量子遗传粒子滤波算法matlab程序

### 实现量子遗传粒子滤波算法的MATLAB代码

量子遗传粒子滤波(QGPF)是一种融合了量子计算、遗传算法和粒子滤波技术的方法，在处理复杂优化问题方面具有优势。下面提供了一个简化版的QGPF算法框架，用于说明如何在MATLAB中实现这一过程。

function [bestPosition, bestFitness] = QGPF(fitnessFunc, numParticles, numIterations, lowerBound, upperBound)
    % 初始化种群
    populationSize = size(lowerBound, 2);
    positions = rand(numParticles, populationSize).*(upperBound-lowerBound)+lowerBound;
    
    % 计算初始适应度值并找到全局最优位置
    fitnessValues = arrayfun(@(i)fitnessFunc(positions(i,:)), 1:numParticles);
    [~, idxBest] = min(fitnessValues); 
    globalBestPos = positions(idxBest,:);
    globalBestFit = fitnessValues(idxBest);

    velocity = zeros(size(positions));
    personalBestPositions = positions;

    for iter=1:numIterations
        
        % 更新速度与位置
        r1=rand();r2=rand();
        c1=2;c2=2;w=0.5;
        
        velocity=w*velocity+c1*r1.*(personalBestPositions-positions)+c2*r2.*(globalBestPos-positions);
        positions=positions+velocity;
        
        % 边界条件处理
        positions=max(min(positions,upperBound),lowerBound);
        
        % 应用量子旋转门更新个体状态
        qubitStates = quantumRotationGate(positions);
        
        % 使用遗传操作改进群体质量
        offspringPopulations = geneticOperators(qubitStates);
        
        % 测量得到新样本集
        measuredSamples = measureQuantumState(offspringPopulations);
        
        % 计算新的适应度函数值
        newFitnessValues = arrayfun(@(i)fitnessFunc(measuredSamples(i,:)), 1:size(measuredSamples,1));

        % 更新个人最佳和个人最差记录
        betterIdx=find(newFitnessValues<personalBestFitness);
        personalBestPositions(betterIdx,:) = measuredSamples(betterIdx,:);
        personalBestFitness(betterIdx)=newFitnessValues(betterIdx);
        
        % 更新全局极值
        if any(personalBestFitness<globalBestFit)
            [~,idx]=min(personalBestFitness);
            globalBestPos=personalBestPositions(idx,:);
            globalBestFit=min(personalBestFitness);
        end
    
    end
    
    bestPosition = globalBestPos;
    bestFitness = globalBestFit;
end


% 定义量子旋转门作用于输入向量上
function rotatedVectors = quantumRotationGate(inputVectors)
    theta = pi/8;% 可调参数
    rotationMatrix=[cos(theta) -sin(theta); sin(theta) cos(theta)];
    rotatedVectors=inputVectors*rotationMatrix';
end


% 遗传算子(交叉变异等)，这里仅做简单示意
function childrenPopulation = geneticOperators(parentPopulation)
    crossoverProbability = 0.8;
    mutationProbability = 0.01;
    
    n=size(parentPopulation,1)/2;
    parentsIndex=randsample(n,n,true)*2-1;
    parentPairs=reshape(parentPopulation(parentsIndex,:),[],size(parentPopulation,2),2);
    
    mask=(rand(size(parentPairs))<=crossoverProbability);
    crossedChildren=crossOver(mask,parentPairs(:,:,1),parentPairs(:,:,2));
    
    mutatedChildren=mutate(crossedChildren,mutationProbability);
    childrenPopulation=mutatedChildren(:,:);
end


% 对量子态进行测量获得经典比特串表示的结果
function classicalBits = measureQuantumState(quantumStates)
    probabilities = abs(quantumStates).^2./sum(abs(quantumStates).^2,2);
    cumulativeProbabilities = cumsum(probabilities,2);
    randomNumbers = rand(size(cumulativeProbabilities(:,1)));
    selectedIndices = sum(bsxfun(@lt,cumulativeProbabilities',randomNumbers'),1)';
    classicalBits=zeros(size(selectedIndices,1),log2(size(quantumStates,2)));
    for i=1:length(classicalBits)
        binaryString = dec2bin(selectedIndices(i)-1,floor(log2(length(quantumStates))));
        classicalBits(i,:) = str2num(binaryString')';
    end
end

此段代码展示了量子遗传粒子滤波的核心流程[^1]，包括初始化种群、迭代过程中通过量子旋转门调整方向、应用遗传操作增强多样性以及最终依据测量结果选取更优解的过程。需要注意的是实际应用场景下还需针对具体问题特性进一步细化各部分逻辑设计。