复的,除非该算法充分说明应该如何处理域外产生的解,即使是在简单约束的情况下。目前,在启发式优化领域,由于假定这个问题微不足道或无关紧要,很少有人提及或研究这种说明。在这里,我们证明,至少在基于差分进化的算法中,这种选择会在性能、破坏性和种群多样性方面引起明显不同的行为。我们从理论上(在可能的情况下)证明了标准差分进化算法在没有选择压力的情况下的表现,并从实验上证明了标准差分进化算法和最先进的差分进化算法变体在特殊测试函数和 BBOB 基准测试套件上的表现。此外,我们还证明了这一选择的重要性随着问题维度的增加而迅速增加。差分进化论在这方面并不特殊--我们没有理由认为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正式提出并采用启发式优化器中的新算法组件这一理念,我们将其称为处理不可行解的策略。这个组成部分需要始终如一:(a)在算法描述中具体说明,以保证结果的可重复性;(b)对其进行研究,以更好地理解其对算法性能的广泛影响(即收敛时间、鲁棒性等);(c)将其纳入算法的(自动)设计中。即使对于有约束条件的问题,也应进行所有这些研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Importance of Being Constrained: Dealing with Infeasible Solutions in Differential Evolution and Beyond.

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.

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来源期刊
Evolutionary Computation
Evolutionary Computation 工程技术-计算机:理论方法
CiteScore
6.40
自引率
1.50%
发文量
20
审稿时长
3 months
期刊介绍: Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.
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