Project: First version of the code and report stub

Project/report/report.tex

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+% !TEX TS-program = xelatex
+% !TEX encoding   = UTF-8 Unicode
+% !TEX spellcheck = el-GR
+%
+% Optimization techniques project report
+%
+% Requires compilation with pdfLaTeX or XeLaTeX
+%
+% authors:
+%   Χρήστος Χουτουρίδης ΑΕΜ 8997
+%   cchoutou@ece.auth.gr
+
+%
+% Options:
+%
+% 1) mainlang=<language>
+%    Default:  english
+%    Set the default language of the document which affects hyphenations,
+%    localization (section, dates, etc...)
+%
+%    example: \documentclass[mainlang=greek]{AUThReport}
+%
+% 2) <language>
+%    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}

Project/scripts/main.m

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+% 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