Aiming at the problem that many algorithms could not effectively balance the global search ability and local search ability, a new optimization algorithm is proposed. Inspired by Finite Element Analysis (FEA) approach, a relationship of mapping between Finite Element Analysis approach and a population-based optimization algorithm is constructed through comparing the similarities and differences of FEA node and ideal particle. In algorithm framework, the stiffness coefficient corresponds to a user-defined function of the value of an objective function to be optimized, and the node forces among individuals are defined and an attraction-repulsion rule is established among them. The FEA approach that can simulate multi- states of matter is adopted to balance the global search ability and local search ability in the novel optimization algorithm. A theoretical analysis is made for algorithm parallelism. The conditions for convergence are deduced through analyzing the algorithm based on discrete-time linear system theory. In addition, the performance of the algorithm is compared with PSO for five states which include free state, diffusion state, solid state, entirely solid state, synthesis state. The simulation results of six benchmark functions show that the algorithm is effective. The algorithm supplies a new method to solve optimization problem.

针对目前许多算法无法有效平衡全局搜索能力和局部搜索能力的问题，提出一种新的优化算法。受有限元分析（FEA）方法的启发，通过比较FEA节点与理想粒子的异同，构建了有限元分析方法与基于群体的优化算法之间的映射关系。在算法框架中，刚度系数对应于待优化目标函数值的用户定义函数，定义了个体之间的节点力并建立了它们之间的吸引-排斥规则。采用可模拟物质多态的有限元分析方法来平衡新型优化算法的全局搜索能力和局部搜索能力。对算法的并行性进行了理论分析。基于离散时间线性系统理论，通过分析该算法，推导了收敛条件。此外，在自由态、扩散态、固态、全固态、合成态五种状态下，该算法与PSO的性能进行了比较。6个基准函数的仿真结果表明该算法是有效的。该算法为解决优化问题提供了一种新的方法。