A Runtime Analysis of Parallel Evolutionary Algorithms in Dynamic Optimization

A simple island model with λλ islands and migration occurring after every ττ iterations is studied on the dynamic fitness function Maze. This model is equivalent to a (1+λ)(1+λ) EA if τ=1τ=1 , i. e., migration occurs during every iteration. It is proved that even for an increased offspring population size up to λ=O(n1−ϵ)λ=O(n1−ϵ) , the (1+λ)(1+λ) EA is still not able to track the optimum of Maze. If the migration interval is chosen carefully, the algorithm is able to track the optimum even for logarithmic λλ . The relationship of τ,λτ,λ , and the ability of the island model to track the optimum is then investigated more closely. Finally, experiments are performed to supplement the asymptotic results, and investigate the impact of the migration topology

Complex System Optimization using Biogeography-Based Optimization

Complex systems are frequently found in modern industry. But with their multisubsystems, multiobjectives, and multiconstraints, the optimization of complex systems is extremely hard. In this paper, a new algorithm adapted from biogeography-based optimization (BBO) is introduced for complex system optimization. BBO/Complex is the combination of BBO with a multiobjective ranking system, an innovative migration approach, and effective diversity control. Based on comparisons with three complex system optimization algorithms (multidisciplinary feasible (MDF), individual discipline feasible (IDF), and collaborative optimization (CO)) on four real-world benchmark problems, BBO/Complex demonstrates competitive performance. BBO/Complex provides the best performance in three of the benchmark problems and the second best in the fourth problem

Complex System Optimization using Biogeography-Based Optimization

Complex systems are frequently found in modern industry. But with their multisubsystems, multiobjectives, and multiconstraints, the optimization of complex systems is extremely hard. In this paper, a new algorithm adapted from biogeography-based optimization (BBO) is introduced for complex system optimization. BBO/Complex is the combination of BBO with a multiobjective ranking system, an innovative migration approach, and effective diversity control. Based on comparisons with three complex system optimization algorithms (multidisciplinary feasible (MDF), individual discipline feasible (IDF), and collaborative optimization (CO)) on four real-world benchmark problems, BBO/Complex demonstrates competitive performance. BBO/Complex provides the best performance in three of the benchmark problems and the second best in the fourth problem

The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization

Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to (Formula presented.) islands optimizing the so-called Maze fitness function (Kötzing and Molter in Proceedings of parallel problem solving from nature (PPSN XII), Springer, Berlin, pp 113–122, 2012). Previous work has shown that when a complete migration topology is used, migration must not occur too frequently, nor too soon before the optimum changes, to track the optimum of the Maze function. We show that using a sparse migration topology alleviates these restrictions. More specifically, we prove that there exist choices of model parameters for which using a unidirectional ring of logarithmic diameter as the migration topology allows the model to track the oscillating optimum through nMaze-like phases with high probability, while using any graph of diameter less than (Formula presented.) for some sufficiently small constant (Formula presented.) results in the island model losing track of the optimum with overwhelming probability. Experimentally, we show that very frequent migration on a ring topology is not an effective diversity mechanism, while a lower migration rate allows the ring topology to track the optimum for a wider range of oscillation patterns. When migration occurs only rarely, we prove that dense migration topologies of small diameter may be advantageous. Combined, our results show that the sparse migration topology is able to track the optimum through a wider range of oscillation patterns, and cope with a wider range of migration frequencies

Ring Migration Topology Helps Bypassing Local Optima

Running several evolutionary algorithms in parallel and occasionally exchanging good solutions is referred to as island models. The idea is that the independence of the different islands leads to diversity, thus possibly exploring the search space better. Many theoretical analyses so far have found a complete (or sufficiently quickly expanding) topology as underlying migration graph most efficient for optimization, even though a quick dissemination of individuals leads to a loss of diversity. We suggest a simple fitness function FORK with two local optima parametrized by $r \geq 2$ and a scheme for composite fitness functions. We show that, while the (1+1) EA gets stuck in a bad local optimum and incurs a run time of $\Theta(n^{2r})$ fitness evaluations on FORK, island models with a complete topology can achieve a run time of $\Theta(n^{1.5r})$ by making use of rare migrations in order to explore the search space more effectively. Finally, the ring topology, making use of rare migrations and a large diameter, can achieve a run time of $\tilde{\Theta}(n^r)$, the black box complexity of FORK. This shows that the ring topology can be preferable over the complete topology in order to maintain diversity.Comment: 12 page

