多目标优化与相变
Multiobjective Optimization and Phase Transitions
摘要：
许多复杂系统服从通常不简单的最优性条件。多目标优化（MOO）方法通常会相互作用。最近的MOO研究复杂系统的帕累托前沿（实现最佳权衡的最佳设计）的定性方式报告。同时，传统的简单目标优化（SOO）研究往往发现相变和临界点。我们总结了一个强大的框架，占相变位于通过SOO技术，并指出什么MOO功能坚决导致相变。这些似乎是由帕累托前沿的形状决定的，而帕累托前沿同时又与热力学吉布斯曲面密切相关。事实上，热力学可以写成一个MOO，从那里可以很简单地推导出它的相变;这表明MOO-SOO和统计力学中的相变之间的相似性不仅仅是巧合。
英文摘要：
Many complex systems obey to optimality conditions that are usually not simple. Conflicting traits often interact making a Multi Objective Optimization (MOO) approach necessary. Recent MOO research on complex systems report about the Pareto front (optimal designs implementing the best trade-off) in a qualitative manner. Meanwhile, research on traditional Simple Objective Optimization (SOO) often finds phase transitions and critical points. We summarize a robust framework that accounts for phase transitions located through SOO techniques and indicates what MOO features resolutely lead to phase transitions. These appear determined by the shape of the Pareto front, which at the same time is deeply related to the thermodynamic Gibbs surface. Indeed, thermodynamics can be written as an MOO from where its phase transitions can be parsimoniously derived; suggesting that the similarities between transitions in MOO-SOO and Statistical Mechanics go beyond mere coincidence.
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