A suposta ubiquidade de sistemas decomponíveis foi interpretada por Holland (1975) como o principal motivo para o desempenho dos algoritmos genéticos (Genetic Algorithms (GAs)). A hipótese de Building Blocks (BBs) sugere que algoritmos genéticos mais eficientes poderiam ser implementados, contudo, apenas anos depois essas ideias puderam ser avaliadas experimentalmente no contexto de algoritmos de estimação de distribuição (Estimation of Distribution Algorithms (EDAs)). EDAs utilizam modelos probabilísticos, estimados a partir da população, para inferir características do espaço de busca que poderiam ser utilizadas para implementar operadores de reprodução mais eficazes. Tanto em problemas mono- quanto multi-objetivo, EDAs emergiram sob a premissa de que a eficácia dos operadores de reprodução seria proporcional à representatividade dos modelos probabilísticos utilizados. No entanto, estudos recentes tem demonstrado que a dificuldade em se construir modelos confiáveis pode tornar essa premissa inviável. Ou seja, para certos problemas de otimização os modelos probabilísticos utilizados seriam, em geral, de baixa qualidade e, portanto, não produziriam operadores eficazes. Esta tese trata das limitações encontradas na construção de modelos probabilísticos (linkage learning) sob a perspectiva da multimodalidade dos problemas em questão. A análise teórica considerou problemas aditivamente separáveis, enquanto a generalização das conclusões foi investigada em instâncias do modelo NK-landscapes e do problema da mochila multidimensional (Multidimensional Knapsack Problem (MKP)). Os resultados indicaram que a acurácia dos modelos probabilísticos é se relaciona inversamente ao grau de multimodalidade da função objetivo e que, em casos de extrema multimodalidade a construção de modelos probabilísticos confiáveis pode ser tornar infactível. Este resultado poderia inviabilizar o uso de EDAs no contexto multiobjetivo, devido a intrínseca multimodalidade de tais problemas. No entanto, observou-se que apesar da ausência de estatísticas confiáveis sobre cada uma das funções objetivo, a correlação entre elas se torna estatisticamente observável e útil aos operadores de reprodução na manutenção da diversidade e controle convergência da população. / The supposed ubiquity of nearly-decomposable systems was interpreted by Holland (1975) as the rationale for the performance of Genetic Algorithms (GAs), the Building Block (BB) hypothesis. His seminal studies suggest more efficient GAs as viable, but only later on his ideas have become practically tangible in the context of Estimation of Distribution Algorithms (EDAs). EDAs employ probabilistic modeling so as to infer properties of the search space (BBs) that could be useful for the effectiveness of reproduction operators. In both, single- and multi-objective contexts, EDAs have emerged on the assumption there is a correlation between how much information a model can conceive and how effective reproduction operators can be. However, more recent results suggest the difficulties in producing accurate linkage models can prevent such a relation to be true. In other words, for some optimization problems linkage learning might not be able to produce accurate linkage models, hence EDAs would not outperform GAs. This thesis addresses the limits of linkage learning in the context of single- and bi-objective problems, regarding the influence of multimodality on the accuracy of the linkage models and the efficiency of EDAs. A theoretical analysis was performed in terms of additively separable functions and general conclusions are assessed through experimentation with instances of the NK-model and the Multidimensional Knapsack Problem (MKP). The results indicated that the accuracy of the linkage models tends to decrease as a result of increasing multimodality, which weakens pairwise dependencies and might lead to pairwise independence in extreme cases. Since most EDAs rely on bivariate statistics to estimate multivariate distributions, their applicability is limited to optimization problems within a certain range of multimodality. In multi-objective problems, on the other hand, some EDAs have shown better performance than GAs, which seemed as a contradiction since multi-objective problems are inherently multimodal. Our results suggest that in such cases the correlation among the objective functions becomes statistically evident, as a consequence, linkage learning models such correlation instead of problems substructures, which is useful to obtain a better exploration of extreme regions of the objective space.