Graphics Processing Unit–Enhanced Genetic Algorithms for Solving the Temporal Dynamics of Gene Regulatory Networks

Understanding the regulation of gene expression is one of the key problems in current biology. A promising method for that purpose is the determination of the temporal dynamics between known initial and ending network states, by using simple acting rules. The huge amount of rule combinations and the nonlinear inherent nature of the problem make genetic algorithms an excellent candidate for finding optimal solutions. As this is a computationally intensive problem that needs long runtimes in conventional architectures for realistic network sizes, it is fundamental to accelerate this task. In this article, we study how to develop efficient parallel implementations of this method for the fine-grained parallel architecture of graphics processing units (GPUs) using the compute unified device architecture (CUDA) platform. An exhaustive and methodical study of various parallel genetic algorithm schemes—master-slave, island, cellular, and hybrid models, and various individual selection methods (roulette, elitist)—is carried out for this problem. Several procedures that optimize the use of the GPU’s resources are presented. We conclude that the implementation that produces better results (both from the performance and the genetic algorithm fitness perspectives) is simulating a few thousands of individuals grouped in a few islands using elitist selection. This model comprises 2 mighty factors for discovering the best solutions: finding good individuals in a short number of generations, and introducing genetic diversity via a relatively frequent and numerous migration. As a result, we have even found the optimal solution for the analyzed gene regulatory network (GRN). In addition, a comparative study of the performance obtained by the different parallel implementations on GPU versus a sequential application on CPU is carried out. In our tests, a multifold speedup was obtained for our optimized parallel implementation of the method on medium class GPU over an equivalent sequential single-core implementation running on a recent Intel i7 CPU. This work can provide useful guidance to researchers in biology, medicine, or bioinformatics in how to take advantage of the parallelization on massively parallel devices and GPUs to apply novel metaheuristic algorithms powered by nature for real-world applications (like the method to solve the temporal dynamics of GRNs)

Complex System Optimization Using Biogeography-Based Optimization

Complex systems are frequently found in modern industry. But with their multisubsystems, multiobjectives, and multiconstraints, the optimization of complex systems is extremely hard. In this paper, a new algorithm adapted from biogeography-based optimization (BBO) is introduced for complex system optimization. BBO/Complex is the combination of BBO with a multiobjective ranking system, an innovative migration approach, and effective diversity control. Based on comparisons with three complex system optimization algorithms (multidisciplinary feasible (MDF), individual discipline feasible (IDF), and collaborative optimization (CO)) on four real-world benchmark problems, BBO/Complex demonstrates competitive performance. BBO/Complex provides the best performance in three of the benchmark problems and the second best in the fourth problem

Design and Analysis of Schemes for Adapting Migration Intervals in Parallel Evolutionary Algorithms

The migration interval is one of the fundamental parameters governing the dynamic behaviour of island models. Yet, there is little understanding on how this parameter affects performance, and how to optimally set it given a problem in hand. We propose schemes for adapting the migration interval according to whether fitness improvements have been found. As long as no improvement is found, the migration interval is increased to minimise communication. Once the best fitness has improved, the migration interval is decreased to spread new best solutions more quickly. We provide a method for obtaining upper bounds on the expected running time and the communication effort, defined as the expected number of migrants sent. Example applications of this method to common example functions show that our adaptive schemes are able to compete with, or even outperform the optimal fixed choice of the migration interval, with regard to running time and communication effort

