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针对约束多目标区间非线性优化问题,利用泰勒一阶展开将非线性函数转化成线性形式,降低了计算量,提出一种改进的NSGA-II(INSGA-II)解决上述线性形式的优化问题.该算法基于可能度定义了P占优支配关系,依据此关系求出解的序值,进而根据序值对解进行排序.利用区间数距离公式,求出各序值中解的区间拥挤距离(ICD),并对各序值中的解进行进一步排序.此外引入约束锦标赛准则,通过计算约束违背度并与约束允许违背度比较选择出种群中相对满足约束条件的解.本文将传统的NSGA-II改进成可以解决约束多目标区间优化问题的INSGA-II.仿真结果表明该算法的有效性.
In order to solve the multi-objective constrained nonlinear optimization problem, Taylor’s first-order expansion transforms the nonlinear function into a linear form and reduces the computational complexity. An improved NSGA-II solution to the above linear form optimization problem is proposed. The algorithm defines the dominant relation of P based on the degree of probability, and obtains the order value of the solution according to the relation, and then sorts the solution according to the order value. Using the interval number distance formula, the interval crowded distance ICD), and further order the solutions in each order value.In addition, the introduction of the constraint tournament criteria, by calculating the degree of constraint violation and compared with the allowable degree of constraint to select the relative satisfaction of the population constraint solution.In this paper, the traditional NSGA- II to INSGA-II, which can solve the problem of constrained multi-objective interval optimization. Simulation results show the effectiveness of the proposed algorithm.