Hi Said,
I understand that you are interested in learning about graph formation for optimization to increase coverage area while maintaining energy efficiency.
I can provide an example to help you get started. Below is an example that generates a random wireless sensor network, creates edges based on the maximum communication range, and plots the resulting graph. For the optimization function, I have used a Particle Swarm Optimization (PSO) algorithm to optimize the placement of nodes, minimizing the total communication distance and indirectly improving energy efficiency. Feel free to use an alternative optimization.
% Parameters
numNodes = 50; % Number of nodes
areaSize = 100; % Size of the area (100x100)
maxRange = 20; % Maximum communication range
numParticles = 30; % Number of particles in PSO
maxIterations = 100; % Maximum number of iterations in PSO
% Generate random node positions
nodePositions = rand(numNodes, 2) * areaSize;
% Initialize adjacency matrix
adjMatrix = zeros(numNodes);
% Create edges based on communication range
for i = 1:numNodes
for j = i+1:numNodes
distance = norm(nodePositions(i,:) - nodePositions(j,:));
if distance <= maxRange
adjMatrix(i,j) = 1;
adjMatrix(j,i) = 1;
end
end
end
% PSO parameters
w = 0.5; % Inertia weight
c1 = 1.5; % Cognitive (personal) weight
c2 = 1.5; % Social (global) weight
% Initialize particles
particles = rand(numParticles, numNodes * 2) * areaSize;
velocities = zeros(numParticles, numNodes * 2);
personalBestPositions = particles;
personalBestScores = inf(numParticles, 1);
globalBestPosition = particles(1, :);
globalBestScore = inf;
% PSO optimization loop
for iter = 1:maxIterations
for p = 1:numParticles
% Update adjacency matrix for current particle
currentPositions = reshape(particles(p, :), [numNodes, 2]);
adjMatrix = zeros(numNodes);
for i = 1:numNodes
for j = i+1:numNodes
distance = norm(currentPositions(i,:) - currentPositions(j,:));
if distance <= maxRange
adjMatrix(i,j) = 1;
adjMatrix(j,i) = 1;
end
end
end
% Calculate fitness (total distance)
totalDistance = optimizeGraph(adjMatrix, currentPositions);
% Update personal best
if totalDistance < personalBestScores(p)
personalBestScores(p) = totalDistance;
personalBestPositions(p, :) = particles(p, :);
end
% Update global best
if totalDistance < globalBestScore
globalBestScore = totalDistance;
globalBestPosition = particles(p, :);
end
end
% Update particle velocities and positions
for p = 1:numParticles
velocities(p, :) = w * velocities(p, :) ...
+ c1 * rand * (personalBestPositions(p, :) - particles(p, :)) ...
+ c2 * rand * (globalBestPosition - particles(p, :));
particles(p, :) = particles(p, :) + velocities(p, :);
% Ensure particles stay within bounds
particles(p, :) = max(min(particles(p, :), areaSize), 0);
end
end
% Display results
optimizedPositions = reshape(globalBestPosition, [numNodes, 2]);
adjMatrix = zeros(numNodes);
for i = 1:numNodes
for j = i+1:numNodes
distance = norm(optimizedPositions(i,:) - optimizedPositions(j,:));
if distance <= maxRange
adjMatrix(i,j) = 1;
adjMatrix(j,i) = 1;
end
end
end
G = graph(adjMatrix);
figure;
plot(G, 'XData', optimizedPositions(:,1), 'YData', optimizedPositions(:,2));
title('Optimized Wireless Sensor Network Graph');
xlabel('X Position');
ylabel('Y Position');
disp(['Optimized Total Distance: ', num2str(globalBestScore)]);
% Optimization function (example: minimize total distance)
function totalDistance = optimizeGraph(adjMatrix, nodePositions)
totalDistance = 0;
[rows, cols] = find(adjMatrix);
for k = 1:length(rows)
totalDistance = totalDistance + norm(nodePositions(rows(k),:) - nodePositions(cols(k),:));
end
end
The provided optimization code can serve as a placeholder for any custom or improved optimizations. The code generates a graph as illustrated below:
Please note that the points generated are random and the graph might vary accordingly.
I hope this helps!
