One of the widely used models for studying economics of climate change is the Dynamic Integrated model of Climate and Economy (DICE), which has been developed by Professor William Nordhaus, one of the laureates of the 2018 Nobel Memorial Prize in Economic Sciences. Originally a single-objective optimal control problem has been defined on DICE dynamics, which is aimed to maximize the social welfare. In this paper, a bi-objective optimal control problem defined on DICE model, objectives of which are maximizing social welfare and minimizing the temperature deviation of atmosphere. This multi-objective optimal control problem solved using Non-Dominated Sorting Genetic Algorithm II (NSGA-II) also it is compared to previous works on single-objective version of the problem. The resulting Pareto front rediscovers the previous results and generalizes to a wide range of non-dominant solutions to minimize the global temperature deviation while optimizing the economic welfare. The previously used single-objective approach is unable to create such a variety of possibilities, hence, its offered solution is limited in vision and reachable performance. Beside this, resulting Pareto-optimal set reveals the fact that temperature deviation cannot go below a certain lower limit, unless we have significant technology advancement or positive change in global conditions.

中文翻译：

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气候与经济动态综合模型的多目标优化控制：进化在行动

研究气候变化经济学的广泛使用的模型之一是气候与经济动态综合模型 (DICE)，该模型由 2018 年诺贝尔经济学奖获得者之一威廉·诺德豪斯教授开发。最初在 DICE 动力学上定义了一个单目标最优控制问题，其目的是最大化社会福利。在本文中，定义了一个基于 DICE 模型的双目标最优控制问题，其目标是最大化社会福利和最小化大气温度偏差。这个使用非支配排序遗传算法 II (NSGA-II) 解决的多目标最优控制问题也与之前在该问题的单目标版本上的工作进行了比较。由此产生的帕累托前沿重新发现了先前的结果，并推广到广泛的非主导解决方案，以在优化经济福利的同时最小化全球温度偏差。以前使用的单目标方法无法创造如此多种可能性，因此其提供的解决方案在视觉和可达到的性能方面受到限制。除此之外，由此产生的帕累托最优集揭示了温度偏差不能低于某个下限的事实，除非我们有重大的技术进步或全球条件的积极变化。其提供的解决方案在视觉和可达到的性能方面受到限制。除此之外，由此产生的帕累托最优集揭示了温度偏差不能低于某个下限的事实，除非我们有重大的技术进步或全球条件的积极变化。其提供的解决方案在视觉和可达到的性能方面受到限制。除此之外，由此产生的帕累托最优集揭示了温度偏差不能低于某个下限的事实，除非我们有重大的技术进步或全球条件的积极变化。