A suposta ubiquidade de sistemas decomponíveis foi interpretada por Holland (1975) como o principal motivo para o desempenho dos algoritmos genéticos (Genetic Algorithms (GAs)). A hipótese de Building Blocks (BBs) sugere que algoritmos genéticos mais eficientes poderiam ser implementados, contudo, apenas anos depois essas ideias puderam ser avaliadas experimentalmente no contexto de algoritmos de estimação de distribuição (Estimation of Distribution Algorithms (EDAs)). EDAs utilizam modelos probabilísticos, estimados a partir da população, para inferir características do espaço de busca que poderiam ser utilizadas para implementar operadores de reprodução mais eficazes. Tanto em problemas mono- quanto multi-objetivo, EDAs emergiram sob a premissa de que a eficácia dos operadores de reprodução seria proporcional à representatividade dos modelos probabilísticos utilizados. No entanto, estudos recentes tem demonstrado que a dificuldade em se construir modelos confiáveis pode tornar essa premissa inviável. Ou seja, para certos problemas de otimização os modelos probabilísticos utilizados seriam, em geral, de baixa qualidade e, portanto, não produziriam operadores eficazes. Esta tese trata das limitações encontradas na construção de modelos probabilísticos (linkage learning) sob a perspectiva da multimodalidade dos problemas em questão. A análise teórica considerou problemas aditivamente separáveis, enquanto a generalização das conclusões foi investigada em instâncias do modelo NK-landscapes e do problema da mochila multidimensional (Multidimensional Knapsack Problem (MKP)). Os resultados indicaram que a acurácia dos modelos probabilísticos é se relaciona inversamente ao grau de multimodalidade da função objetivo e que, em casos de extrema multimodalidade a construção de modelos probabilísticos confiáveis pode ser tornar infactível. Este resultado poderia inviabilizar o uso de EDAs no contexto multiobjetivo, devido a intrínseca multimodalidade de tais problemas. No entanto, observou-se que apesar da ausência de estatísticas confiáveis sobre cada uma das funções objetivo, a correlação entre elas se torna estatisticamente observável e útil aos operadores de reprodução na manutenção da diversidade e controle convergência da população. / The supposed ubiquity of nearly-decomposable systems was interpreted by Holland (1975) as the rationale for the performance of Genetic Algorithms (GAs), the Building Block (BB) hypothesis. His seminal studies suggest more efficient GAs as viable, but only later on his ideas have become practically tangible in the context of Estimation of Distribution Algorithms (EDAs). EDAs employ probabilistic modeling so as to infer properties of the search space (BBs) that could be useful for the effectiveness of reproduction operators. In both, single- and multi-objective contexts, EDAs have emerged on the assumption there is a correlation between how much information a model can conceive and how effective reproduction operators can be. However, more recent results suggest the difficulties in producing accurate linkage models can prevent such a relation to be true. In other words, for some optimization problems linkage learning might not be able to produce accurate linkage models, hence EDAs would not outperform GAs. This thesis addresses the limits of linkage learning in the context of single- and bi-objective problems, regarding the influence of multimodality on the accuracy of the linkage models and the efficiency of EDAs. A theoretical analysis was performed in terms of additively separable functions and general conclusions are assessed through experimentation with instances of the NK-model and the Multidimensional Knapsack Problem (MKP). The results indicated that the accuracy of the linkage models tends to decrease as a result of increasing multimodality, which weakens pairwise dependencies and might lead to pairwise independence in extreme cases. Since most EDAs rely on bivariate statistics to estimate multivariate distributions, their applicability is limited to optimization problems within a certain range of multimodality. In multi-objective problems, on the other hand, some EDAs have shown better performance than GAs, which seemed as a contradiction since multi-objective problems are inherently multimodal. Our results suggest that in such cases the correlation among the objective functions becomes statistically evident, as a consequence, linkage learning models such correlation instead of problems substructures, which is useful to obtain a better exploration of extreme regions of the objective space.

This study first introduces an order-free chromosome encoding to enhance the performance of genetic algorithms by learning the linkage of building blocks in non-binary encodings. The method introduces a measure called affinity which is based on the statistical properties of gene valuations in the population. It uses the affinity values of the local and global gene pairs to construct a global permutation with tight building block positioning. Method is tested and experimental results are shown for a group of deceptive and real life test problems. Then, study proposes a gene level concurrency model where each gene position is implemented on a different process. This combines the advantages of implicit parallelism and a chromosome structure free approach. It also helps implementation of gene reordering method introduced and probably other non-linear chromosome encodings.

As the problem of urban-rural inequality in China becomes increasingly severe, urban-rural integration has become a hot topic among both researchers and policymakers. However, to achieve urban-rural integration faces the challenges from dualism in institutional arrangements, diversity in territorial contexts, and uncertainty in development environments. In response to these challenges, this research employs the idea of ‘economic linkages of small towns’ to develop a rural-centred, place-based, and process-oriented approach towards urban-rural integration. This research examines the functions, patterns, and dynamics of economic linkages of small towns under the wider economic-spatial restructuring process brought by rapid economic growth and urbanisation in China. More specifically, this research explores the implications of small towns’ economic linkages for integrated development of urban and rural areas. Based on the idea of ‘problem-solving’, this research develops the conceptual framework of ‘Learning-based Territorial Economic System (TES)’ which includes ‘knowledge system’, ‘organisational system’, and ‘territorial system’. This conceptual framework conceptualises ‘economic linkages’ as interactions between economic actors who participated in various ‘interactive situations’ in solving local development problems. This research carried out two case studies of successful small town and rural development in Kunshan, Jiangsu and Shunde, Guangdong. The empirical findings demonstrate that economic linkages are crucial in identifying local development problems, getting access to key economic resources, and coordinating economic activities in uncertain circumstances. Based on the empirical findings, this research develops two development models of Learning-based TES – the Kunshan Model and the Shunde Model – as coherent systems of economic linkages in problem-solving processes. Explicitly, the Kunshan Model features interactive situations of competitive positioning, elite coalition-building, and synchronised operation and the Shunde Model features interactive situations of reflective monitoring, skill matching, and communicative mediation. In application of these two development models, this research formulates a ‘3-step formula’ as key policy implication, including assessment, experiment, and institutionalisation. Such ‘3-step formula’ can contribute to build up local problem-solving capacities that lead to more substantial urban-rural integration.