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\documentclass[mainlang=greek]{AUThReport} +% +% 2) +% Add hyphenation and typesetting support for other languages +% Currently supports: english, greek, german, frenc +% +% example: \documentclass[english, greek]{AUThReport} +% +% 3) short: Requests a shorter title for the document +% Default: no short +% +% example: \documentclass[short]{AUThReport} +% +\documentclass[a4paper, 11pt, mainlang=greek, english]{AUThReport} + +\CurrentDate{\today} + +% Document setup +%--------------------------------- + +% \WorkGroup{Ομάδα Χ} + +\AuthorName{Χρήστος Χουτουρίδης} +\AuthorMail{cchoutou@ece.auth.gr} +\AuthorAEM{8997} + +%\CoAuthorName{Όνομα Επίθετο} +%\CoAuthorAEM{AEM} +%\CoAuthorMail{xxx@ece.auth.gr} + +\DocTitle{Project: Γενετικοί αλγόριθμοι} +\DocSubTitle{Ελαχιστοποίηση συνάρτησης πολλών μεταβλητών} + +\Department{Τμήμα ΗΜΜΥ. Τομέας Ηλεκτρονικής} +\ClassName{Τεχνικές Βελτιστοποίησης} +% +\InstructorName{Γ. Ροβιθάκης} +\InstructorMail{rovithak@auth.gr} + +\CoInstructorName{Θ. Αφορόζη} +\CoInstructorMail{taforozi@ece.auth.gr} + + +% Local package requirements +%--------------------------------- + +\usepackage{enumitem} +\usepackage{tabularx} +\usepackage{array} +\usepackage{multirow} +\usepackage{float} +\usepackage{xcolor} +\usepackage{soul} +\usepackage{amsmath} +\usepackage{footnote} +\usepackage{footmisc} + + +\begin{document} + + \InsertTitle + + %\tableofcontents + + + \section{Εισαγωγή} + + Η παρούσα εργασία αφορά ... + +\end{document} diff --git a/Project/scripts/main.m b/Project/scripts/main.m new file mode 100644 index 0000000..2a7198a --- /dev/null +++ b/Project/scripts/main.m @@ -0,0 +1,84 @@ +% Genetic Algorithm for Minimizing Network Traversal Time + +clc; +clear; +close all; + +% Problem Parameters +N = 17; % Number of roads +t = 1.5 * ones(1, N); % Fixed time for each road +a = [1.25 * ones(1, 5), 1.5 * ones(1, 5), ones(1, 7)]; % Weighting factor +c = [ + 54.13, 21.56, 34.08, 49.19, 33.03, 21.84, 29.96, 24.87, 47.24, 33.97, ... + 26.89, 32.76, 39.98, 37.12, 53.83, 61.65, 59.73]; % Road capacities +V = 100; % Incoming vehicle rate + +% Travel Time Function +travelTime = @(xi, ti, ai, ci) ti + ai * xi / (1 - xi / ci); +% Normalization Function (Infinite norm normalized to S) +normalizeSum = @(x, S) (x ./ sum(x)) * S; % Ensure sum of single row x equals S +normalizeSum2 = @(x, S) (x ./ sum(x, 2)) * S; % Ensure sum of each row of 2D matrix x equals S + +% Genetic Algorithm Parameters +popSize = 100; % Population size +maxGen = 2000; % Maximum number of generations +mutationRate = 0.05; % Mutation probability + +% Initialize Population +pop = rand(popSize, N) .* c; % Random initial solutions (0 <= x <= c) +pop = normalizeSum2(pop, V); % Ensure sum of each solution equals V + +newPop = zeros(popSize, N); % Pre-allocate new population buffer + +% Genetic Algorithm Execution +for gen = 1:maxGen + % Fitness Calculation + fitness = arrayfun(@(i) fitnessFunction(pop(i, :), t, a, c, V, travelTime), 1:popSize); + + % Selection + [~, idx] = sort(fitness); % Sort based on fitness (ascending order) + pop = pop(idx, :); % Retain the best solutions + + % Crossover + newPop(1:popSize/2, :) = pop(1:popSize/2, :); % Retain top half + for i = 1:popSize/2 + parent1 = newPop(randi(popSize/2), :); + parent2 = newPop(randi(popSize/2), :); + crossPoint = randi(N); + child = [parent1(1:crossPoint), parent2(crossPoint+1:end)]; + child = normalizeSum(child, V); + newPop(popSize/2 + i, :) = child; + end + + % Mutation + for i = 1:popSize + if rand < mutationRate + mutationIdx = randi(N); + newPop(i, mutationIdx) = rand * c(mutationIdx); + newPop(i, :) = normalizeSum(newPop(i, :), V); + end + end + + % Replacement + pop = newPop; +end + +% Final Solution +bestSolution = pop(1, :); +bestFitness = fitnessFunction(bestSolution, t, a, c, V, travelTime); + +% Results +disp('Best Solution [veh/min]:'); +disp(bestSolution); +disp(['Best Objective Value: ', num2str(bestFitness), ' [min]']); + +% Fitness Function +function T_total = fitnessFunction(x, t, a, c, V, travelTime) + if abs(sum(x) - V) > 1e-6 || any(x < 0) || any(x > c) + T_total = inf; % Infeasible solutions + return; + end + + T = arrayfun(@(xi, ti, ai, ci) travelTime(xi, ti, ai, ci), x, t, a, c); % Apply function to all elements + T_total = sum(T .* x); % Total traversal time +end \ No newline at end of file

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