Non-standard approaches to evolutionary algorithms in an optimization dilemma

Este artículo pretende ser un ensayo de tipo crítico-reflexivo, que toma como base el conocido problema que se presenta en el Dilema Exploración-Explotación (DEE) cuando se trabaja con Algoritmos Evolutivos (AEs) y se centra en las propuestas, en este aspecto, tanto de los enfoques tradicionales, como de los enfoques recientes que manejan la población de soluciones (individuos) de manera distinta a los AEs estándar, a saber: el Modelo Evolutivo Aprendible (MEVA) y los Algoritmos de Estimación de Distribuciones (AEDs).This article is intended to be a critical-reflexive essay based on a well-known problem: the Exploration-Exploitation Dilemma (DEE, in spanish) when working with Evolutionary Algorithms (AEs, in Spanish) and, in this respect, focuses on the proposals that study both: traditional approaches and recent ones handling the population of solutions (individuals) differently from the AEs standard, which are: the Learnable Evolution Model (MEVA, in spanish) and the Estimation of Distribution Algorithms (AEDs, in spanish

Otimização multiobjetivo com estimação de distribuição guiada por tomada de decisão multicritério

Orientadores: Fernando José Von Zuben, Guilherme Palermo CoelhoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Considerando as meta-heurísticas estado-da-arte para otimização multiobjetivo (MOO, do inglês Multi-Objective Optimization), como NSGA-II, NSGA-III, SPEA2 e SMS-EMOA, apenas um critério de preferência por vez é levado em conta para classificar soluções ao longo do processo de busca. Neste trabalho, alguns dos critérios de seleção adotados por esses algoritmos estado-da-arte, incluindo classe de não-dominância e contribuição para a métrica de hipervolume, são utilizados em conjunto por uma técnica de tomada de decisão multicritério (MCDM, do inglês Multi-Criteria Decision Making), mais especificamente o algoritmo TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), responsável por ordenar todas as soluções candidatas. O algoritmo TOPSIS permite o uso de abordagens baseadas em múltiplas preferências, ao invés de apenas uma como na maioria das técnicas híbridas de MOO e MCDM. Cada preferência é tratada como um critério com uma importância relativa determinada pelo tomador de decisão. Novas soluções candidatas são então amostradas por meio de um modelo de distribuição, neste caso uma mistura de Gaussianas, obtido a partir da lista ordenada de soluções candidatas produzida pelo TOPSIS. Essencialmente, um operador de roleta é utilizado para selecionar um par de soluções candidatas de acordo com o seu mérito relativo, adequadamente determinado pelo TOPSIS, e então uma novo par de soluções candidatas é gerado a partir de perturbações Gaussianas centradas nas correspondentes soluções candidatas escolhidas. O desvio padrão das funções Gaussianas é definido em função da distância das soluções no espaço de decisão. Também foram utilizados operadores para auxiliar a busca a atingir regiões potencialmente promissoras do espaço de busca que ainda não foram mapeadas pelo modelo de distribuição. Embora houvesse outras opções, optou-se por seguir a estrutura do algoritmo NSGA-II, também adotada no algoritmo NSGA-III, como base para o método aqui proposto, denominado MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Assim, os aspectos distintos da proposta, quando comparada com o NSGA-II e o NSGA-III, são a forma como a população de soluções candidatas é ordenada e a estratégia adotada para gerar novos indivíduos. Os resultados nos problemas de teste ZDT mostram claramente que nosso método é superior aos algoritmos NSGA- II e NSGA-III, e é competitivo com outras meta-heurísticas bem estabelecidas na literatura de otimização multiobjetivo, levando em conta as métricas de convergência, hipervolume e a medida IGDAbstract: Considering the state-of-the-art meta-heuristics for multi-objective optimization (MOO), such as NSGA-II, NSGA-III, SPEA2 and SMS-EMOA, only one preference criterion at a time is considered to properly rank candidate solutions along the search process. Here, some of the preference criteria adopted by those state-of-the-art algorithms, including non-dominance level and contribution to the hypervolume, are taken together as inputs to a multi-criteria decision making (MCDM) strategy, more specifically the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), responsible for sorting all candidate solutions. The TOPSIS algorithm allows the use of multiple preference based approaches, rather than focusing on a particular one like in most hybrid algorithms composed of MOO and MCDM techniques. Here, each preference is treated as a criterion with a relative relevance to the decision maker (DM). New candidate solutions are then generated using a distribution model, in our case a Gaussian mixture model, derived from the sorted list of candidate solutions produced by TOPSIS. Essentially, a roulette wheel is used to choose a pair of the current candidate solutions according to the relative quality, suitably determined by TOPSIS, and after that a new pair of candidate solutions is generated as Gaussian perturbations centered at the corresponding parent solutions. The standard deviation of the Gaussian functions is defined in terms of the parents distance in the decision space. We also adopt refreshing operators, aiming at reaching potentially promising regions of the search space not yet mapped by the distribution model. Though other choices could have been made, we decided to follow the structural conception of the NSGA-II algorithm, also adopted in the NSGA-III algorithm, as basis for our proposal, denoted by MOMCEDA (Multi-Objective Multi-Criteria Estimation of Distribution Algorithm). Therefore, the distinctive aspects, when compared to NSGA-II and NSGA-III, are the way the current population of candidate solutions is ranked and the strategy adopted to generate new individuals. The results on ZDT benchmarks show that our method is clearly superior to NSGA-II and NSGA-III, and is competitive with other wellestablished meta-heuristics for multi-objective optimization from the literature, considering convergence to the Pareto front, hypervolume and IGD as performance metricsMestradoEngenharia de ComputaçãoMestre em Engenharia Elétrica2016/21031-0FAPESPCAPE

