金鹰优化算法（golden eagle optimizer, GEO）是于2020年提出的新型智能优化算法，该算法建立于金鹰个体 捕食过程中的巡航和攻击行为之上，通过平衡两者关系，帮助函数寻找最优值，已经在许多方面得到了应用。

关于金鹰算法的原理本篇文章就不再细讲，作者采用金鹰算法在CEC2005函数上进行测试，结果如下：

金鹰算法的核心代码如下：

function [x,fval,ConvergenceCurve] = GEO (fun,nvars,lb,ub,options)
%% initialization
PopulationSize = options.PopulationSize;
MaxIterations = options.MaxIterations;
ConvergenceCurve  = zeros (1, MaxIterations);
if length(lb) ~= (nvars)
    lb=lb.*ones(1,nvars);
    ub=ub.*ones(1,nvars);
end
x = lb + rand (PopulationSize,nvars) .* (ub-lb);
for i = 1:size(x,1)
    FitnessScores(i,:) = fun (x(i,:));
end
% solver-specific initialization
FlockMemoryF = FitnessScores;
FlockMemoryX = x;
AttackPropensity = linspace (options.AttackPropensity(1), options.AttackPropensity(2), MaxIterations);
CruisePropensity = linspace (options.CruisePropensity(1), options.CruisePropensity(2), MaxIterations);
%% main loop
for CurrentIteration = 1 : MaxIterations
  % prey selection (one-to-one mapping)
  DestinationEagle = randperm (PopulationSize)';


  % calculate AttackVectorInitial (Eq. 1 in paper)
  AttackVectorInitial = FlockMemoryX (DestinationEagle,:) - x;


  % calculate Radius
  Radius = VecNorm (AttackVectorInitial, 2, 2);


  % determine converged and unconverged eagles
  ConvergedEagles = sum (Radius,2) == 0;
  UnconvergedEagles = ~ ConvergedEagles;


  % initialize CruiseVectorInitial
  CruiseVectorInitial = 2 .* rand (PopulationSize, nvars) - 1; % [-1,1]


  % correct vectors for converged eagles
  AttackVectorInitial (ConvergedEagles, :) = 0;
  CruiseVectorInitial (ConvergedEagles, :) = 0;


  % determine constrained and free variables
  for i1 = 1 : PopulationSize
    if UnconvergedEagles (i1)
      vConstrained = false ([1, nvars]); % mask
      idx = datasample (find(AttackVectorInitial(i1,:)), 1, 2);
      vConstrained (idx) = 1;
      vFree = ~vConstrained;
      CruiseVectorInitial (i1,idx) = - sum(AttackVectorInitial(i1,vFree).*CruiseVectorInitial(i1,vFree),2) ./ (AttackVectorInitial(i1,vConstrained)); % (Eq. 4 in paper)
    end
  end


  % calculate unit vectors
  AttackVectorUnit = AttackVectorInitial ./ VecNorm (AttackVectorInitial, 2, 2);
  CruiseVectorUnit = CruiseVectorInitial ./ VecNorm (CruiseVectorInitial, 2, 2);


  % correct vectors for converged eagles
  AttackVectorUnit(ConvergedEagles,:) = 0;
  CruiseVectorUnit(ConvergedEagles,:) = 0;


  % calculate movement vectors
  AttackVector = rand (PopulationSize, 1) .* AttackPropensity(CurrentIteration) .* Radius .* AttackVectorUnit; % (first term of Eq. 6 in paper)
  CruiseVector = rand (PopulationSize, 1) .* CruisePropensity(CurrentIteration) .* Radius .* CruiseVectorUnit; % (second term of Eq. 6 in paper)
  StepVector = AttackVector + CruiseVector;


  % calculate new x
  x = x + StepVector;


  % enforce bounds
  lbExtended = repmat (lb,[PopulationSize,1]);
  ubExtended = repmat (ub,[PopulationSize,1]);


  lbViolated = x < lbExtended;
  ubViolated = x > ubExtended;


  x (lbViolated) = lbExtended (lbViolated);
  x (ubViolated) = ubExtended (ubViolated);


  % calculate fitness
    for i = 1:size(x,1)
        FitnessScores(i,:) = fun (x(i,:));
    end


  % update memory
  UpdateMask = FitnessScores < FlockMemoryF;
  FlockMemoryF (UpdateMask) = FitnessScores (UpdateMask);
  FlockMemoryX (UpdateMask,:) = x (UpdateMask,:);


  % update convergence curve
  ConvergenceCurve (CurrentIteration) = min (FlockMemoryF);


end


%% return values


[fval, fvalIndex] = min (FlockMemoryF);
x = FlockMemoryX (fvalIndex, :);


fprintf ('Best solution obtained by GEO: %s\n', num2str(x,'%e  '));
fprintf ('Best objective function value obtained by GEO: %e \n', fval);

需要的同学直接粘贴用于自己的实际问题即可。下期内容会对金鹰算法进行改进，敬请关注。

后台回复关键词：TGDM1209，获取完整代码。

参考文献：

Mohammadi-Balani, A., Dehghan Nayeri, M., Azar, A., Taghizadeh-Yazdi, M., Golden Eagle Optimizer: A nature-inspired metaheuristic algorithm, Computers & Industrial Engineering (2020).