多目标优化非支配关系实现
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规则
- 如果个体A在所有目标上都小于等于个体B且在有至少一个目标上小于个体B则称个体A支配B。
- 如果不存在个体A支配个体B的情况并且A在至少一个目标上比B小并且B在至少一个目标上比A小,则称A和B是非支配关系
- 详细思路可以参见NSGA-II入门
matlab
% 遍历所有M个目标值
for obj_index=1:Global.M
if NewPop.obj(obj_index)<=Population(i).obj(obj_index)
% 如果目标值小于等于则计数值加1
offspringless_or_equal= offspringless_or_equal+1;
if NewPop.obj(obj_index)<Population(i).obj(obj_index)
% 如果目标值完全小于则计数值加1
offspringless=offspringless+1;
end
else parentless=parentless+1;
end
end
% 如果新解可以支配旧解
if((offspringless_or_equal==Global.M)&&(offspringless>0))
Population(i)=NewPop;
%如果两者非支配
elseif((offspringless>0)&&(parentless>0))
java
/**
* Compares two solutions.
*
* @param object1
* Object representing the first <code>Solution</code>.
* @param object2
* Object representing the second <code>Solution</code>.
* @return -1, or 0, or 1 if solution1 dominates solution2, both are
* non-dominated, or solution1 is dominated by solution22,
* respectively.
*/
public int compare(Object object1, Object object2) {
if (object1 == null)
return 1;
else if (object2 == null)
return -1;
Solution solution1 = (Solution) object1;
Solution solution2 = (Solution) object2;
int dominate1; // dominate1 indicates if some objective of solution1
// dominates the same objective in solution2. dominate2
int dominate2; // is the complementary of dominate1.
dominate1 = 0;
dominate2 = 0;
int flag; // stores the result of the comparison
// Test to determine whether at least a solution violates some
// constraint
if (violationConstraintComparator_.needToCompare(solution1, solution2))
return violationConstraintComparator_.compare(solution1, solution2);
/*
* if (solution1.getOverallConstraintViolation()!=
* solution2.getOverallConstraintViolation() &&
* (solution1.getOverallConstraintViolation() < 0) ||
* (solution2.getOverallConstraintViolation() < 0)){ return
* (overallConstraintViolationComparator_.compare(solution1,solution2));
* }
*/
// Equal number of violated constraints. Applying a dominance Test then
double value1, value2;
for (int i = 0; i < solution1.getNumberOfObjectives(); i++) {
// solution1.getNumberofbjectives中存储的是所有Task的目标函数数,而此处仅仅评价的是isChosen出来的目标函数
if (!isChosen_[i])
continue;
value1 = solution1.getObjective(i);
value2 = solution2.getObjective(i);
if (value1 < value2) {
flag = -1;
} else if (value1 > value2) {
flag = 1;
} else {
flag = 0;
}
if (flag == -1) {
dominate1 = 1;
}
if (flag == 1) {
dominate2 = 1;
}
}
if (dominate1 == dominate2) {
return 0; // No one dominate the other 两个解都至少有一个目标比另一个目标好
}
if (dominate1 == 1) {
return -1; // solution1 dominate 这几个函数的位置十分关键,如果两者非支配,return语句直接返回0值,此处还能进行到,必定是不满足以上条件。
}
return 1; // solution2 dominate
} // compare
} // DominanceComparator
better or worst
count=0;
frontnumbers=[];
for i=1:pop
for j=i:pop
if i==j
continue;
end
better=0;
worse=0;
if population(i).convio < population(j).convio
% convio是ZDT4-RC才会使用的属性
population(i).dominatedset=[population(i).dominatedset j];% 但是j是索引,不是个体还是需要注意!
population(i).dominatedsetlength=population(i).dominatedsetlength+1;% 支配解的数量
population(j).dominationcount=population(j).dominationcount+1;% 被支配解的数量
% 相对而言,如果j支配了i的话
elseif population(i).convio > population(j).convio
population(j).dominatedset=[population(j).dominatedset i];
population(j).dominatedsetlength=population(j).dominatedsetlength+1;
population(i).dominationcount=population(i).dominationcount+1;
else
% 最后是为非ZDT-RC问题设计的,因为非ZDT4-RC中没有convio参数
for k = 1:no_of_objs
if population(1).skill_factor == 1
if population(i).objs_T1(k) < population(j).objs_T1(k)
better=1;
elseif population(i).objs_T1(k) > population(j).objs_T1(k)
worse=1;
end
else
if population(i).objs_T2(k) < population(j).objs_T2(k)
better=1;
elseif population(i).objs_T2(k) > population(j).objs_T2(k)
worse=1;
end
end
end
if worse==0 && better>0 %如果j在任何一个目标上都不比i好,并且i在一个目标上比j好
population(i).dominatedset=[population(i).dominatedset j];
population(i).dominatedsetlength=population(i).dominatedsetlength+1;
population(j).dominationcount=population(j).dominationcount+1;
elseif better==0 && worse>0%如果i在任何一个目标上都不比i好,并且j在一个目标上比j好
population(i).dominationcount=population(i).dominationcount+1;
population(j).dominatedset=[population(j).dominatedset i];
population(j).dominatedsetlength=population(j).dominatedsetlength+1;
end
end
end
% 如果没有解可以支配当前解,则被认为是非支配前沿
if population(i).dominationcount==0
population(i).front=1;
count=count+1;
end
end