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

A Multi-gaussian Component Eda With Restarting Applied To Direction Of Arrival Tracking

This paper analyzes the application of a multi-population Gaussian-based estimation of distribution algorithm equipped with a restarting strategy and mutation, named MGcEDA, to the problem of estimating the Direction of Arrival (DOA) of time-varying plane waves impinging on a uniform linear array of sensors. This problem requires the minimization of a dynamic cost function which is non-linear, non-quadratic, multimodal and variant with respect to the signal-to-noise ratio. Experiments showed that MGcEDA was able to quickly respond to changes in the source features in scenarios with different levels of noise and number of signals. Moreover, MGcEDA outperforms a previously proposed approach in all considered experiments in terms of well known performance measures. © 2013 IEEE.15561563Bacardit, J., Stout, M., Hirst, J., Valencia, A., Smith, R., Krasnogor, N., Automated alphabet reduction for protein datasets (2009) BMC Bioinformat-ics, 10 (1), p. 6Badidi, L., Radouane, L., A neural network approach for doa estimation and tracking (2000) Statistical Signal and Array Processing 2000. Proceedings of the Tenth, pp. 434-438. , IEEE Workshop onBoccato, L., De França, F., Krummenauer, R., Attux, R., Von Zuben, F., Lopes, A., Immune-inspired dynamic optimization for the direction of arrival estimation problem (2009) Proceedings of the XXVII Brazilian Telecommunications Symposium (In Portuguese)Boccato, L., Krummenauer, R., Attux, R., Lopes, A., Improving the efficiency of natural computing algorithms in DOA estimation using a noise filtering approach (2012) Circuits, Systems, and Signal Processing, pp. 1-11Application of natural computing algorithms to maximum likelihood estimation of direction of arrival (2012) Signal Processing, 92 (5), pp. 1338-1352Chen, C.-H., Chen, Y., Real-coded ecga for economic dispatch (2007) Proceedings of the 9th Conference on Genetic and Evolutionary Computation, Ser. GECCO '07, pp. 1920-1927Chen, Y., Wiesel, A., Eldar, Y., Hero, A., Shrinkage algorithms for MMSE covariance estimation (2010) Signal Processing IEEE Transactions on, 58 (10), pp. 5016-5029De Castro, L., Von Zuben, F., Learning and optimization using the clonal selection principle (2002) Evolutionary Computation IEEE Transac-tions on, 6 (3), pp. 239-251De França, F.O., Von Zuben, F.J., De Castro, L.N., An artificial immune network for multimodal function optimization on dynamic environments (2005) Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, Ser. GECCO '05, pp. 289-296Gershman, A., Stoica, P., MODE with extra-roots (MODEX): A new DOA estimation algorithm with an improved threshold performance (1999) IEEE International Conference on Acoustics, Speech, and Signal Processing, 5, pp. 2833-2836Gershman, A.B., Array signal processing (2006) Space-Time Wireless Sys-tems: From Array Processing to MIMO Communications, , H. Bölcskel D. G. Papadias, and A.-J. van der Veen, Eds. Cambridge University PressGonçalves, A.R., Von Zuben, F.J., Online learning in estimation of distribution algorithms for dynamic environments (2011) Evolutionary Computation (CEC) 2011, pp. 62-69. , IEEE Congress onHanda, H., The effectiveness of mutation operation in the case of estimation of distribution algorithms (2007) Biosystems, 87 (2), pp. 243-251Hansen, N., (2011) The CMA Evolution Strategy: A Tutorial, , https://www.lri.fr/hansen/cmatutorial.pdf, Jun. [Online]. AvailableHauschild, M., Pelikan, M., An introduction and survey of estimation of distribution algorithms (2011) Swarm and Evolutionary Computation, 1 (3), pp. 111-128Hayes, M.S., Minsker, B.S., (2005) Evaluation of Advanced Genetic Algorithms Applied to Groundwater Remediation Design, , Ph.D. dissertation University of Illinois at Urbana-ChampaignHung, J.