我想在Shortest Path中使用PSO来解决MATLAB问题。我使用优先级编码[1]对路径进行编码，我正在使用收缩和速度钳制[2]。
我遇到的问题是，与Dijkstra相比，代码速度极慢。首先，我使用Dijkstra进行测试以获得基准时间，然后运行PSO以找到它在那段时间内可以实现的最低成本。 PSO的结果总是高得多。
如果我检查每次迭代的完成速度，我发现在Intel Core i3-2120处理器上有1000多个节点的路径需要几秒钟。
在下面的代码中，您需要首先运行data.m以初始化成本矩阵，然后运行Dijkstra以获得时间基准。之后，在几秒钟内修改allowedTime中的pso.m变量。
参数：
data.m
pso.m
dimensions范围内）dimensions范围内）dijkstra.m
costMatrix，<start_node_id>，<end_node_id>）我对乱码并不使用函数感到抱歉，但是我需要在代码完成或者中断后查看所有值inline并查看所有值。
的 data.m 的
% <<<<<<<<<<<<<<<<<< data definition >>>>>>>>>>>>>>>> %
clear;
clc;
fprintf('Generating data ...\n\n');
dimensions = 5000;
costMatrix = randi(dimensions, dimensions);
fprintf('DONE!\n\n');
的 pso.m 的
%% initialization
clc;
fprintf('Initialising swarm ...\n\n');
% parameters
% >>>>>>>>>>>>>>>>>>> edit <<<<<<<<<<<<<<<<<<< %
allowedTime = 15 * 60;
swarm_size = 50;
% SP algorithm specific.
startNode = 1;
endNode = 2;
% velocity equation params.
correction_factor_p = 2.05;
correction_factor_g = 2.05;
contrictionFactor = 0.72984;
% ^^^^^^^^^^^^^^^^^^^ end ^^^^^^^^^^^^^^^^^^^ %
gbest = 1;
oldFitness = 1000000001;
iterations = 0;
% pre-allocate arrays.
swarmPos = zeros(swarm_size, dimensions);
swarmVel = zeros(swarm_size, dimensions);
swarmBestPos = zeros(swarm_size, dimensions);
swarmBestPath = cell(swarm_size, 1);
swarmBestFit = zeros(1, swarm_size);
result = zeros(1, swarm_size);
upperBound = zeros(1, dimensions);
lowerBound = zeros(1, dimensions);
% set bounds.
for i = 1 : dimensions
upperBound(i) = 100;
lowerBound(i) = -100;
end
% ---- initiate swarm -----
for i = 1 : swarm_size
for j = 2 : dimensions
swarmPos(i,j) = lowerBound(j) + rand * (upperBound(j) - lowerBound(j));
swarmVel(i,j) = rand * (upperBound(j) - lowerBound(j)) / 2;
swarmBestPos(i,j) = swarmPos(i,j);
swarmBestPath{i}(j) = -1;
swarmBestFit(i) = 1000000000; % best fitness so far
end
end
% set starting node to avoid on accidental access.
for i = 1 : swarm_size
swarmPos(i,1) = -99999999;
swarmVel(i,1) = -99999999;
swarmBestPos(i,1) = -99999999;
swarmBestPath{i}(1) = startNode;
end
% ^^^^^^^^^^^^^^^^ END: initialisation ^^^^^^^^^^^^^^^^ %
% >>>>>>>>>>>>>>>>>>> START: swarming <<<<<<<<<<<<<<<<<<< %
clc;
fprintf('Swarming ...\n\n');
tic;
%% iterations
while true
% reset results to allow summing.
parfor i = 1 : swarm_size
result(i) = 0;
end
% <<<<<<<<<<<<<<<<< START: movement and fitness >>>>>>>>>>>>>>>>> %
for i = 1 : swarm_size
for j = 2 : dimensions
swarmPos(i,j) = swarmPos(i,j) + swarmVel(i,j); % update x position
if (swarmPos(i,j) > upperBound(j))
swarmPos(i,j) = swarmPos(i,j) - (swarmPos(i,j) - lowerBound(j)) / 2;
elseif (swarmPos(i,j) < lowerBound(j))
swarmPos(i,j) = swarmPos(i,j) + (lowerBound(j) - swarmPos(i,j)) / 2;
end
end
%tic;
% <<< inline fitness function >>> %
tempPath = [];
tempPath(1) = startNode;
invalidBuild = false;
tempPos = swarmPos(i,:);
for j = 2 : dimensions
for k = 2 : dimensions
[discard, maxPos] = max(tempPos);
cost = costMatrix(tempPath(j - 1), maxPos);
tempPos(maxPos) = -9999999 - k;
if (cost < 100000000)
tempPath(j) = maxPos;
result(i) = result(i) + cost;
break;
elseif (k == dimensions)
invalidBuild = true;
end
end
if (invalidBuild)
result(i) = 1000000000;
break;
elseif (tempPath(j) == endNode)
break;
end
end
% ^^^ END: fitness function ^^^ %
% if new position is better
if result(i) < swarmBestFit(i)
for d = 1 : dimensions
swarmBestPos(i,d) = swarmPos(i,d); % update best x,
end
swarmBestPath{i} = tempPath;
swarmBestFit(i) = result(i); % and best value
end
end
% ^^^^^^^^^ END: movement and fitness ^^^^^^^^^ %
% <<<<<<<<<<<<<<<<< update global best >>>>>>>>>>>>>>>>> %
for i = 1 : swarm_size
if swarmBestFit(i) < swarmBestFit(gbest)
gbest = i; % global best i.
