On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem

We contribute to the efficient approximation of the Pareto-set for the classical $\mathcal{NP}$-hard multi-objective minimum spanning tree problem (moMST) adopting evolutionary computation. More precisely, by building upon preliminary work, we analyse the neighborhood structure of Pareto-optimal spanning trees and design several highly biased sub-graph-based mutation operators founded on the gained insights. In a nutshell, these operators replace (un)connected sub-trees of candidate solutions with locally optimal sub-trees. The latter (biased) step is realized by applying Kruskal's single-objective MST algorithm to a weighted sum scalarization of a sub-graph. We prove runtime complexity results for the introduced operators and investigate the desirable Pareto-beneficial property. This property states that mutants cannot be dominated by their parent. Moreover, we perform an extensive experimental benchmark study to showcase the operator's practical suitability. Our results confirm that the sub-graph based operators beat baseline algorithms from the literature even with severely restricted computational budget in terms of function evaluations on four different classes of complete graphs with different shapes of the Pareto-front

Roteamento multicast multisessão: modelos e algoritmos

Multicast Technology has been studied over the last two decades and It has shown to be a good approach to save network resources. Many approaches have been considered to solve the multicast routing problem considering only one session and one source to attending session‘s demand, as well, multiple sessions with more than one source per session. In this thesis, the multicast routing problem is explored taking in consideration the models and the algorithms designed to solve it when where multiple sessions and sources. Two new models are proposed with different focuses. First, a mono-objective model optimizing residual capacity, Z, of the network subject to a budget is designed and the objective is to maximize Z. Second, a multi-objective model is designed with three objective functions: cost, Z and hops counting. Both models consider multisession scenario with one source per session. Besides, a third model is examined. This model was designed to optimize Z in a scenario with multiple sessions with support to more than one source per session. An experimental analysis was realized over the models considered. For each model, a set of algorithms were designed. First, an ACO, a Genetic algorithm, a GRASP and an ILS algorithm were designed to solve the mono-objective model – optimizing Z subject to a budget. Second, a set of algorithm were designed to solve the multi-objective model. The classical approaches were used: NSGA2, ssNSGA2, SMS-EMOA, GDE3 and MOEA/D. In addition, a transgenetic algorithm was designed to solve the problem and it was compared against the classical approaches. This algorithm considers the use of subpopulations during the evolution. Each subpopulation is based on a solution construction operator guided by one of the objective functions. Some solutions are considered as elite solutions and they are considered to be improved by a transposon operator. Eight versions of the transgenetic algorithm were evaluated. Third, an algorithm was designed to solve the problem with multiple sessions and multiple sources per sessions. This algorithm is based on Voronoi Diagrams and it is called MMVD. The algorithm designed were evaluated on large experimental analysis. The sample generated by each algorithm on the instances were evaluated based on non-parametric statistical tests. The analysis performed indicates that ILS and Genetic algorithm have outperformed the ACO and GRASP. The comparison between ILS and Genetic has shown that ILS has better processing time performance. In the multi-objective scenario, the version of Transgenetic called cross0 has shown to be statistically better than the other algorithms in most of the instances based on the hypervolume and addictive/multiplicative epsilon quality indicators. Finally, the MMVD algorithm has shown to be better than the algorithm from literature based on the experimental analysis performed for the model with multiple session and multiple sources per session.A tecnologia multicast tem sido amplamente estudada ao longo dos anos e apresenta-se como uma solução para melhor utilização dos recursos da rede. Várias abordagens já foram avaliadas para o problema de roteamento desde o uso de uma sessão com apenas uma fonte a um cenário com múltiplas sessões e múltiplas fontes por sessão. Neste trabalho, é feito um estudo dos modelos matemáticos para o problema com múltiplas sessões e múltiplas fontes. Dois modelos matemáticos foram propostos: uma versão multissessão mono-objetivo que visa a otimização da capacidade residual sujeito a um limite de custo e uma versão multiobjetivo com três funções-objetivo. Ambos os modelos levam em conta o cenário multissessão com uma fonte por sessão. Além disso, um estudo algorítmico foi realizado sobre um modelo da literatura que utiliza múltiplas fontes por sessão. Três conjuntos de algoritmos foram propostos. O primeiro conjunto trata do problema mono-objetivo proposto e considera as abordagens ACO, Genético, GRASP e ILS. O segundo conjunto consiste dos algoritmos propostos para o modelo multiobjetivo. Foram projetados os seguintes algoritmos: NSGA2, ssNSGA2, GDE3, MOEA/D e SMS-EMOA. Além disso, foi projetado um algoritmo transgenético com subpopulações baseadas em operadores de criação de solução direcionados por objetivos do problema. Também foi utilizado o conceito de soluções de elite. No total, 8 versões do algoritmo transgenético foram avaliadas. O terceiro conjunto de algoritmos consiste da heurística MMVD proposta para o modelo da literatura com múltiplas fontes por sessão. Esta heurística é baseada no uso de diagramas de Voronoi. O processo experimental foi realizado com amplo número de instâncias configuradas de modo a avaliar diferentes situações. Os resultados foram comparados utilizando métodos estatísticos não-paramétricos. A análise final indicou que o ILS e o Genético obtiveram resultados muito similares, entretanto o ILS possui melhor tempo de processamento. A versão cross0 do algoritmo transgenético obteve o melhor resultado em praticamente todos os cenários avaliados. A heurística MMVD obteve excelentes resultados sobre algoritmos da literatura