Estimation Of Distribution Algorithm Research Articles

An evolutionary correlation-aware feature selection method for classification problems

As global search techniques, population-based optimization algorithms have provided promising results in feature selection (FS) problems. However, their major challenge is high time complexity associated with the exploration of a large search space and consequently a large number of fitness function evaluations. Moreover, the interaction between features is another key issue in FS problems, directly affecting the classification performance through selecting correlated features. In this paper, an estimation of distribution algorithm (EDA)-based method is proposed with three important contributions. Firstly, as an extension of EDA, the proposed method in each iteration generates only two individuals competing based on a fitness function, evolving during the algorithm using our proposed update procedure. Secondly, we provide a guiding technique to determine the number of features to be selected for individuals in each iteration. As a result, the number of selected features in the final solution would be optimized during the evolution process. These two would lead to increasing the convergence speed of the algorithm. Thirdly, as the main contribution of the paper, in addition to considering the importance of each feature alone, the proposed method can consider the interaction between features, being able to deal with complementary features and consequently increase classification performance. To do this, we provide a conditional probability scheme that considers the joint probability distribution of selecting two features. The introduced probabilities successfully detect correlated features. Experimental results on a synthetic dataset with correlated features proved the performance of our proposed approach facing these types of features. Furthermore, the results on 13 real-world datasets obtained from the UCI repository showed the superiority of the proposed method in comparison with some state-of-the-art approaches. To evaluate the effectiveness of each feature subset, support vector machines are used as classifier. The efficiency analysis of the experimental results using two non-parametric statistical tests proved that the proposed method had significant advantages in comparison to other approaches.

Online Learning of Minmax Solutions for Distributed Estimation and Tracking Control of Sensor Networks in Graphical Games

In this article, a new target tracking algorithm that is based on a distributed estimation-based control protocol is developed for multiple moving sensors subject to adversarial inputs. An augmented system composed of both the estimation error dynamics and the tracking error dynamics is introduced for the distributed estimation and target tracking control problem. We integrate estimation and control to simultaneously minimize infinite-horizon estimation and tracking errors in sensor networks with disturbances. A Minmax strategy as an alternative goal to Nash equilibrium is proposed to compute the sensor’s optimal motion controls in the presence of worst-case neighbor controls and disturbances. In contrast to Nash, Minmax yields a distributed algebraic Riccati equation that is easily solved locally by each sensor. A method based on reinforcement learning is given to compute sensor motion inputs so that all sensors estimate and track the target states. Value function approximation using neural networks is used to solve the distributed Bellman equations online based on the real-time observed data. Proofs are given to guarantee the performance of the combined distributed estimation and tracking algorithms. Finally, the simulation examples show the effectiveness of the proposed algorithm.

An improved differential evolution by hybridizing with estimation-of-distribution algorithm

To fully exploit the strong exploitation of differential evolution (DE) and the strong exploration of the estimation-of-distribution algorithm (EDA), an improved differential evolution by hybridizing the estimation-of-distribution algorithm named IDE-EDA is proposed in the study. Firstly, a novel cooperative evolutionary framework is proposed to hybridize LSHADE-RSP, a state-of-the-art DE variant incorporating DE-based effective improvement strategies, with EDA. Secondly, the dominant individuals generated by LSHADE-RSP are used to establish the probability distribution model for EDA to enhance its exploitation in each generation, and a new control parameter is introduced to balance exploitation and exploration. Then, the use of greed strategy works via EDA to fully retain high-quality solutions to the next generation to improve the convergence speed. Finally, the greedy strategy is used to shrink the external archive when its size decreases due to the reduction of the population size. A comparison of IDE-EDA with cutting-edge DE-based and EDA-based variants, including AAVS-EDA, EB-LSHADE, ELSHADE-SPACMA, jSO, LSHADE-RSP, RWGEDA, HSES, and APGSK-IMODE, was implemented to verify its efficiency. The statistical test results on the IEEE CEC 2018 and IEEE CEC 2021 test suites demonstrate that IDE-EDA is an excellent hybrid algorithm. The MATLAB source code of IDE-EDA can be downloaded from https://github.com/Yintong-Li/IDE-EDA.