took = toc; % time taken to reach this best.
end
end
% <<<<<<<<<<<<<<<<< update velocity >>>>>>>>>>>>>>>>> %
for i = 1 : swarm_size
for j = 2 : dimensions
swarmVel(i,j) = contrictionFactor * (swarmVel(i,j) ...
+ correction_factor_p * rand * (swarmBestPos(i,j) - swarmPos(i,j)) ...
+ correction_factor_g * rand * (swarmBestPos(gbest,j) - swarmPos(i,j)));
if (swarmVel(i,j) > (upperBound(j) - lowerBound(j)) / 2)
swarmVel(i,j) = (upperBound(j) - lowerBound(j)) / 2;
end
end
end
% <<<<<<<<<<<<<<<<< print global bests if changed >>>>>>>>>>>>>>>>> %
if ( oldFitness ~= swarmBestFit(gbest) )
oldFitness = swarmBestFit(gbest);
% update display
clc
fprintf('Best particle position:\n');
sizeTemp = size(swarmBestPath{gbest}, 2);
for i = 1 : sizeTemp
if (swarmBestPath{gbest}(i) ~= 0)
fprintf('%d\n', swarmBestPath{gbest}(i));
end
end
fprintf('\nBest fitness: %d\n\n', swarmBestFit(gbest));
end
iterations = iterations + 1;
% end on timeout
elapsedTime = toc;
if (elapsedTime > allowedTime)
break;
end
end
clc;
fprintf('>>>>>>>>>>>>>>> FINISHED <<<<<<<<<<<<<<<\n\n\n');
fprintf('Best path:\n');
sizeTemp = size(swarmBestPath{gbest}, 1);
for i = 1 : sizeTemp
if (swarmBestPath{gbest}(i) ~= 0)
fprintf('%d\n', swarmBestPath{gbest}(i));
end
end
fprintf('\nBest cost: %d\n\n', swarmBestFit(gbest));
fprintf('\nTook: %d iterations, and %.2f seconds.\n\n', iterations, took);
的 dijkstra.m 的
function dijkstra(matriz_costo, s, d)
% This is an implementation of the dijkstra´s algorithm, wich finds the
% minimal cost path between two nodes. It´s supoussed to solve the problem on
% possitive weighted instances.
% the inputs of the algorithm are:
%farthestNode: the farthest node to reach for each node after performing
% the routing;
% n: the number of nodes in the network;
% s: source node index;
% d: destination node index;
%For information about this algorithm visit:
%http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
%This implementatios is inspired by the Xiaodong Wang's implememtation of
%the dijkstra's algorithm, available at
%http://www.mathworks.com/matlabcentral/fileexchange
%file ID 5550
%Author: Jorge Ignacio Barrera Alviar. April/2007
n=size(matriz_costo,1);
S(1:n) = 0; %s, vector, set of visited vectors
dist(1:n) = inf; % it stores the shortest distance between the source node and any other node;
prev(1:n) = n+1; % Previous node, informs about the best previous node known to reach each network node
dist(s) = 0;
iterations = 0;
tic;
while sum(S)~=n
candidate=[];
for i=1:n
if S(i)==0
candidate=[candidate dist(i)];
else
candidate=[candidate inf];
end
end
[u_index u]=min(candidate);
S(u)=1;
for i=1:n
if(dist(u)+matriz_costo(u,i))<dist(i)
dist(i)=dist(u)+matriz_costo(u,i);
prev(i)=u;
end
end
iterations = iterations + 1;
end
sp = [d];
while sp(1) ~= s
if prev(sp(1))<=n
sp=[prev(sp(1)) sp];
else
error;
end
end;
spcost = dist(d);
took = toc;
fprintf('Best path:\n');
fprintf('%d\n', sp);
fprintf('\nBest cost: %d\n\n', spcost);
fprintf('\nTook: %d iterations, and %.2f seconds.\n\n', iterations, took);
（1）A Nondominated Sorting Genetic Algorithm for SP Routing Problem
（2）Constriction factors and Parameters
答案 0 :(得分：2)
我是人工智能世界的新手。我尽力帮助你。
PSO是一种元启发式方法。可以使用元启发式来解决信息不完整或不完善或计算能力有限的问题。使用Dijkstra无法解决这些问题，因为它需要完整的拓扑细节。因此，算法的使用取决于问题域。
由于PSO是一个随机过程，初始结果不是最优的。随着迭代的执行，成本函数值减小。 Dijkstra通过一次迭代找到最短路径的地方。
因此，与Dijkstra相比，PSO的时间消耗更多。使用这些算法是特定于问题的。
希望这会对你有所帮助！