Variance analysis and adaptive control in intelligent system based on Gaussian model

Evolutionary algorithms and elliptical copulas applied to continuous optimization problems

A comparative study of hybrid estimation distribution algorithms in solving the facility layout problem

Robust estimation of distribution algorithms via fitness landscape analysis for optimal low-thrust orbital maneuvers

As a typical model-based evolutionary algorithm, estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied in global optimization. However, the commonly used Gaussian EDA (GEDA) usually suffers from premature convergence, which severely limits its search efficiency. This paper first systematically analyzes the reasons for the deficiency of traditional GEDA, then tries to enhance its performance by exploiting the evolution direction, and finally develops a new GEDA variant named EDA2. Instead of only utilizing some good solutions produced in the current generation to estimate the Gaussian model, EDA2 preserves a certain number of high-quality solutions generated in the previous generations into an archive and employs these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model, which in turn can guide EDA2 toward more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA2 since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA2, we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs. The experimental results demonstrate that EDA2 is efficient and competitive.

This paper presents our work on Estimation of Distribution Algorithms (EDAs) that address sequencing problems, i.e., the task of finding the best ordering of a set of items or an optimal schedule to perform a given set of operations. Specifically, we focus on using probabilistic models based on $n$-gram statistics. These models have been used extensively in modeling the statistical properties of sequences. We start with an EDA that uses a bigram model, then extend this scheme to higher-order models. However, directly replacing the bigram model with a higher-order model results in premature convergence. We give an explanation on this situation, along with some empirical support. We then introduce a technique for combining multiple models of different orders, which allows for smooth transition from lower-order models to higher-order ones. Furthermore, this technique can also be used to incorporate other heuristics as well as prior knowledge about the problem into the search process. Promising preliminary results on solving Traveling Salesman Problems (TSPs) are presented.

In agriculture, the soil properties influence the productivity and quality of crops. The farmer expects that in a specific area of the land, the physicochemical characteristics of the soil will be homogeneous as the selected crop has the desired quality and minimizes the use of fertilizers. There are three approaches to determining the correct delimitation of the land in the state-of-the art. The first one (k-means and fuzzy k-means) is impractical for current agricultural technology. The second approach is based on integer linear programming and a pre-processing step. This approach limits the shapes of delimited zones to rectangular, and the third approach extends the solution search space and generates orthogonal regions using Estimation of Distribution Algorithms (EDA). In this work, we generate orthogonal regions with a different approach to the EDA, a greedy construction heuristic. Our heuristic produces feasible solutions with a reasonable running time compared with the running times of EDA.

In this paper, a new approach for motion generation and optimization of the flexible macro-micro manipulator system is proposed based on Estimation of Distribution Algorithm (EDA). The macro-micro manipulator system is a redundant system, of which inverse kinematics remains challenging, with no generic solution to date. Here, the manipulator system configurations, or the optimal joint motions, are generated using the EDA algorithm base on Gaussian probability model. Compared with simple genetic algorithms (SGA), this approach uses fewer parameters and the time for motion optimization is remarkably reduced. The proposed approach shows excellent performance on motion generation and optimization of a flexible macro-micro manipulator system, as demonstrated by the simulation results.

Particle Swarm Optimization (PSO) is a stochastic optimization approach that originated from early attempts to simulate the behavior of birds looking for food. Estimation of distributions algorithms (EDAs) are a class of evolutionary algorithms that build and maintain a probabilistic model capturing the search space characteristics and continuously use this model to generate new individuals. In this work, we propose a new PSO and EDA hybrid algorithm that uses the particles' distribution in the search space in order to adjust the search space bounds, hence, restricting the particles movement as well as their allowable maximum velocity. The algorithms is augmented with a mechanism to overcome premature convergence and escape local minima. The algorithm is compared to the standard PSO algorithm using a suite of well-known benchmark optimization functions. Experimental results show that the proposed algorithm has a promising performance.

Genetic Algorithms (GAs) are known for their capacity to explore large search spaces and due to this ability, they were to some extent applied to Inductive Logic Programming (ILP) problem. Although Estimation of Distribution Algorithms (EDAs) perform better in most problems when compared to standard GAs, this kind of algorithm have not been applied to ILP. This work presents an ILP system based on EDA. Preliminary results show that the proposed system is superior when compared to a "standard" GA and it is very competitive when compared to the state of the art ILP system Aleph.