Influence of GEOTRACES data distribution and misfit function choice on objective parameter retrieval in a marine zinc cycle model

Abstract. Biogeochemical model behaviour for micronutrients is typically hard to constrain because of the sparsity of observational data, the difficulty of determining parameters in situ, and uncertainties in observations and models. Here, we assess the influence of data distribution, model uncertainty, and the misfit function on objective parameter optimisation in a model of the oceanic cycle of zinc (Zn), an essential micronutrient for marine phytoplankton with a long whole-ocean residence time. We aim to investigate whether observational constraints are sufficient for reconstruction of biogeochemical model behaviour, given that the Zn data coverage provided by the GEOTRACES Intermediate Data Product 2017 is sparse. Furthermore, we aim to assess how optimisation results are affected by the choice of the misfit function and by confounding factors such as analytical uncertainty in the data or biases in the model related to either seasonal variability or the larger-scale circulation. The model framework applied herein combines a marine Zn cycling model with a state-of-the-art estimation of distribution algorithm (Covariance Matrix Adaption Evolution Strategy, CMA-ES) to optimise the model towards synthetic data in an ensemble of 26 optimisations. Provided with a target field that can be perfectly reproduced by the model, optimisation retrieves parameter values perfectly regardless of data coverage. As differences between the model and the system underlying the target field increase, the choice of the misfit function can greatly impact optimisation results, while limitation of data coverage is in most cases of subordinate significance. In cases where optimisation to full or limited data coverage produces relatively distinct model behaviours, we find that applying a misfit metric that compensates for differences in data coverage between ocean basins considerably improves agreement between optimisation results obtained with the two data situations.

A Coevolutionary Estimation of Distribution Algorithm for Group Insurance Portfolio

With the rapid development of the insurance industry, more diverse insurance products are produced for consumers. Insurance portfolio problems have received increasing attention. While most studies focus on insurance portfolio problem for a single insured, insurance portfolio problems for a specific group of insured are even more intricate but little attention has been paid to. In this article, we propose a group insurance portfolio model for investment allocation of several insurance policies so that the total payout of the whole group can be maximized. The statistical average value of each parameter is considered in the model to approximate the expectation payout of the group insurance portfolio problem. To solve this problem, a coevolutionary estimation of distribution algorithm (EDA) utilizing the divide-and-conquer strategy is proposed. First, as the payout of each insured under a certain portfolio plan can be calculated separately, the proposed approach decomposes the group insurance portfolio problem into several single-insured insurance portfolio problems. In this way, the dimension of the optimization problem becomes lower compared to the original problem. An adaptive EDA is proposed to optimize the portfolio plan of each insured independently. Second, the group insurance portfolio problem remains a nonseparable problem since the investment amount of each insured is limited by the total investable amount of the whole group. A particle swarm optimization algorithm is adopted to cooperate with the EDA to optimize the proportion of allocation to each insured. The proposed algorithm is verified on various scenarios. The experimental results validate that the proposed approach is effective for the group insurance portfolio problem.

Centralized and Distributed Robust State Estimation Over Sensor Networks Using Elliptical Distribution

We consider the robust state estimation over sensor networks with non-Gaussian noise, which is often encountered in many applications. Motivated by the fact that the elliptical distribution is the natural extension of the Gaussian distribution and includes a variety of non-Gaussian distributions with heavy-tailed characteristics, we here adopt the elliptical distribution to model the heavy-tailed process and measurement noise. The general state evolution model is used to replace the process equation and the elliptical distribution is denoted as a Gaussian mixture form. Based on that, the posterior estimation of the system state together with the parameters of the process and measurement noises can be inferred by the variational Bayes method. Moreover, the corresponding distributed estimation algorithm is then provided, which enables distributed implementation. The target tracking over sensor networks is used to show the estimation accuracy of the proposed algorithms.

