The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA)– another simple EDA–, the cGA has been subject to extensive mathematical runtime analyses, often showcasing a similar or even superior performance to competing approaches. Surprisingly though, up to date and in contrast to the UMDA and many other heuristics, we lack a rigorous runtime analysis of the cGA on the LEADINGONES benchmark–one of the most studied theory benchmarks in the domain of evolutionary computation. We fill this gap in the literature by conducting a formal runtime analysis of the cGA on LEADINGONES. For the cGA’s single parameter–called the hypothetical population size–at least polylogarithmically larger than the problem size, we prove that the cGA samples the optimum of LEADINGONES with high probability within a number of function evaluations quasi-linear in the problem size and linear in the hypothetical population size. For the best hypothetical population size, our result matches, up to polylogarithmic factors, the typical quadratic runtime that many randomized search heuristics exhibit on LEADINGONES. Our analysis exhibits some noteworthy differences in the working principles of the two algorithms which were not visible in previous works.

Convolutional neural networks (CNNs) are widely used for image classification; however, setting the appropriate hyperparameters before training is subjective and time consuming, and the search space is not properly explored. This paper presents a novel method for the automatic neural architecture search based on an estimation of distribution algorithm (EDA) for binary classification problems. The hyperparameters were coded in binary form due to the nature of the metaheuristics used in the automatic search stage of CNN architectures which was performed using the Boltzmann Univariate Marginal Distribution algorithm (BUMDA) chosen by statistical comparison between four metaheuristics to explore the search space, whose computational complexity is O(229). Moreover, the proposed method is compared with multiple state-of-the-art methods on five databases, testing its efficiency in terms of accuracy and F1-score. In the experimental results, the proposed method achieved an F1-score of 97.2%, 98.73%, 97.23%, 98.36%, and 98.7% in its best evaluation, better results than the literature. Finally, the computational time of the proposed method for the test set was ≈0.6 s, 1 s, 0.7 s, 0.5 s, and 0.1 s, respectively.

The electricity market faces numerous challenges due to the growing demand for energy, increasing penetration of renewable energy sources, and the need for grid reliability and efficiency. To address these challenges, optimization algorithms have emerged as essential tools for optimizing various aspects of the electricity market, including generation, transmission, distribution, and demand-side management. The review can be done by providing an overview of the key components and challenges of the electricity market, including generation dispatch, unit commitment, economic dispatch, transmission network optimization, and demand response management. It then systematically examines a wide range of optimization techniques employed in addressing these challenges, including linear programming, mixed-integer linear programming, nonlinear programming, dynamic programming, genetic algorithms, particle swarm optimization, simulated annealing, and machine learning-based approaches. This paper presents a comparison of optimization algorithms, RCEDUMDA (Ring-Cellular Encode-Decode Univariate Marginal Distribution Algorithm) and CL_HC2RCEDUMDA (Hill Climbing to Ring Cellular Encode-Decode Univariate Marginal Distribution Algorithm) for the profit maximization of Electricity Market consumers & prosumers.

The electricity market faces numerous challenges due to the growing demand for energy, increasing penetration of renewable energy sources, and the need for grid reliability and efficiency. To address these challenges, optimization algorithms have emerged as essential tools for optimizing various aspects of the electricity market, including generation, transmission, distribution, and demand-side management. The review can be done by providing an overview of the key components and challenges of the electricity market, including generation dispatch, unit commitment, economic dispatch, transmission network optimization, and demand response management. It then systematically examines a wide range of optimization techniques employed in addressing these challenges, including linear programming, mixed-integer linear programming, nonlinear programming, dynamic programming, genetic algorithms, particle swarm optimization, simulated annealing, and machine learning-based approaches. This paper presents a comparison of optimization algorithms, RCEDUMDA (Ring-Cellular Encode-Decode Univariate Marginal Distribution Algorithm) and CL_HC2RCEDUMDA (Hill Climbing to Ring Cellular Encode-Decode Univariate Marginal Distribution Algorithm) for the profit maximization of Electricity Market consumers & prosumers.

