Distributed evolutionary algorithms and their models: A survey of the state-of-the-art

The increasing complexity of real-world optimization problems raises new challenges to evolutionary computation. Responding to these challenges, distributed evolutionary computation has received considerable attention over the past decade. This article provides a comprehensive survey of the state-of-the-art distributed evolutionary algorithms and models, which have been classified into two groups according to their task division mechanism. Population-distributed models are presented with master-slave, island, cellular, hierarchical, and pool architectures, which parallelize an evolution task at population, individual, or operation levels. Dimension-distributed models include coevolution and multi-agent models, which focus on dimension reduction. Insights into the models, such as synchronization, homogeneity, communication, topology, speedup, advantages and disadvantages are also presented and discussed. The study of these models helps guide future development of different and/or improved algorithms. Also highlighted are recent hotspots in this area, including the cloud and MapReduce-based implementations, GPU and CUDA-based implementations, distributed evolutionary multiobjective optimization, and real-world applications. Further, a number of future research directions have been discussed, with a conclusion that the development of distributed evolutionary computation will continue to flourish

Populações baseadas em multisets para algoritmos evolutivos

Os algoritmos evolutivos simulam a evolução natural de uma população de indivíduos aplicando iterativamente operadores genéticos, recombinação, mutação e seleção dos mais aptos. O processo evolutivo pode ser visto como um processo de otimização. Nesse caso, os indivíduos representam soluções do problema e as variáveis do problema são codificados no equivalente aos genes. Estes algoritmos podem ser facilmente implementados e existem variantes especializadas para resolver várias classes de problemas. Uma das maiores dificuldades apresentadas por estes algoritmos é a convergência prematura da população para soluções sub-ótimas antes do espaço de procura ser devidamente explorado. Várias estratégias foram desenvolvidas para reduzir este risco e, neste trabalho, estudamos a possibilidade de substituir a representação da população. Tradicionalmente as populações são representadas como coleções de indivíduos e nesta tese propomos a sua substituição por um multiconjunto (multiset). Esta nova forma de representação das populações, que denominamos multipopulações, permite manipular um conjunto de genomas e os seus clones, multi-indivíduos, de uma forma muito eficiente. Adaptamos o processo evolutivo para otimizar multipopulações, estudamos o seu comportamento em vários tipos de algoritmos e problemas e desenvolvemos operadores genéticos especializados para trabalhar com a nova representação. Em resultado disso obtemos uma forma inovadora de manter uma elevada diversidade genética na população. As experiências realizadas permitiram-nos compreender melhor a dinâmica que a nova representação introduz no processo evolutivo e mostrar a sua eficácia.Evolutionary algorithms simulate the natural evolution of a population of individuals by iteratively applying genetic operators, recombination, mutation and selection of the fittest. The evolutionary process can be viewed as an optimization process. In this case, individuals represent problem solutions and the problem variables are encoded in that equivalent to the gene. These algorithms can be easily implemented and there are specialized variants to solve different classes of problems. One of the biggest difficulties presented by these algorithms is the premature convergence of the population to suboptimal solutions before the search space is properly explored. Several strategies were developed to reduce this risk and, in this thesis, we studied the possibility of replacing the representation of the population. Traditionally populations are represented as collections of individuals and in this thesis we propose its replacement by a multiset. This new form of population representation, which we call multipopulations, allows manipulating a set of genomes and their clones, multi-individuals, in a very efficient way. We adapt the evolutionary process to optimize multipopulations, study their behavior on various types of algorithms and problems, and develop specialized genetic operators to work with the new representation. As a result, we get an innovative way to maintain a high genetic diversity in the population. The experiments allowed us to better understand the dynamics that the new representation introduces in the evolutionary process and show its effectiveness

