Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional algorithms may struggle to deal with such problems. A current trend is to use nature-inspired algorithms due to their flexibility and effectiveness. However, there are some key issues concerning nature-inspired computation and swarm intelligence. This paper provides an in-depth review of some recent nature-inspired algorithms with the emphasis on their search mechanisms and mathematical foundations. Some challenging issues are identified and five open problems are highlighted, concerning the analysis of algorithmic convergence and stability, parameter tuning, mathematical framework, role of benchmarking and scalability. These problems are discussed with the directions for future research.

受复杂非线性约束的影响，科学和工程中的许多问题都可以表述为优化问题。高度非线性问题的解决方案通常需要复杂的优化算法，而传统算法可能很难解决此类问题。由于其灵活性和有效性，当前的趋势是使用自然启发算法。但是，存在一些与自然相关的计算和群智能有关的关键问题。本文对一些最近的自然启发式算法进行了深入的综述，重点是它们的搜索机制和数学基础。确定了一些具有挑战性的问题，并突出了五个未解决的问题，涉及算法收敛性和稳定性分析，参数调整，数学框架，基准测试和可伸缩性的作用。对这些问题进行了讨论，并提出了今后研究的方向。