【WSN覆盖优化Matlab代码】基于改进花朵授粉算法实现带障碍物的异构无线传感器网络部署优化

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智能优化算法       神经网络预测       雷达通信      无线传感器        电力系统

信号处理              图像处理               路径规划       元胞自动机        无人机

🔥 内容介绍

针对监测区域内含有障碍物的无线传感器网络(Wireless Sensor Networks,WSNs)异构节点部署优化问题,在花朵授粉算法(Flower Pollination Algorithm,FPA)的基础之上,提出了一种改进的花朵授粉算法(Improved Flower Pollination Algorithm,FPA)用于改善原有算法收敛速度慢、精度不够高的不足.设计非线性收敛因子以约束原有的缩放因子,采用Tent映射以维持迭代后期种群的多样性,而贪心交叉策略则是以较优的个体辅助较差个体搜索.基准函数实验验证了IFPA具有较好的收敛性能,而WSN部署的仿真实验表明IFPA可得到较高的覆盖率,可节约网络部署成本.    

📣 部分代码

function [rowsol,cost,v,u,costMat] = lapjv(costMat,resolution)% LAPJV  Jonker-Volgenant Algorithm for Linear Assignment Problem.%% [ROWSOL,COST,v,u,rMat] = LAPJV(COSTMAT, resolution) returns the optimal column indices,% ROWSOL, assigned to row in solution, and the minimum COST based on the% assignment problem represented by the COSTMAT, where the (i,j)th element% represents the cost to assign the jth job to the ith worker.% The second optional input can be used to define data resolution to% accelerate speed.% Other output arguments are:% v: dual variables, column reduction numbers.% u: dual variables, row reduction numbers.% rMat: the reduced cost matrix.%% For a rectangular (nonsquare) costMat, rowsol is the index vector of the% larger dimension assigned to the smaller dimension.%% [ROWSOL,COST,v,u,rMat] = LAPJV(COSTMAT,resolution) accepts the second% input argument as the minimum resolution to differentiate costs between% assignments. The default is eps.%% Known problems: The original algorithm was developed for integer costs.% When it is used for real (floating point) costs, sometime the algorithm% will take an extreamly long time. In this case, using a reasonable large% resolution as the second arguments can significantly increase the% solution speed.%% See also munkres, Hungarian​% version 1.0 by Yi Cao at Cranfield University on 3rd March 2010% version 1.1 by Yi Cao at Cranfield University on 19th July 2010% version 1.2 by Yi Cao at Cranfield University on 22nd July 2010% version 2.0 by Yi Cao at Cranfield University on 28th July 2010% version 2.1 by Yi Cao at Cranfield University on 13th August 2010% version 2.2 by Yi Cao at Cranfield University on 17th August 2010% version 3.0 by Yi Cao at Cranfield University on 10th April 2013​% This Matlab version is developed based on the orginal C++ version coded% by Roy Jonker @ MagicLogic Optimization Inc on 4 September 1996.% Reference:% R. Jonker and A. Volgenant, "A shortest augmenting path algorithm for% dense and spare linear assignment problems", Computing, Vol. 38, pp.% 325-340, 1987.​%% Examples% Example 1: a 5 x 5 example%{[rowsol,cost] = lapjv(magic(5));disp(rowsol); % 3 2 1 5 4disp(cost);   %15%}% Example 2: 1000 x 1000 random data%{n=1000;A=randn(n)./rand(n);tic[a,b]=lapjv(A);toc                 % about 0.5 seconds %}% Example 3: nonsquare test%{n=100;A=1./randn(n);tic[a,b]=lapjv(A);toc % about 0.2 secA1=[A zeros(n,1)+max(max(A))];tic[a1,b1]=lapjv(A1);toc % about 0.01 sec. The nonsquare one can be done faster!%check resultsdisp(norm(a-a1))disp(b-b)%}​if nargin<2    maxcost=min(1e16,max(max(costMat)));    resolution=eps(maxcost);end% Prepare working data[rdim,cdim] = size(costMat);M=min(min(costMat));if rdim>cdim    costMat = costMat';    [rdim,cdim] = size(costMat);    swapf=true;else    swapf=false;enddim=cdim;costMat = [costMat;2*M+zeros(cdim-rdim,cdim)];costMat(costMat~=costMat)=Inf;maxcost=max(costMat(costMat<Inf))*dim+1;if isempty(maxcost)    maxcost = Inf;endcostMat(costMat==Inf)=maxcost;% free = zeros(dim,1);      % list of unssigned rows% colist = 1:dim;         % list of columns to be scaed in various ways% d = zeros(1,dim);       % 'cost-distance' in augmenting path calculation.% pred = zeros(dim,1);    % row-predecessor of column in augumenting/alternating path.v = zeros(1,dim);         % dual variables, column reduction numbers.rowsol = zeros(1,dim)-1;  % column assigned to row in solutioncolsol = zeros(dim,1)-1;  % row assigned to column in solution​numfree=0;free = zeros(dim,1);      % list of unssigned rowsmatches = zeros(dim,1);   % counts how many times a row could be assigned.% The Initilization Phase% column reductionfor j=dim:-1:1 % reverse order gives better results    % find minimum cost over rows    [v(j), imin] = min(costMat(:,j));    if ~matches(imin)        % init assignement if minimum row assigned for first time        rowsol(imin)=j;        colsol(j)=imin;    elseif v(j)<v(rowsol(imin))        j1=rowsol(imin);        rowsol(imin)=j;        colsol(j)=imin;        colsol(j1)=-1;    else        colsol(j)=-1; % row already assigned, column not assigned.    end    matches(imin)=matches(imin)+1;end​% Reduction transfer from unassigned to assigned rowsfor i=1:dim    if ~matches(i)      % fill list of unaasigned 'free' rows.        numfree=numfree+1;        free(numfree)=i;    else        if matches(i) == 1 % transfer reduction from rows that are assigned once.            j1 = rowsol(i);            x = costMat(i,:)-v;            x(j1) = maxcost;            v(j1) = v(j1) - min(x);        end    endend​% Augmenting reduction of unassigned rowsloopcnt = 0;while loopcnt < 2    loopcnt = loopcnt + 1;    % scan all free rows    % in some cases, a free row may be replaced with another one to be scaed next    k = 0;    prvnumfree = numfree;    numfree = 0;    % start list of rows still free after augmenting row reduction.    