Purpose Marine transportation has been faced with an increasing demand for containerized cargo during the past decade. Marine container terminals (MCTs), as the facilities for connecting seaborne and inland transportation, are expected to handle the increasing amount of containers, delivered by vessels. Berth scheduling plays an important role for the total throughput of MCTs as well as the overall effectiveness of the MCT operations. This study aims to propose a novel island-based metaheuristic algorithm to solve the berth scheduling problem and minimize the total cost of serving the arriving vessels at the MCT. Design/methodology/approach A universal island-based metaheuristic algorithm (UIMA) was proposed in this study, aiming to solve the spatially constrained berth scheduling problem. The UIMA population was divided into four sub-populations (i.e. islands). Unlike the canonical island-based algorithms that execute the same metaheuristic on each island, four different population-based metaheuristics are adopted within the developed algorithm to search the islands, including the following: evolutionary algorithm (EA), particle swarm optimization (PSO), estimation of distribution algorithm (EDA) and differential evolution (DE). The adopted population-based metaheuristic algorithms rely on different operators, which facilitate the search process for superior solutions on the UIMA islands. Findings The conducted numerical experiments demonstrated that the developed UIMA algorithm returned near-optimal solutions for the small-size problem instances. As for the large-size problem instances, UIMA was found to be superior to the EA, PSO, EDA and DE algorithms, which were executed in isolation, in terms of the obtained objective function values at termination. Furthermore, the developed UIMA algorithm outperformed various single-solution-based metaheuristic algorithms (including variable neighborhood search, tabu search and simulated annealing) in terms of the solution quality. The maximum UIMA computational time did not exceed 306 s. Research limitations/implications Some of the previous berth scheduling studies modeled uncertain vessel arrival times and/or handling times, while this study assumed the vessel arrival and handling times to be deterministic. Practical implications The developed UIMA algorithm can be used by the MCT operators as an efficient decision support tool and assist with a cost-effective design of berth schedules within an acceptable computational time. Originality/value A novel island-based metaheuristic algorithm is designed to solve the spatially constrained berth scheduling problem. The proposed island-based algorithm adopts several types of metaheuristic algorithms to cover different areas of the search space. The considered metaheuristic algorithms rely on different operators. Such feature is expected to facilitate the search process for superior solutions.

This work proposes a hybrid algorithm called Probabilistic Incremental Cartesian Genetic Pro- gramming (PI-CGP), which integrates an Estimation of Distribution Algorithm (EDA) with Carte- sian Genetic Programming (CGP). PI-CGP uses a fixed-length problem representation and the algorithm constructs a probabilistic model of promising solutions. PI-CGP was evaluated on sym- bolic regression problems and next trading day stock price forecasting. On the symbolic regression problems PI-CGP did not outperform other approaches. The reason could be premature convergence and being trapped at a local minimum. However, PI-CGP was competitive at stock market forecasting. It was comparable to a fusion model employing a Hidden Markov Model (HMM). HMMs are extensively used for time-series forecasting. This result is promising considering the volatile nature of the stock market and that PI-CGP was not customized toward forecasting.

Adaptive estimated maximum-entropy distribution model

In recent years, program evolution algorithms based on the estimation of distribution algorithm (EDA) have been proposed to improve search ability of genetic programming (GP) and to overcome GP-hard problems. One such method is the probabilistic prototype tree (PPT) based algorithm. The PPT based method explores the optimal tree structure by using the full tree whose number of child nodes is maximum among possible trees. This algorithm, however, suffers from problems arising from function nodes having different number of child nodes. These function nodes cause intron nodes, which do not affect the fitness function. Moreover, the function nodes having many child nodes increase the search space and the number of samples necessary for properly constructing the probabilistic model. In order to solve this problem, we propose binary encoding for PPT. In this article, we convert each function node to a subtree of binary nodes where the converted tree is correct in grammar. Our method reduces ineffectual search space, and the binary encoded tree is able to express the same tree structures as the original method. The effectiveness of the proposed method is demonstrated through the use of two computational experiments.

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.

Summary Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty-quantification study, reservoir models must be updated using the observed response from the reservoir by a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir. However, this requires multiple expensive multiphase-flow simulations. Thus, uncertainty-quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory because of slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by estimation-of-distribution algorithms (EDAs). EDAs are population-based algorithms that use models to estimate the probability distribution of promising solutions and then generate new candidate solutions. This paper explores the application of EDAs, including univariate and multivariate models. We discuss two histogram-based univariate models and one multivariate model, the Bayesian optimization algorithm (BOA), which employs Bayesian networks for modeling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDAs can accelerate the search process while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian network allows the BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. The BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir-uncertainty quantification. We demonstrate the effectiveness of EDA by applying the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well-controlled case. Results show better estimation of uncertainty when compared with some other traditional population-based algorithms.