The calculation of phase equilibrium with or without chemical reaction is an important problem in the field of chemistry and chemical engineering.One formulation of this problem is the minimization of Gibbs free energy with constraints.The often-used method

sequence quadratic programming(SQP)is easily trapped in the local point and depends on the initial point despite its quick convergence.The artificial immune system(AIS)is able to find the global point

but its local searching is poor and finding the trace solution is difficult.In this paper

a hybrid artificial immune system(HAIS) is constructed by making use of the advantages of AIS and SQP and adding the SQP operation to the AIS method.In order to quickly get the feasible solution or antibody and shorten the run time of HAIS

the variables of mole were transformed to the new variables of mole fraction

and an appropriate strategy is employed in dealing with the constraints.The antibodies are based on the basic feasible solution.Its performance is better than other methods

such as SQP and AIS

as shown by analyzing several phase equilibrium cases.