中文摘要：

提出了采用基因表达式编程（Gene Expression Programming,GEP）和混合粒子群相结合计算边坡可靠度的新方法。该方法采用均匀设计法确定样本点,通过数值计算求解安全系数,应用GEP方法拟合边坡的功能函数;借鉴遗传算法中的杂交概念,将其引入标准粒子群方法（Particle Swarm Optimization,PSO）,形成混合粒子群方法（MPSO）,改善了PSO方法的全局搜索能力,提高了方法的收敛速度和计算精度,可用于计算可靠度指标及相应的验算点。以2个典型的边坡为例,通过算例1与其他方法对比,验证了MPSO方法较标准PSO方法计算精度高、收敛速度快;分析了算法中各控制参数对可靠度指标的影响;算例2为隐式功能函数问题,将MPSO方法与GEP方法相结合求解可靠度指标。结果表明：MPSO-GEP方法对求解隐式功能函数的边坡可靠性问题具有很好的适应性,该方法科学可行且具有很好的应用前景。

英文摘要：

This paper puts forward using a new method to combine gene expression programming（GEP） with mixed particle swarm optimization （MPSO） to calculate reliability of slope. It adopts uniform de- sign to determine the sample points, and uses numerical method to solve safety factor. It can be used to fit the performance function of slope. Using the concept of hybrid genetic algorithms for reference, by introducing the standard Particle Swarm methods （particle swarm optimization, PSO）, it forms a mixed particle swarm optimization （MPSO）. This method can improve the global searching ability, conver- gence rate and computational accuracy, and can be used to calculate reliability index and the correspond- ing check points. Taking two typical slopes for examples, by comparing to other methods, the first ex- ample shows that MPSO method has higher precision and fast convergence speed than standard PSO; It also analyzes the effect of each control parameter in algorithm on reliability index; The second example is a problem about implicit performance function, in which the reliability index is calculated by combining MPSO method and GEP method. The results show that, this method has good adaptive ability to solve the reliability analysis problem with implicit performance function, and it is scientific and feasible and has st good application prospect.