A study on the deployment of GA in a grid computing framework

Dissertação de Mestrado, Engenharia Informática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2015Os algoritmos genéticos (AG) desempenham um papel importante na resolução de muitos problemas de otimização, incluindo científicos, económicos e socialmente relevantes. Os AGs, conjuntamente com a programação genética (PG), a programação evolutiva (PE), e as estratégias de evolução, são as principais classes de algoritmos evolutivos (AEs), ou seja, algoritmos que simulam a evolução natural. Em aplicações do mundo real o tempo de execução dos AGs pode ser computacionalmente exigente, devido, principalmente, aos requerimentos relacionados com o tamanho da população. Este problema pode ser atenuado através da paralelização, que pode levar a GAs mais rápidos e com melhor desempenho. Embora a maioria das implementações existentes de Algoritmos Genéticos Paralelos (AGPs) utilize clusters ou processamento massivamente paralelo (PMP), a computação em grid é economicamente relevante (uma grid pode ser construída utilizando computadores obsoletos) e tem algumas vantagens sobre os clusters, como por exemplo a não existência de controlo centralizado, segurança e acesso a recursos heterogéneos distribuídos em organizações virtuais dinâmicas em todo o mundo. Esta investigação utiliza o problema do mundo real denominado de Problema do Caixeiro Viajante (PCV) como referência (benchmark) para a paralelização de AGs numa infraestrutura de computação em grid. O PCV é um problema NP-difícil de otimização combinatória, bem conhecido, que pode ser formalmente descrito como o problema de encontrar, num grafo, o ciclo hamiltoniano mais curto. De facto, muitos problemas de roteamento, produção e escalonamento encontrados na engenharia, na indústria e outros tipos de negócio, podem ser equiparados ao PCV, daí a sua importância. Informalmente, o problema pode ser descrito da seguinte forma: Um vendedor tem um grande número de cidades para visitar e precisa encontrar o caminho mais curto para visitar todas as cidades, sem revisitar nenhuma delas. A principal dificuldade em encontrar as melhores soluções para o PCV é o grande número de caminhos possíveis; (n-1)! / 2 para um caminho de n cidades simétricas. À medida que o número de cidades aumenta, o número de caminhos possíveis também aumenta de uma forma fatorial. O PCV é, portanto, computacionalmente intratável, justificando plenamente a utilização de um método de otimização estocástica, como os AGs. No entanto, mesmo um algoritmo de otimização estocástica pode demorar demasiado tempo para calcular, à medida que o tamanho do problema aumenta. Num AG para grandes populações, o tempo necessário para resolver o problema pode até ser excessivamente longo. Uma forma de acelerar tais algoritmos é usar recursos adicionais, tais como elementos adicionais de processamento funcionando em paralelo e colaborando para encontrar a solução. Isto leva a implementações simultâneas de AGs, adequadas para a implementação em recursos colaborando em paralelo e/ou de forma distribuída. Os Algoritmos evolutivos paralelos (AEPs) destinam-se a implementar algoritmos mais rápidos e com melhor desempenho, usando populações estruturadas, ou seja, distribuições espaciais dos indivíduos. Uma das maneiras possíveis de descentralizar a população é distribuí-la por um conjunto de nós de processamento (ilhas) que trocam periodicamente (migram) potenciais soluções; o chamado modelo de ilhas. O modelo de ilhas permite um número considerável de topologias de migração e, pela Informação que foi possível apurar, há uma carência de trabalhos de investigação sobre a comparação dessas topologias de migração, ao implementar AEPs em infraestruturas de computação em grid. De facto, a comparação de topologias de migração, utilizando uma infraestrutura de computação em grid, como proposto neste trabalho, parece não estar disponível na literatura. Esta comparação tem como objetivo fornecer uma resposta tecnicamente sólida para a questão de investigação: Qual é a topologia, de modelo de ilhas, mais rápida para resolver instâncias do PCV usando um algoritmo genético baseado em ordem, num ambiente de computação em grid, heterogéneo e distribuído, sem uma perda significativa de fitness, comparativamente com a implementação sequencial e panmítica do mesmo algoritmo? Uma hipótese para responder à questão de investigação pode ser expressa da seguinte forma: Para resolver instâncias TSP, usando um algoritmo genético baseado em ordem, num ambiente de computação em grid, heterogéneo e distribuído, sem uma perda significativa de fitness, comparativamente com a implementação sequencial e panmítica do mesmo algoritmo, escolha qualquer uma das topologias coordenadas do modelo de ilhas, de entre as topologias testadas (estrela, roda, árvore, matriz totalmente conectada, árvore-anel, anel) com o maior número de nós possível (mesmo os mais lentos) e selecione a frequência de migração g que otimiza o tempo de execução para a topologia escolhida. A metodologia de investigação é essencialmente experimental, observando e analisando o comportamento do algoritmo ao alterar as propriedades do modelo de ilhas. Os resultados mostram que o AG é acelerado quando implementado num ambiente grid, mantendo a qualidade dos resultados obtidos na versão sequencial. Além disso, mesmo os computadores obsoletos podem ser usados como nós contribuindo para acelerar o tempo de execução do algoritmo. Este trabalho também discute a adequação de uma abordagem assíncrona para a implementação do AG num ambiente de computação em grid