In this paper, a novel method for the automatic classification of coronary stenosis based on a feature selection strategy driven by a hybrid evolutionary algorithm is proposed. The main contribution is the characterization of the coronary stenosis anomaly based on the automatic selection of an efficient feature subset. The initial feature set consists of 49 features involving intensity, texture and morphology. Since the feature selection search space was O(2n), being n=49, it was treated as a high-dimensional combinatorial problem. For this reason, different single and hybrid evolutionary algorithms were compared, where the hybrid method based on the Boltzmann univariate marginal distribution algorithm (BUMDA) and simulated annealing (SA) achieved the best performance using a training set of X-ray coronary angiograms. Moreover, two different databases with 500 and 2700 stenosis images, respectively, were used for training and testing of the proposed method. In the experimental results, the proposed method for feature selection obtained a subset of 11 features, achieving a feature reduction rate of 77.5% and a classification accuracy of 0.96 using the training set. In the testing step, the proposed method was compared with different state-of-the-art classification methods in both databases, obtaining a classification accuracy and Jaccard coefficient of 0.90 and 0.81 in the first one, and 0.92 and 0.85 in the second one, respectively. In addition, based on the proposed method’s execution time for testing images (0.02 s per image), it can be highly suitable for use as part of a clinical decision support system.

A hybrid method based on estimation of distribution algorithms to train convolutional neural networks for text categorization

In their recent work, Lehre and Nguyen (2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by the choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most λ(n2+2elnn) fitness evaluations. Since an offspring population size λ of order nlogn can prevent genetic drift, the UMDA can solve the DLB problem with O(n2logn) fitness evaluations. In contrast, for classic evolutionary algorithms no better runtime guarantee than O(n3) is known (which we prove to be tight for the (1+1) EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than many classic evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.

The automatic detection of coronary stenosis is a very important task in computer aided diagnosis systems in the cardiology area. The main contribution of this paper is the identification of a suitable subset of 20 features that allows for the classification of stenosis cases in X-ray coronary images with a high performance overcoming different state-of-the-art classification techniques including deep learning strategies. The automatic feature selection stage was driven by the Univariate Marginal Distribution Algorithm and carried out by statistical comparison between five metaheuristics in order to explore the search space, which is O(249) computational complexity. Moreover, the proposed method is compared with six state-of-the-art classification methods, probing its effectiveness in terms of the Accuracy and Jaccard Index evaluation metrics. All the experiments were performed using two X-ray image databases of coronary angiograms. The first database contains 500 instances and the second one 250 images. In the experimental results, the proposed method achieved an Accuracy rate of 0.89 and 0.88 and Jaccard Index of 0.80 and 0.79, respectively. Finally, the average computational time of the proposed method to classify stenosis cases was ≈0.02 s, which made it highly suitable to be used in clinical practice.

We perform rigorous runtime analyses for the univariate marginal distribution algorithm (UMDA) and the population-based incremental learning (PBIL) Algorithm on LeadingOnes. For the UMDA, the currently known expected runtime on the function is {mathcal {O}}left( nlambda log lambda +n^2right) under an offspring population size lambda =Omega (log n) and a parent population size mu le lambda /(e(1+delta )) for any constant delta >0 (Dang and Lehre, GECCO 2015). There is no lower bound on the expected runtime under the same parameter settings. It also remains unknown whether the algorithm can still optimise the LeadingOnes function within a polynomial runtime when mu ge lambda /(e(1+delta )). In case of the PBIL, an expected runtime of {mathcal {O}}(n^{2+c}) holds for some constant c in (0,1) (Wu, Kolonko and Möhring, IEEE TEVC 2017). Despite being a generalisation of the UMDA, this upper bound is significantly asymptotically looser than the upper bound of {mathcal {O}}left( n^2right) of the UMDA for lambda =Omega (log n)cap {mathcal {O}}left( n/log nright). Furthermore, the required population size is very large, i.e., lambda =Omega (n^{1+c}). Our contributions are then threefold: (1) we show that the UMDA with mu =Omega (log n) and lambda le mu e^{1-varepsilon }/(1+delta ) for any constants varepsilon in (0,1) and 0<delta le e^{1-varepsilon }-1 requires an expected runtime of e^{Omega (mu )} on LeadingOnes, (2) an upper bound of {mathcal {O}}left( nlambda log lambda +n^2right) is shown for the PBIL, which improves the current bound {mathcal {O}}left( n^{2+c}right) by a significant factor of Theta (n^{c}), and (3) we for the first time consider the two algorithms on the LeadingOnes function in a noisy environment and obtain an expected runtime of {mathcal {O}}left( n^2right) for appropriate parameter settings. Our results emphasise that despite the independence assumption in the probabilistic models, the UMDA and the PBIL with fine-tuned parameter choices can still cope very well with variable interactions.

Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes

Cellular estimation of distribution algorithm designed to solve the energy resource management problem under uncertainty

This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.

A simplified run time analysis of the univariate marginal distribution algorithm on LeadingOnes

The compact Genetic Algorithm (cGA) evolves a probability distribution favoring optimal solutions in the underlying search space by repeatedly sampling from the distribution and updating it according to promising samples. We study the intricate dynamics of the cGA on the test function OneMax, and how its performance depends on the hypothetical population size K, which determines how quickly decisions about promising bit values are fixated in the probabilistic model. It is known that the cGA and the Univariate Marginal Distribution Algorithm (UMDA), a related algorithm whose population size is called lambda, run in expected time O(n log n) when the population size is just large enough (K = varTheta (sqrt{n}log n) and lambda = varTheta (sqrt{n}log n), respectively) to avoid wrong decisions being fixated. The UMDA also shows the same performance in a very different regime (lambda =varTheta (log n), equivalent to K = varTheta (log n) in the cGA) with much smaller population size, but for very different reasons: many wrong decisions are fixated initially, but then reverted efficiently. If the population size is even smaller (o(log n)), the time is exponential. We show that population sizes in between the two optimal regimes are worse as they yield larger runtimes: we prove a lower bound of varOmega (K^{1/3}n + n log n) for the cGA on OneMax for K = O(sqrt{n}/log ^2 n). For K = varOmega (log ^3 n) the runtime increases with growing K before dropping again to O(Ksqrt{n} + n log n) for K = varOmega (sqrt{n} log n). This suggests that the expected runtime for the cGA is a bimodal function in K with two very different optimal regions and worse performance in between.

The problem of scheduling parallel tasks graphs (PTGs) represented by directed acyclic graphs (DAGs) in heterogeneous distributed computing systems (HDCSs) is considered an nondeterministic polynomial time (NP) problem due to the diversity of characteristics and parameters, generally opposed, intended to be optimized. The PTGs are scheduled by a scheduler that determines the best location for the sub-tasks that constitute the PTGs and is responsible for allocating the resources of the HDCS to the sub-tasks of the PTGs. To optimize scheduling and allocations, the scheduler extracts characteristics from the internal structure of the PTGs. The prevailing characteristic in existing research is the critical path (CP), which is limited to providing execution paths of PTGs; considering this limitation, we extend the array method proposed in Velarde, which extracts two additional characteristics to the CP: the layering and the density of the graph for scheduling. These characteristics are represented as integer values of the PTGs to be scheduled; the values obtained from the characteristics are stored in arrays representing populations that are evaluated with the heuristic univariate marginal distribution algorithm (UMDA) and in terms of comparison with the genetic algorithm. With the best allocations produced by the algorithms, two performance parameters are evaluated: makespan and waiting time. The results indicate that when more PTGs characteristics are considered, resource allocations are optimized, and scheduling times are reduced. The results obtained with the heuristic algorithms show that UMDA provides shorter scheduling and allocation times compared with the genetic algorithm; UMDA widely distributes the sub-tasks in the clusters, whereas the genetic algorithm compacts the assignments of the PTGs in the clusters with a longer convergence time that translates into longer scheduling and allocation times. Extensive explanations of these conclusions are provided in this work, based on the conducted experiments.

