Complex systems typically have a large parameter space and by definition have the potential for strong emergent behavior, especially when operating in a complex environment. A method is needed to design a system that will be resilient in a complex target operating environment. Here, we propose a maximin optimization approach to support the exploration of system design, based on co‐evolutionary system/environment models, which emphasizes the importance of the operating environment in the system evolution, resulting in increased system resilience. In this paper, this method is demonstrated on an air defense system and shows an increase in resilience when compared to the system resulting from the application of a genetic algorithm such as has been previously demonstrated for other systems. For the air defense system used here, the proposed maximin optimization process significantly (, via a one‐sided paired t‐test) increased the resulting system resilience from 0.64 (the resilience of the system designed by a genetic algorithm) to 0.92 (the resilience of the system designed by maximin optimization).

中文翻译：

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利用maximin优化方法来最大化系统弹性

复杂的系统通常具有较大的参数空间，并且根据定义，它具有产生强烈紧急行为的潜力，尤其是在复杂环境中运行时。需要一种方法来设计一种在复杂目标操作环境中具有弹性的系统。在此，我们基于共同进化的系统/环境模型提出了一种最大化优化方法，以支持系统设计的探索，该方法强调了操作环境在系统演进中的重要性，从而提高了系统的弹性。在本文中，此方法在防空系统上进行了演示，与以前应用其他系统证明的遗传算法所产生的系统相比，该方法具有更高的弹性。对于这里使用的防空系统，，通过单面配对t检验，将系统的弹性从0.64（由遗传算法设计的系统的弹性）提高到0.92（由maximin最优化设计的系统的弹性）。