-C., Modified particle swarm optimization structure approach to direction of arrival estimation (2013) Applied Soft Computing, 13 (1), pp. 315-320Karamalis, P., Marousis, A., Kanatas, A., Constantinou, P., Direction of arrival estimation using genetic algorithms (2001) Vehicular Technology Conference IEEE 53rd, 1, pp. 162-166Kay, S.M., (1993) Fundamentals of Statistical Signal Processing, 1. , Estimation Theory. Englewood Cliffs, NJ Prentice Hall Signal Processing SeriesKrim, H., Viberg, M., Two decades of array signal processing research: The parametric approach (1996) Signal Processing Magazine IEEE, 13 (4), pp. 67-94Krummenauer, R., Cazarotto, M., Lopes, A., Larzabal, P., Forster, P., Improving the threshold performance of maximum likelihood estimation of direction of arrival (2010) Signal Processing, 90 (5), pp. 1582-1590Larrañaga, P., Lozano, J., (2002) Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, , Springer NetherlandsLedoit, O., Wolf, M., Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003) Journal of Empirical Finance, 10 (5), pp. 603-621Li, C., Yang, S., Nguyen, T., Yu, E., Yao, X., Jin, Y., Beyer, H., Suganthan, P., Benchmark generator for CEC'2009 competition on dynamic optimization (2008) Dept. Comput. Sci., , Univ. Leicester, Leicester, UK, Tech. RepLiu, K., O'Leary, D., Stewart, G., Wu, Y.-J., URV ESPRIT for tracking time-varying signals," Signal Processing (1994) IEEE Transactions on, 42 (12), pp. 3441-3448Luo, N., Qian, F., Estimation of distribution algorithm sampling under gaussian and cauchy distribution in continuous domain (2010) 8th IEEE International Conference on Control and Automation (ICCA), pp. 1716-1720Stein, J., Inadmissibility of the usual estimator for the mean of a multivariate normal distribution (1956) Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, Ed, pp. 197-206. , University of California PressStoica, P., Nehorai, A., Performance study of conditional and unconditional direction-of-arrival estimation (1990) IEEE Transactions on Acoustics, Speech, and Signal Processing, 38 (10), pp. 1783-1795Stoica, P., Sharman, K.C., Maximum likelihood methods for direction-of-arrival estimation (1990) IEEE Trans. on Acoustic, Speech and Signal Processing, 38 (7), pp. 1132-1143Novel eigenanalysis method for direction estimation (1990) IEEE Proceedings Part F (Radar and Signal Processing), 137 (1), pp. 19-26Stoica, P., Sharman, K., Novel eigenanalysis method for direction estimation (1990) Radar and Signal Processing IEEE Proceedings of, 137 (1), pp. 19-26Van Trees, H.L., (2001) Optimum Array Processing Part IV of Detection, Estimation and Modulation Theory, , New York, USA: John Wiley & SonsYang, S., Yao, X., Experimental study on population-based incremental learning algorithms for dynamic optimization problems (2005) Soft Comp, 9, pp. 815-834. , 0Population-based incremental learning with associative memory for dynamic environments (2008) Evolutionary Computation IEEE Transac-tions on, 12 (5), pp. 542-561Yu, T.-L., Santarelli, S., Goldberg, D., Military antenna design using a simple genetic algorithm and hboa (2006) Scalable Optimization Via Probabilistic Modeling, Ser. Studies in Computational Intelligence, 33, pp. 275-289. , M. Pelikan, K. Sastry, and E. CantúPaz, Eds Springer Berlin HeidelbergYuan, B., Orlowska, M., Sadiq, S., Extending a class of continuous estimation of distribution algorithms to dynamic problems (2008) Optimiza-tion Letters, 2 (3), pp. 433-44