Improved NSGA-II for Constrained Multi-objective Optimization Problems with Interval Numbers
Chen Zhi-wan · Journal of Chinese Computer Systems · 2014
For the constrained multi-objective nonlinear optimization problems with interval numbers,firstly,in order to reduce the computational complexity,nonlinear functions of optimization problems are transformed into linear ones by using the first-order Taylor expansion,then the improved NSGA-II( INSGA-II) is proposed for the transformed linear optimization problems. In INSGA-II,P dominance relationship is defined based on the interval possibility degree,which is applied in getting the rank values of solutions. Furthermore,each solution is sorted according to its rank value. Secondly,the proposed algorithm utilizes the interval distance formula to evaluate the interval crowding distance( ICD) of solutions of the same rank value then sorts solutions in order of their interval crowding distance. Finally,a constrained tournament rule is used to select the solutions of correspondingly satisfying constraint from the population,and the constraint violation degree of solutions are compared with the allowable constraint violation degree in the rule. In the paper,the traditional NSGA-II for the certainty optimization is improved so that it can solve the constrained multi-objective optimization problems with interval numbers. The feasibility of the proposed algorithm is validated by simulation results.