Integrasi Kromosom Buatan Dinamis untuk Memecahkan Masalah Konvergensi Prematur pada Algoritma Genetika untuk Traveling Salesman Problem

Genetic Algorithm (GA) adalah metode adaptif yang digunakan untuk memecahkan masalah pencarian dan optimasi, diantaranya adalah Travelling Salesman Problem (TSP) yang merupakan persoalan optimasi, dimana rute terpendek merupakan solusi yang paling optimal. GA juga salah satu metode optimisasi global yang bekerja dengan baik dan efisien pada fungsi tujuan yang kompleks dalam hal nonlinear, tetapi GA mempunyai masalah yaitu konvergensi prematur. Untuk mengatasi masalah konvergensi prematur, maka pada penelitian ini diusulkan Dynamic Artificial Chromosomes (DAC) yang digunakan untuk mengkontrol keragaman populasi dan juga seleksi kromosom terbaik untuk memilih individu atau kromosom terbaik yang tujuannya untuk membuat keragaman pada populasi menjadi beragam dan keluar dari konvergensi prematur. Beberapa eksperimen dilakukan dengan menggunakan Genetic Algorithm Dynamic Artificial Chromosomes (GA-DAC), dimana threshold terbaik adalah 0.5, kemudian juga mendapatkan hasil perbaikan pada jarak terpendek yang dibandingkan dengan GA standar dengan dataset KroA100 sebesar 12.60%, KroA150 sebesar 13.92% dan KroA200 sebesar 12.92%. Untuk keragaman populasi mendapatkan hasil pada KroA100 sebesar 24.97%, KroA150 sebesar 50.84% dan KroA200 sebesar 49.08% dibandingkan dengan GA standar. Maka dapat disimpulkan bahwa GA-DAC bisa mendapatkan hasil lebih baik dibandingkan dengan GA standar, sehingga ini akan membuat GA bisa keluar dari konvergensi prematur

The Steiner Traveling Salesman Problem With Online Edge Blockages

We consider the online Steiner Traveling Salesman Problem. In this problem, we are given an edge-weighted graph G = (V, E) and a subset D⊆V of destination vertices, with the optimization goal to find a minimum weight closed tour that traverses every destination vertex of D at least once. During the traversal, the salesman could encounter at most k non-recoverable blocked edges. The edge blockages are real-time, meaning that the salesman knows about a blocked edge whenever it occurs. We first show a lower bound on the competitive ratio and present an online optimal algorithm for the problem. While this optimal algorithm has non-polynomial running time, we present another online polynomial-time near optimal algorithm for the problem. Experimental results show that our online polynomial-time algorithm produces solutions very close to the offline optimal solutions

Algoritmos de aproximação para problemas de roteamento e conectividade com múltiplas funções de distância

Orientador: Lehilton Lelis Chaves PedrosaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta dissertação, estudamos algumas generalizações de problemas clássicos de roteamento e conectividade cujas instâncias são compostas por um grafo completo e múltiplas funções de distância. Por exemplo, existe o Problema do Caixeiro Alugador (CaRS), no qual um viajante deseja visitar um conjunto de cidades alugando um ou mais carros disponíveis. Cada carro tem uma função de distância e uma taxa de retorno ao local do aluguel. CaRS é uma generalização do Problema do Caixeiro Viajante (TSP). Nós lidamos com esses problemas usando algoritmos de aproximação, que são algoritmos eficientes que produzem soluções com garantia de qualidade. Neste trabalho, são apresentadas duas abordagens, uma baseada em uma redução linear que preserva o fator de aproximação e outra baseada na construção de instâncias de dois problemas distintos. Os problemas considerados são o Steiner TSP, o Problema do Passeio com Coleta de Prêmios e o Problema da Floresta Restrita. Generalizamos cada um desses problemas considerando múltiplas funções de distância e, para cada um deles, apresentamos um algoritmo de aproximação com fator O(logn), onde n é o número de vértices (cidades). Essas aproximações são assintoticamente ótimas, já que não há algoritmos com fator o(log n), a não ser que P = NPAbstract: In this dissertation, we study some generalizations of classical routing and connectivity problems whose instances are composed of a complete graph and multiple distance functions. As an example, there is the Traveling Car Renter Problem (CaRS) in which a traveler wants to visit a set of cities by renting one or more available cars. Each car is associated to a distance function and a service fee to return to the rental location. CaRS is a generalization of the Traveling Salesman Problem (TSP). We deal with these problems using approximation algorithms which are efficient algorithms that produce solutions with quality guarantee. In this work, two approaches are presented, one based on a linear reduction that preserves the approximation factor and the other based on the construction of instances of two distinct problems. The studied problems are the Steiner TSP, the Profitable Tour Problem, and the Constrained Forest Problem. We generalize these problems by considering multiple distance functions and, for each of them, we present an O(log n)-approximation algorithm, where n is the number of vertices (cities). The factor is asymptotically optimal, since there is no approximation algorithm with factor o(log n) unless P = NPMestradoCiência da ComputaçãoMestra em Ciência da Computação001CAPE