A computational methodology based on inverse modeling and metaheuristics is presented for determining the best parameters of kinetic models aimed to predict the behavior of biomass depolymerization processes during size scaling up. The Univariate Marginal Distribution algorithm, particle swarm optimization, and Interior-Point algorithm were applied to obtain the values of the kinetic parameters (KM and Vmax) of four mathematical models based on the Michaelis–Menten equation: (i) Traditional Michaelis–Menten, (ii) non-competitive inhibition, (iii) competitive inhibition, and (iv) substrate inhibition. The kinetic data were obtained from our own experimentation in micro-scale. The parameters obtained from an optimized micro-scale experiment were compared with a bench scale experiment (0.5 L). Regarding the metaheuristic optimizers, it is concluded that the Interior-Point algorithm is effective in solving inverse modeling problems and has the best prediction power. According to the results, the Traditional model adequately describes the micro-scale experiments. It was found that the Traditional model with optimized parameters was able to predict the behavior of the depolymerization process during size scaling up. The methodology followed in this study can be adopted as a starting point for the solution of future inverse modeling problems.

Estimation of distribution algorithms (EDAs) are a successful branch of evolutionary algorithms (EAs) that evolve a probabilistic model instead of a population. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that the random sampling in the model update can move the sampling frequencies to boundary values not justified by the fitness. This can result in a considerable performance loss. This article gives the first tight quantification of this effect for three EDAs and one ant colony optimizer, namely, for the univariate marginal distribution algorithm, the compact genetic algorithm, population-based incremental learning, and the max-min ant system with iteration-best update. Our results allow to choose the parameters of these algorithms in such a way that within a desired runtime, no sampling frequency approaches the boundary values without a clear indication from the objective function.

El análisis cuantitativo de la arquitectura de las venas temporales superior e inferior y su monitoreo sobre el tiempo puede facilitar el diagnóstico y tratamiento oportuno de la retinopatía diabética. En este trabajo se presenta un novedoso método que consiste de dos etapas correspondientes a la segmentación automática y modelado parabólico de las venas temporales superior e inferior en imágenes de fondo de ojo. En la primera etapa, el detector lineal multiescala (DLM) es empleado para detectar estructuras de tipo arterial en imágenes de la retina. Debido a que DLM es un método de realzado arterial, es necesario aplicar una estrategia de umbralización para clasificar pixeles de tipo arterial con respecto al fondo de la imagen, donde un valor de umbral determinado de forma experimental es comparado con cinco métodos de umbralización del estado del arte. En esta etapa, el método de segmentación propuesto es comparado con seis métodos especializados del estado del arte en términos de eficiencia de segmentación. En la segunda etapa, se desempeña un modelado parabólico mediante una estrategia de optimización utilizando un Algoritmo de Distribución Marginal Univariada sobre las arterias previamente segmentadas, y los resultados son comparados con dos métodos paramétricos del estado del arte y con las delineaciones realizadas por especialistas. Los resultados de segmentación arterial utilizando el detector lineal multiescala demostraron una alta eficiencia de segmentación obteniendo un valor de 0.9618 utilizando la base de datos DRIVE de imágenes de fondo de ojo. De igual forma, los resultados de modelado parabólico entregaron una eficiencia promedio de 0.825 con respecto a las delineaciones realizadas por especialistas oftalmólogos de las venas temporales superior e inferior. En base a los resultados de eficiencia y al tiempo computacional (5.62 segundos), el método propuesto puede considerarse como altamente apropiado para desempeñar diagnóstico asistido por computadora en el área de oftalmología.

Glucose forecasting combining Markov chain based enrichment of data, random grammatical evolution and Bagging

Parameter optimization for the smoothed-particle hydrodynamics method by means of evolutionary metaheuristics