How to Start Least Cost Routing Projects Using MATLAB

To create a Least Cost Routing (LCR) contains the finding paths by the minimum cost for sample distance, latency, or bandwidth consumption in a network. This is generally used in telecommunication networks, computer networks, and transportation systems. Here’s how to start a Least Cost Routing Project in MATLAB:

Steps to Start Least Cost Routing Projects Using MATLAB

  1. Understand Least Cost Routing
  • LCR goals to detect the path through the minimum cumulative cost among the source and destination nodes.
  • Technique such as Dijkstra’s or Bellman-Ford is typically used measures the least-cost paths.
  1. Set Project Objectives

Define the scope of your project:

  • Least-cost routing replicate in a static or dynamic network.
  • Calculate the least-cost paths for precise node pairs or all-pairs.
  • Examine the performance below various network environments..
  1. Define Network Topology

Characterize the network for adjacency matrix or edge list. Every edge is allocated a cost of classify the resource consumption, delay, or distance.

Example:

% Adjacency matrix for network topology

adjMatrix = [

0 4 0 0 0 0;

4 0 8 0 0 0;

0 8 0 7 0 4;

0 0 7 0 9 14;

0 0 0 9 0 10;

0 0 4 14 10 0

];

% Visualize the graph

G = graph(adjMatrix, ‘upper’);

plot(G, ‘EdgeLabel’, G.Edges.Weight);

title(‘Network Topology’);

  1. Choose a Routing Algorithm

Choose the method we calculate the least-cost paths:

(a) Dijkstra’s Algorithm

  • Effective the non-negative edge weights.
  • Calculates the minimum path from a source to all other nodes.

(b) Bellman-Ford Algorithm

  • Maintain the negative edge weights method.
  • Useful this environment through cost reductions or penalties.
  1. Implement the Algorithm

Write MATLAB code for your chosen algorithm.

(a) Dijkstra’s Algorithm Implementation:

function [dist, pred] = dijkstra(adjMatrix, src)

numNodes = size(adjMatrix, 1);

dist = inf(1, numNodes);  % Initialize distances to infinity

pred = -ones(1, numNodes); % Predecessor array

dist(src) = 0;  % Distance to source is 0

visited = false(1, numNodes);

for i = 1:numNodes

% Find the unvisited node with the smallest distance

[~, u] = min(dist + visited * inf);

visited(u) = true;

% Update distances to neighbors

for v = 1:numNodes

if adjMatrix(u, v) > 0 && ~visited(v)

alt = dist(u) + adjMatrix(u, v);

if alt < dist(v)

dist(v) = alt;

pred(v) = u;

end

end

end

end

end

(b) Bellman-Ford Algorithm Implementation:

function [dist, pred] = bellmanFord(edges, numNodes, src)

dist = inf(1, numNodes); % Initialize distances to infinity

pred = -ones(1, numNodes); % Predecessor array

dist(src) = 0; % Distance to source is 0

% Relax all edges (V-1) times

for i = 1:numNodes-1

for j = 1:size(edges, 1)

u = edges(j, 1);

v = edges(j, 2);

weight = edges(j, 3);

if dist(u) + weight < dist(v)

dist(v) = dist(u) + weight;

pred(v) = u;

end

end

end

% Check for negative weight cycles

for j = 1:size(edges, 1)

u = edges(j, 1);

v = edges(j, 2);

weight = edges(j, 3);

if dist(u) + weight < dist(v)

error(‘Negative weight cycle detected.’);

end

end

end

  1. Compute Least Cost Routes

Use the execution performance we calculate the least cost path from a source node to a destination.

Example Using Dijkstra:

% Compute least-cost routes

srcNode = 1; % Source node

[dist, pred] = dijkstra(adjMatrix, srcNode);

% Display shortest distances

fprintf(‘Shortest distances from Node %d:\n’, srcNode);

disp(dist);

% Reconstruct path to a specific destination

function path = reconstructPath(pred, dest)

path = [];

current = dest;

while current ~= -1

path = [current, path];

current = pred(current);

end

end

% Example: Path from Node 1 to Node 6

destNode = 6;

path = reconstructPath(pred, destNode);

fprintf(‘Path from Node %d to Node %d: %s\n’, srcNode, destNode, mat2str(path));

  1. Visualize the Results

Highlight the least cost path on the network graph.

% Visualize the graph and least-cost path

G = graph(adjMatrix, ‘upper’);

plot(G, ‘EdgeLabel’, G.Edges.Weight);

highlightPath = reconstructPath(pred, destNode);

highlight(plot(G), highlightPath, ‘EdgeColor’, ‘r’, ‘LineWidth’, 2);

title(‘Least Cost Routing Path’);

  1. Evaluate Performance

Examine the outcomes:

  • Cost Efficiency: Verify the path’s cost is minimal for efficiency.
  • Scalability: Validate on larger graphs in scalability.
  • Resilience: Checked on how static paths perform below failures or dynamic conditions.
  1. Extend the Project

Add more features:

  • Replicate the dynamic cost changes such as varying traffic load.
  • Associate the technique such as Dijkstra, Bellman-Ford, and Floyd-Warshall.
  • Apply the multipath least-cost routing.

Complete MATLAB Code

Here’s a complete sample using Dijkstra’s algorithm:

% Define adjacency matrix

adjMatrix = [

0 4 0 0 0 0;

4 0 8 0 0 0;

0 8 0 7 0 4;

0 0 7 0 9 14;

0 0 0 9 0 10;

0 0 4 14 10 0

];

% Run Dijkstra’s algorithm

srcNode = 1; % Source node

[dist, pred] = dijkstra(adjMatrix, srcNode);

% Display results

fprintf(‘Shortest distances from Node %d:\n’, srcNode);

disp(dist);

% Reconstruct path to Node 6

destNode = 6;

path = reconstructPath(pred, destNode);

fprintf(‘Path from Node %d to Node %d: %s\n’, srcNode, destNode, mat2str(path));

% Visualize network and path

G = graph(adjMatrix, ‘upper’);

plot(G, ‘EdgeLabel’, G.Edges.Weight);

highlight(plot(G), path, ‘EdgeColor’, ‘r’, ‘LineWidth’, 2);

title(‘Least Cost Routing Path’);

Let me know if you need help extending this or integrating additional features!

In this simulation setup, we have been clearly understood the concepts and learn the essential procedures to simulate the Least Cost projects that has contain to generating the network system and then visualized the outcomes through MATLAB analysis too. Further details will be provided later.