多目标优化非支配关系实现

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