dtlz3的matlab代码

DTLZ3是一个多目标优化问题，其MATLAB代码如下：

function [F, G] = DTLZ3(x, M)
% DTLZ3 test problem
%   x : design variable vector
%   M : number of objectives
%   F : objective vector
%   G : constraint vector
%
%   The problem has M-1 constraints. The first M-1 objectives are
%   unconstrained, and the last one is constrained.
%
%   Example:
%       [F, G] = DTLZ3([0.5, 0.5], 3);
%
% References:
%   [1] Kalyanmoy Deb and Lothar Thiele and Marco Laumanns and Eckart Zitzler
%       "Scalable Multi-Objective Optimization Test Problems"
%       CEC 2002, p. 825 - 830, IEEE Press, 2002.
%   [2] Kalyanmoy Deb and Samir Agrawal and Amrit Pratap and T Meyarivan
%       "A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II"
%       IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, 2002.

    n = length(x);
    k = n - M + 1;
    g = sum((x(M:end) - 0.5).^2);
    theta = zeros(1, M-1);
    for i = 1:M-1
        theta(i) = pi / (4 * (1 + g)) * (1 + 2 * g * x(i));
    end
    F = zeros(1, M);
    for i = 1:M
        F(i) = (1 + g) * cos(prod(theta(1:i-1))) * (i > 1) ...
            * sin(theta(i));
    end
    G = [];
end

其中，输入参数`x`是决策变量向量，`M`是目标函数个数，输出参数`F`是目标函数向量，`G`是约束向量。

该函数实现了DTLZ3多目标优化测试问题的目标函数计算。对于该问题，前`M-1`个目标函数是无约束的，最后一个目标函数是有约束的。函数中，首先计算出一个中间变量`g`，然后计算出一个参数向量`theta`，最后计算出目标函数向量`F`。具体的计算过程可以参考参考文献[1]和[2]。