[Practical Exercise] MATLAB Algorithm for Optimizing Cargo Delivery Routes

# Practical Exercise: Optimizing Freight Delivery Routes with MATLAB Algorithms

## 2.1 Greedy Algorithm

### 2.1.1 Algorithm Principle

The greedy algorithm is a heuristic algorithm that, at each decision point, selects what appears to be the most optimal choice without considering the possible consequences in the future. In the optimization of freight delivery routes, the greedy algorithm typically follows these steps:

1. **Initialization:** Mark all delivery points as unvisited.
2. **Choose a Starting Point:** Select a point from all unvisited delivery points as the starting point.
3. **Select the Next Delivery Point:** From the starting point, calculate the distance to all unvisited delivery points. Choose the delivery point with the smallest distance as the next point.
4. **Update:** Mark the next delivery point as visited and update the distance from the starting point to the next delivery point.
5. **Repeat Steps 3 and 4:** Until all delivery points have been visited.
6. **Return:** Return the sequence of visited delivery points, which is the delivery route.

### 2.1.2 Algorithm Implementation

The MATLAB code to implement the greedy algorithm is as follows:

function path = greedy_path(distances)
     % Initialization
     n = size(distances, 1);
     visited = zeros(1, n);
     path = zeros(1, n);
     path(1) = 1;
     visited(1) = 1;

     % Loop to select the next delivery point
     for i = 2:n
         min_dist = inf;
         next_node = 0;
         for j = 1:n
             if ~visited(j) && distances(path(i-1), j) < min_dist
                 min_dist = distances(path(i-1), j);
                 next_node = j;
             end
         end
         path(i) = next_node;
         visited(next_node) = 1;
     end
end

# 2. Theoretical Foundations of Freight Delivery Route Optimization Algorithms

## 2.1 Greedy Algorithm

### 2.1.1 Algorithm Principle

The greedy algorithm is a heuristic algorithm that, at every decision point, selects what appears to be the optimal choice at the moment, without considering the impact on the future. In freight delivery route optimization, the greedy algorithm typically uses the nearest neighbor method, where at each delivery point, the nearest unvisited point is selected as the next delivery point.

### 2.1.2 Algorithm Implementation

% Greedy Algorithm Implementation

% Input: Delivery point coordinates, delivery sequence
% Output: Optimal delivery route

function path = greedy_algorithm(points, order)

     % Initialize the optimal route
     path = [];

     % Iterate through delivery points
     for i = 1:length(order)
         % Get the current delivery point
         current_point = points(order(i), :);

         % Calculate the distance from the current delivery point to unvisited points
         distances = pdist2(current_point, points(order(i+1:end), :));

         % Choose the nearest unvisited point
         [~, idx] = min(distances);
         next_point = order(i+idx);

         % Update the optimal route
         path = [path, next_point];
     end

end

## 2.2 Genetic Algorithm

### 2.2.1 Algorithm Principle

The genetic algorithm is an optimization algorithm based on natural selection and genetic principles. In freight delivery route optimization, the genetic algorithm represents delivery routes as chromosomes and evolves these chromosomes through operations such as selection, crossover, and mutation to find the optimal route.

### 2.2.2 Algorithm Implementation

% Genetic Algorithm Implementation

% Input: Delivery point coordinates, population size, maximum number of iterations
% Output: Optimal delivery route

function path = genetic_algorithm(points, population_size, max_iterations)

     % Initialize the population
     population = generate_population(population_size, points);

     % Evolve the population
     for i = 1:max_iterations
         % Selection
         parents = select_parents(population);

         % Crossover
         offspring = crossover(parents);

         % Mutation
         offspring = mutate(offspring);

         % Evaluate offspring
         offspring = evaluate_offspring(offspring, points);

         % Update population
         population = [population; offspring];
     end

     % Select the best individual
     best_individual = select_best_individual(population);

     % Return the optimal delivery route
     path = best_individual.path;

end

## 2.3 Particle Swarm Optimization Algorithm

### 2.3.1 Algorithm Principle

The particle swarm optimization algorithm is an optimization algorithm based on swarm intelligence. In freight delivery route optimization, the particle swarm optimization algorithm represents delivery routes as particles and finds the optimal route through information sharing and collaboration among particles.

### 2.3.2 Algorithm Implementation

% Particle Swarm Optimization Algorithm Implementation

% Input: Delivery point coordinates, population size, maximum number of iterations
% Output: Optimal delivery route

function path = particle_swarm_optimization(points, population_size, max_iterations)

     % Initialize the particle swarm
     swarm = generate_swarm(population_size, points);

     % Evolve the particle swarm
     for i = 1:max_iterations
         % Update particle velocity and position
         for j = 1:population_size
             % Update velocity
             swarm(j).velocity = update_velocity(swarm(j), swarm.gbest, swarm.p