Data-driven predictive control for floating offshore wind turbines based on deep learning and multi-objective optimization

In order to deal with the problems of complicated modeling and the conflicts of control objectives in the control of floating offshore wind turbines (FOWTs), a multi-objective predictive control strategy for FOWTs based on a deep learning model and multi-objective optimization is proposed. In this strategy, the dynamic prediction model of the FOWT based on a gated recurrent neural network is established. Based on the dynamic prediction model, a multi-objective predictive control algorithm for individual pitch control of FOWTs is developed. The multi-objective distribution estimation algorithm is used to optimize the pitch angle considering the constraints of the pitch angle setting. The proposed method is simulated in different wind conditions by FAST. The results show that, compared with the collective pitch control and the gain scheduling PI individual pitch control, the output power of the proposed method is closer to the rated power, and the proposed method significantly reduces the mechanical load of the blade root. Moreover, compared with the gain scheduling PI individual pitch control, the proposed method effectively restrains platform pitching motion.

Trajectory optimization of space vehicle in rendezvous proximity operation with evolutionary feasibility conserving techniques

In this paper, a direct approach is developed for discovering optimal transfer trajectories of close-range rendezvous of satellites considering disturbances in elliptical orbits. The control vector representing the inputs is parameterized via different interpolation methods, and an Estimation of Distribution Algorithm (EDA) that implements mixtures of probability models is presented. To satisfy the terminal conditions, which are represented as non-linear inequality constraints, several feasibility conserving mechanisms associated with learning and sampling methods of the EDAs are proposed, which guarantee the feasibility of the explored solutions. They include a particular implementation of a clustering algorithm, outlier detection, and several heuristic mapping methods. The combination of the proposed operators guides the optimization process in achieving the optimal solution by surfing the regions of the search domain associated with feasible solutions. Numerical simulations confirm that space transfer trajectories with minimum-fuel consumption for the chaser spacecraft can be obtained with terminal condition satisfaction in rendezvous proximity operation.

EDA++: Estimation of Distribution Algorithms With Feasibility Conserving Mechanisms for Constrained Continuous Optimization

Handling nonlinear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and nonlinear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this article, we adopt the framework of estimation of distribution algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with nonlinear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning, and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint-handling methods. Conducted experiments confirm the speed, robustness, and efficiency of the proposed algorithm in tackling various problems with linear and nonlinear constraints.

An Estimation of Distribution Algorithm Based on Variational Bayesian for Point-Set Registration

Point-set registration is widely used in computer vision and pattern recognition. However, it has become a challenging problem since the current registration algorithms suffer from the complexities of the point-set distributions. To solve this problem, we propose a robust registration algorithm based on the estimation of distribution algorithm (EDA) to optimize the complex distributions from a global search mechanism. We propose an EDA probability model based on the asymmetric generalized Gaussian mixture model, which describes the area in the solution space as comprehensively as possible and constructs a probability model of complex distribution points, especially for missing and outliers. We propose a transformation and a Gaussian evolution strategy in the selection mechanism of EDA to process the deformation, rotation, and denoising of selected dominant individuals. Considering the complexity of the model, we choose to optimize from the perspective of variational Bayesian, and introduce a prior probability distribution through local variation to reinforce the convergence of the algorithm in dealing with complex point sets. In addition, a local search mechanism based on the simulated annealing algorithm is added to realize the coarse-to-fine registration. Experimental results show that our method has the best robustness compared with the state-of-the-art registration algorithms.

