绘制(动态)约束多目标优化问题真实前沿

目标优化问题真实前沿"/>

绘制(动态)约束多目标优化问题真实前沿

编程了一种采点约束多目标优化基准测试问题(包括动态约束多目标优化基准测试问题)真实前沿的程序。点击获取程序

get_ptrue(name,f1_step,f1_up,f2_step,f2_up,t,flag1,flag2,flag3)

%% 参数意义

% name    测试函数名

% f1_step 目标1采点步长

% f1_up   目标1最大长度

% f2_step 目标2采点步长

% f2_up   目标2最大长度

% t       时间

% flag1   为1输出可行域和真实前沿

% flag2   为1输出前沿数据至文件夹

% flag3   为1在flag1为1的基础上输出无约束真实前沿

约束多目标测试函数[1]

CTP1

目的：使得无约束真实前沿一部分变的不可行

当J=2时

 每个约束都是非线性隐函数，在边界上找到许多可行解可能是困难的

get_ptrue('CTP1',0.001,1,0.001,1.25,1,1,0,1)

 CTP2-7

约束使得无约束的最优区域变的不可行，从而使得最优解是离散区域或离散的点的集合。

 get_ptrue('CTP2',0.001,1,0.001,1.25,1,1,0,1)

 get_ptrue('CTP3',0.001,1,0.001,1.25,1,1,0,1)

a是将连续可行区域过度到远离最优解区域的不连续可行区域 

 ,

 get_ptrue('CTP4',0.001,1,0.001,2,1,1,0,1)

c+1可以使得离散的最优解非均匀分散

c>1更多的最优解位于右侧

c<1更多的最优解位于左侧

控制最优区域的斜率,e在目标空间移动约束

 ,

 get_ptrue('CTP5',0.001,1,0.001,1.5,1,1,0,1)

get_ptrue('CTP6',0.001,1,0.001,20,1,1,0,1) 

 get_ptrue('CTP7',0.001,1,0.001,1.5,1,1,0,1)

 动态约束多目标测试函数1[2]

 

  动态约束多目标测试函数2[3]

a = 0.2; b = 5; c = 1; d = 6; e = 1; s1 = -0.25*pi; zt = 6; sl=1; s2=-pi/16;

for t = 0:0.5:20

get_ptrue('DCF1',0.01,1,0.01,7,t,1,0,0)

hold on

pause(0.5)

end

PF 连续→间断→连续

可行域      增大→减小

 for t = 0:0.5:20

get_ptrue('DCF2',0.01,1,0.01,7,t,1,0,0)

hold on

pause(0.5)

end

可行域      减小→增大

PF 间断→连续→间断

for t = 0:0.5:20

get_ptrue('DCF3',0.01,1,0.01,7,t,1,0,0)

hold on

pause(0.5)

end

可行域          增大→减小

PF       间断→连续→间断

for t = 0:0.5:20

get_ptrue('DCF4',0.01,1,0.01,7,t,1,0,0)

hold on

pause(0.5)

end

可行域         减小→增大

PF     连续→间断→连续

参考文献

[1] K. Deb, A. Pratap, and T. Meyarivan, “Constrained test problems for multi-objective evolutionary optimization,” in Proc. Int. Conf. Evol. Multi Criterion Optim. (EMO), 2001, pp. 284–298.

[2]Radhia Azzouz, Slim Bechikh, and Lamjed Ben Said. 2015. Multi-objective Optimization with Dynamic Constraints and Objectives: New Challenges for Evolutionary Algorithms. In Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation (GECCO '15). Association for Computing Machinery, New York, NY, USA, 615–622.

[3]Q. Chen, J. Ding, S. Yang and T. Chai, “A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems,” IEEE Transactions on Evolutionary Computation, vol. 24, no. 4, pp. 792-806, Aug. 2020.