while k < prvnumfree        k = k+1;        i = free(k);        % find minimum and second minimum reduced cost over columns        x = costMat(i,:) - v;        [umin, j1] = min(x);        x(j1) = maxcost;        [usubmin, j2] = min(x);        i0 = colsol(j1);        if usubmin - umin > resolution             % change the reduction of the minmum column to increase the            % minimum reduced cost in the row to the subminimum.            v(j1) = v(j1) - (usubmin - umin);        else % minimum and subminimum equal.            if i0 > 0 % minimum column j1 is assigned.                % swap columns j1 and j2, as j2 may be unassigned.                j1 = j2;                i0 = colsol(j2);            end        end        % reassign i to j1, possibly de-assigning an i0.        rowsol(i) = j1;        colsol(j1) = i;        if i0 > 0 % ,inimum column j1 assigned easier            if usubmin - umin > resolution                % put in current k, and go back to that k.                % continue augmenting path i - j1 with i0.                free(k)=i0;                k=k-1;            else                % no further augmenting reduction possible                % store i0 in list of free rows for next phase.                numfree = numfree + 1;                free(numfree) = i0;            end        end    endend​% Augmentation Phase% augment solution for each free rowsfor f=1:numfree    freerow = free(f); % start row of augmenting path    % Dijkstra shortest path algorithm.    % runs until unassigned column added to shortest path tree.    d = costMat(freerow,:) - v;    pred = freerow(1,ones(1,dim));    collist = 1:dim;    low = 1; % columns in 1...low-1 are ready, now none.    up = 1; % columns in low...up-1 are to be scaed for current minimum, now none.    % columns in up+1...dim are to be considered later to find new minimum,    % at this stage the list simply contains all columns.    unassignedfound = false;    while ~unassignedfound        if up == low    % no more columns to be scaned for current minimum.            last = low-1;            % scan columns for up...dim to find all indices for which new minimum occurs.             % store these indices between low+1...up (increasing up).            minh = d(collist(up));            up = up + 1;            for k=up:dim                j = collist(k);                h = d(j);                if h<=minh                    if h<minh                        up = low;                        minh = h;                    end                    % new index with same minimum, put on index up, and extend list.                    collist(k) = collist(up);                    collist(up) = j;                    up = up +1;                end            end            % check if any of the minimum columns happens to be unassigned.            % if so, we have an augmenting path right away.            for k=low:up-1                if colsol(collist(k)) < 0                    endofpath = collist(k);                     unassignedfound = true;                    break                end            end        end        if ~unassignedfound            % update 'distances' between freerow and all unscanned columns,            % via next scanned column.            j1 = collist(low);            low=low+1;            i = colsol(j1); %line 215            x = costMat(i,:)-v;            h = x(j1) - minh;            xh = x-h;            k=up:dim;            j=collist(k);            vf0 = xh<d;            vf = vf0(j);            vj = j(vf);            vk = k(vf);            pred(vj)=i;            v2 = xh(vj);            d(vj)=v2;            vf = v2 == minh; % new column found at same minimum value            j2 = vj(vf);            k2 = vk(vf);            cf = colsol(j2)<0;             if any(cf) % unassigned, shortest augmenting path is complete.                i2 = find(cf,1);                                endofpath = j2(i2);                unassignedfound = true;            else                 i2 = numel(cf)+1;            end            % add to list to be scaned right away            for k=1:i2-1                collist(k2(k)) = collist(up);                collist(up) = j2(k);                up = up + 1;            end        end    end    % update column prices    j1=collist(1:last+1);    v(j1) = v(j1) + d(j1) - minh;    % reset row and column assignments along the alternating path    while 1        i=pred(endofpath);        colsol(endofpath)=i;        j1=endofpath;        endofpath=rowsol(i);        rowsol(i)=j1;        if (i==freerow)            break        end    endendrowsol = rowsol(1:rdim);u=diag(costMat(:,rowsol))-v(rowsol)';u=u(1:rdim);v=v(1:cdim);cost = sum(u)+sum(v(rowsol));costMat=costMat(1:rdim,1:cdim);costMat = costMat - u(:,ones(1,cdim)) - v(ones(rdim,1),:);if swapf    costMat = costMat';    t=u';    u=v';    v=t;endif cost>maxcost    cost=Inf;end

⛳️ 运行结果

🔗 参考文献

本程序参考以下中文EI期刊，程序注释清晰，干货满满。

[1]王振东,谢华茂,胡中栋,et al.改进花朵授粉算法的无线传感器网络部署优化[J].系统仿真学报, 2021.DOI:10.16182/j.issn1004731x.joss.19-0580.

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