Abstract: The PVD ( Pressure Vessel Design) problem is a classical practical problem to confirm the ability of algorithms． Solving the PVD problem by CGSA is difficult． Thus， CGSA9 + is proposed． First， the interdependence relationship among variables in PVD is analyzed，then the stochastic order of dimensions is identified． After that，the generation rule is updated based on the rule of CGSA and the current position of the global optimum． Finally，the solutions satisfing the constrained conditions is verified to evaluate the objective function． According to the experimental results，this algorithm solves PVD problem effectively and it performs well．

Key words: chaotic gravitational constants for the gravitational search algorithm, pressure vessel design problem, constrained optimization