Co-evolutionary Hybrid Bi-level Optimization

Multi-level optimization stems from the need to tackle complex problems involving multiple decision makers. Two-level optimization, referred as ``Bi-level optimization'', occurs when two decision makers only control part of the decision variables but impact each other (e.g., objective value, feasibility). Bi-level problems are sequential by nature and can be represented as nested optimization problems in which one problem (the ``upper-level'') is constrained by another one (the ``lower-level''). The nested structure is a real obstacle that can be highly time consuming when the lower-level is $\mathcal{NP}-hard$. Consequently, classical nested optimization should be avoided. Some surrogate-based approaches have been proposed to approximate the lower-level objective value function (or variables) to reduce the number of times the lower-level is globally optimized. Unfortunately, such a methodology is not applicable for large-scale and combinatorial bi-level problems. After a deep study of theoretical properties and a survey of the existing applications being bi-level by nature, problems which can benefit from a bi-level reformulation are investigated. A first contribution of this work has been to propose a novel bi-level clustering approach. Extending the well-know ``uncapacitated k-median problem'', it has been shown that clustering can be easily modeled as a two-level optimization problem using decomposition techniques. The resulting two-level problem is then turned into a bi-level problem offering the possibility to combine distance metrics in a hierarchical manner. The novel bi-level clustering problem has a very interesting property that enable us to tackle it with classical nested approaches. Indeed, its lower-level problem can be solved in polynomial time. In cooperation with the Luxembourg Centre for Systems Biomedicine (LCSB), this new clustering model has been applied on real datasets such as disease maps (e.g. Parkinson, Alzheimer). Using a novel hybrid and parallel genetic algorithm as optimization approach, the results obtained after a campaign of experiments have the ability to produce new knowledge compared to classical clustering techniques combining distance metrics in a classical manner. The previous bi-level clustering model has the advantage that the lower-level can be solved in polynomial time although the global problem is by definition $\mathcal{NP}$-hard. Therefore, next investigations have been undertaken to tackle more general bi-level problems in which the lower-level problem does not present any specific advantageous properties. Since the lower-level problem can be very expensive to solve, the focus has been turned to surrogate-based approaches and hyper-parameter optimization techniques with the aim of approximating the lower-level problem and reduce the number of global lower-level optimizations. Adapting the well-know bayesian optimization algorithm to solve general bi-level problems, the expensive lower-level optimizations have been dramatically reduced while obtaining very accurate solutions. The resulting solutions and the number of spared lower-level optimizations have been compared to the bi-level evolutionary algorithm based on quadratic approximations (BLEAQ) results after a campaign of experiments on official bi-level benchmarks. Although both approaches are very accurate, the bi-level bayesian version required less lower-level objective function calls. Surrogate-based approaches are restricted to small-scale and continuous bi-level problems although many real applications are combinatorial by nature. As for continuous problems, a study has been performed to apply some machine learning strategies. Instead of approximating the lower-level solution value, new approximation algorithms for the discrete/combinatorial case have been designed. Using the principle employed in GP hyper-heuristics, heuristics are trained in order to tackle efficiently the $\mathcal{NP}-hard$ lower-level of bi-level problems. This automatic generation of heuristics permits to break the nested structure into two separated phases: \emph{training lower-level heuristics} and \emph{solving the upper-level problem with the new heuristics}. At this occasion, a second modeling contribution has been introduced through a novel large-scale and mixed-integer bi-level problem dealing with pricing in the cloud, i.e., the Bi-level Cloud Pricing Optimization Problem (BCPOP). After a series of experiments that consisted in training heuristics on various lower-level instances of the BCPOP and using them to tackle the bi-level problem itself, the obtained results are compared to the ``cooperative coevolutionary algorithm for bi-level optimization'' (COBRA). Although training heuristics enables to \emph{break the nested structure}, a two phase optimization is still required. Therefore, the emphasis has been put on training heuristics while optimizing the upper-level problem using competitive co-evolution. Instead of adopting the classical decomposition scheme as done by COBRA which suffers from the strong epistatic links between lower-level and upper-level variables, co-evolving the solution and the mean to get to it can cope with these epistatic link issues. The ``CARBON'' algorithm developed in this thesis is a competitive and hybrid co-evolutionary algorithm designed for this purpose. In order to validate the potential of CARBON, numerical experiments have been designed and results have been compared to state-of-the-art algorithms. These results demonstrate that ``CARBON'' makes possible to address nested optimization efficiently