98 lines
3.4 KiB
Matlab
98 lines
3.4 KiB
Matlab
% Genetic Algorithm for Minimizing Network Traversal Time
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clc;
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clear;
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close all;
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% Problem Parameters
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N = 17; % Number of roads
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t = 1.5 * ones(1, N); % Fixed time for each road
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a = [1.25 * ones(1, 5), 1.5 * ones(1, 5), ones(1, 7)]; % Weighting factor
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c = [
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54.13, 21.56, 34.08, 49.19, 33.03, 21.84, 29.96, 24.87, 47.24, 33.97, ...
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26.89, 32.76, 39.98, 37.12, 53.83, 61.65, 59.73]; % Road capacities
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V = 100; % Incoming vehicle rate
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% Travel Time Function
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travelTime = @(xi, ti, ai, ci) ti + ai * xi / (1 - xi / ci);
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% Normalization Function (Infinite norm normalized to S)
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normalizeSum = @(x, S) (x ./ sum(x)) * S; % Ensure sum of single row x equals S
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normalizeSum2 = @(x, S) (x ./ sum(x, 2)) * S; % Ensure sum of each row of 2D matrix x equals S
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% Genetic Algorithm Parameters
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popSize = 36; % Population size
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maxGen = 2000; % Maximum number of generations
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mutationRate = 0.1; % Mutation probability
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% Initialize Population
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pop = rand(popSize, N) .* c; % Random initial solutions (0 <= x <= c)
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pop = normalizeSum2(pop, V); % Ensure sum of each solution equals V
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newPop = zeros(popSize, N); % Pre-allocate new population buffer
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bestFitness = zeros(maxGen, 1); % Result array
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% Genetic Algorithm Execution
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for gen = 1:maxGen
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% Fitness Calculation
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fitness = arrayfun(@(i) fitnessFunction(pop(i, :), t, a, c, V, travelTime), 1:popSize);
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% Selection
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[~, idx] = sort(fitness); % Sort based on fitness (ascending order)
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pop = pop(idx, :); % Retain the best solutions
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% Keep the best chromosome
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bestFitness(gen) = fitnessFunction(pop(1, :), t, a, c, V, travelTime);
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% Crossover
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newPop(1:popSize/2, :) = pop(1:popSize/2, :); % Retain top half
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for i = 1:popSize/2
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parent1 = newPop(randi(popSize/2), :);
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parent2 = newPop(randi(popSize/2), :);
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crossPoint = randi(N);
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child = [parent1(1:crossPoint), parent2(crossPoint+1:end)];
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child = normalizeSum(child, V);
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newPop(popSize/2 + i, :) = child;
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end
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% Mutation
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for i = 1:popSize
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if rand < mutationRate
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mutationIdx = randi(N);
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newPop(i, mutationIdx) = rand * c(mutationIdx);
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newPop(i, :) = normalizeSum(newPop(i, :), V);
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end
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end
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% Replacement
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pop = newPop;
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end
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% Results
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bestSolution = pop(1, :);
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disp('Best Solution [veh/min]:');
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disp(bestSolution);
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disp(['Best Objective Value: ', num2str(bestFitness(end)), ' [min]']);
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figure('Name', 'Time over generations', 'NumberTitle', 'off');
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set(gcf, 'Position', [100, 100, 960, 640]); % Set the figure size
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plot(1:maxGen, bestFitness, '-b', 'LineWidth', 1);
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% Customize the plot
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title(['Population = ', num2str(popSize), ' - Mutation = ', num2str(mutationRate)], 'Interpreter', 'latex', 'FontSize', 16); % Title of the plot
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xlabel('Generations') ;
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ylabel('T_{total}');
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% save the figure
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print(gcf, ['figures/constV_pop_', num2str(popSize), 'mut_', num2str(mutationRate), '.png'], '-dpng', '-r300');
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% Fitness Function
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function T_total = fitnessFunction(x, t, a, c, V, travelTime)
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if abs(sum(x) - V) > 1e-6 || any(x < 0) || any(x > c)
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T_total = inf; % Infeasible solutions
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return;
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end
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T = arrayfun(@(xi, ti, ai, ci) travelTime(xi, ti, ai, ci), x, t, a, c); % Apply function to all elements
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T_total = sum(T .* x); % Total traversal time
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end |