Open Access
 Issue JNWPU Volume 37, Number 5, October 2019 1000 - 1010 https://doi.org/10.1051/jnwpu/20193751000 14 January 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 基本知识

x到第j个约束的距离定义为

1.2 差分进化算法

1) “DE/rand/1”

2) “DE/best/1”

3) “DE/rand/2”

4) “DE/rand-to-best/1”

5) “DE/current-to-rand/1”

1.3 广义反向学习策略

n维空间中，设是个体xi=(xi, 1, xi, 2, …, xi, n)的反向解，则定义为

for i=1 to NP do

for j=1 to n do

PGOPji, 0=k*(aj+bj)-Pji, 0;

if PGOPji, 0 < ajPGOPji, 0>bj then

PGOPji, 0=rand(aj, bj);

end if

end for

end for

if rand(0, 1) < Jr then//Jr为代跳率

for i=1 to NP do

for j=1 to n do

PGOPji, t=k*(min(Pji, t)+max(Pji, t))-Pji, t;

if PGOPji, t < min(Pji, t)‖PGOPji, t>max(Pji, t)then

PGOPji, t=rand(min(Pji, t), max(Pji, t));

end if

end for

end for

end

2 自适应约束差分进化算法

2.2 改进自适应排序变异操作

2.2.2 选择概率计算

 图 1选择概率与个体排序值关系

2.2.3 变异操作

if rand(0, 1) < then

vi, t=x1, t+FZ·((xr2, t-xi, t)+(xr3, t-xr4, t));

else

vi, t=x1, t+Fz·((xrbest, t-xr2, t)+(xr3, t-xi, t));

end

3 GOBL-ACDE算法流程

t=1;// t为进化代数

while不满足终止条件do

for i=1 to NP do

for j=1 to n do

执行算法3生成vi, j;

if rand(0, 1) < Cri, j or then

ui, j=vi, j

else    ui, j=xi, j

end if

end for

for i=1 to NP do

if f(ui)≤f(xi) then

xi, t+1=ui, t;

else

xi, t+1=xi, t

end if

end for

执行算法2进行种群代跳;

t=t+1;

end while

4 试验测试及结果分析

4.2 广义反向学习性能分析

GOBL-ACDE和ACDE运行结果

GOBL-ACDE和ACDE平均函数评价次数对比

 图 2GOBL-ACDE与ACDE收敛性比较图

4.3 改进自适应排序变异操作性能分析

GOBL-ACDE和GOBL-CDE平均函数评价次数对比

 图 3GOBL-ACDE与ACDE收敛性比较图

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All Tables

GOBL-ACDE和ACDE运行结果

GOBL-ACDE和ACDE平均函数评价次数对比

GOBL-ACDE和GOBL-CDE平均函数评价次数对比

All Figures

 图 1选择概率与个体排序值关系 In the text
 图 2GOBL-ACDE与ACDE收敛性比较图 In the text
 图 3GOBL-ACDE与ACDE收敛性比较图 In the text

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