CSV-PSO and Its Application in Geotechnical Engineering

Abstract

Since the particle swarm optimization (PSO), being a stochastic global optimization technique,was proposed by Kennedy and Eberhart in 1995(Kennedy & Eberhart, 1995; Eberhart & Kennedy, 1995), it has attracted interests of many researchers worldwide and has found many applications in various fields such as autocontrol, machinofacture, geotechnical engineering et al. (Mark & Feng, 2002; Dong et al, 2003; Su & Feng, 2005). There are two main reasons: one is the preferable performance of PSO, the other is its simplicity in operation. In order to avoid the premature and divergence phenomena often occurring in optimization process by using the PSO, especially for multi-dimension and multi-extremum complex problems, as well as to improve the convergence velocity and precision of the PSO to a maximum extent, many kinds of schemes were introduced to enhance the PSO. The following are some representative schemes: inertia weight (Shi & Eberhart, 1998), constriction factor (Eberhart & Shi, 2000), crossover operation (Lovbjerg et al, 2001) and selfadaptation (Lu & Hou, 2004). The PSO modified by introducing the inertia weight or crossover operation or self-adaptation technique has an excellent convergence capability with a decreased velocity of convergence. The PSO with a constriction factor can reach the global goal quickly, but the divergence phenomenon sporadically occurs in the optimized solutions. So we proposed an improved PSO, named CSV-PSO, in which flight velocity limit and flight space of particles are constricted dynamically with flying of particles (Chen & Feng, 2005). A great deal of numerical calculation indicates CSV-PSO has a faster convergence velocity, greater convergence probability and is a more stable. But this algorithm with a random number generator having time as its random seed may obtain different goal values at different running time. It is difficult to determine uniqueness of solution, especially for complicated engineering problem. So a random number generator with mixed congruential method is introduced to solve uncertainty of solution, and its random seed can be set artificially. To indicate advantage of the proposed algorithm, it is compared with other modified vertions and sensitivity analysis is carried out for its several important parameters, which the five benchmark functions are as examples. The results show CSV-PSO with a new random number generator is excellent. Back analysis which is based on monitoring information with numerical method is a very time-consuming job in geotechnical