Multisource Heterogeneous User-Generated Contents-Driven Interactive Estimation of Distribution Algorithms for Personalized Search

Personalized search is essentially a complex qualitative optimization problem, and interactive evolutionary algorithms (EAs) have been extended from EAs to adapt to solving it. However, the multisource user-generated contents (UGCs) in the personalized services have not been concerned on in the adaptation. Accordingly, we here present an enhanced restricted Boltzmann machine (RBM)-driven interactive estimation of distribution algorithms (IEDAs) with multisource heterogeneous data from the viewpoint of effectively extracting users’ preferences and requirements from UGCs to strengthen the performance of IEDA for personalized search. The multisource heterogeneous UGCs, including users’ ratings and reviews, items’ category tags, social networks, and other available information, are sufficiently collected and represented to construct an RBM-based model to extract users’ comprehensive preferences. With this RBM, the probability model for conducting the reproduction operator of estimation of distribution algorithms (EDAs) and the surrogate for quantitatively evaluating an individual (item) fitness are further developed to enhance the EDA-based personalized search. The UGCs-driven IEDA is applied to various publicly released Amazon datasets, e.g., recommendation of Digital Music, Apps for Android, Movies, and TV, to experimentally demonstrate its performance in efficiently improving the IEDA in personalized search with less interactions and higher satisfaction.

A random forest‐regression‐based inverse‐modeling evolutionary algorithm using uniform reference points

The model-based evolutionary algorithms are divided into three groups: estimation of distribution algorithms, inverse modeling, and surrogate modeling. Existing inverse modeling is mainly applied to solve multi-objective optimization problems and is not suitable for many-objective optimization problems. Some inversed-model techniques, such as the inversed-model of multi-objective evolutionary algorithm, constructed from the Pareto front (PF) to the Pareto solution on nondominated solutions using a random grouping method and Gaussian process, were introduced. However, some of the most efficient inverse models might be eliminated during this procedure. Also, there are challenges, such as the presence of many local PFs and developing poor solutions when the population has no evident regularity. This paper proposes inverse modeling using random forest regression and uniform reference points that map all nondominated solutions from the objective space to the decision space to solve many-objective optimization problems. The proposed algorithm is evaluated using the benchmark test suite for evolutionary algorithms. The results show an improvement in diversity and convergence performance (quality indicators).

Distributed Localization of Multiagent Systems With Imperfect Channels Based on Iterative Learning

The real-time localization problem for a class of multiagent systems with imperfect channels under directed graphs is investigated in this article. A successive distributed localization estimation algorithm based on iterative learning is proposed to solve the localization problem of the agent with bounded communication delays. The barycentric coordinates are used to represent the relative position between agents. An estimator is proposed to inspect whether the received data packet is the latest through the iteration stamp on the packet. Meanwhile, an intermittent distributed localization algorithm is devised to handle with the random data loss of agents in real-time localization problem. The relationship between the convergence rate and the probability of the data loss is given in the sense of mathematical expectations. Both numerical simulation and Qbot-2e robot experiment are provided to verify the effectiveness and the feasibility of the aforementioned methods.

Cultural Value and Strategy of Ethnic Music Based on Distribution Estimation Algorithm

The current social construction process is gradually accelerating, and people’s growing spiritual and cultural needs are eager to be satisfied. Spiritual culture is conceived from the material production process of human beings. It is a unique ideology of human beings that is different from other animals. National music culture is a branch of spiritual culture. It occupies an indispensable position in China, and its development is closely related to the inheritance of national culture. At present, the cultural value of ethnic music has not been fully excavated. The reason is that the research methods used are relatively backward, resulting in insufficient optimization of the analysis method. Therefore, this paper applied the distribution estimation algorithm and the information index method to the analysis of the cultural value and strategy of ethnic music. After simulating 120 samples, this paper obtained four results: convergence rate results, average optimal value results, sorting effect results, and final optimization degree results. The experimental results showed that the research method after applying the distribution estimation algorithm can improve the optimization degree of the value and strategy analysis of ethnic music culture by 5.81%, which is conducive to the better value of ethnic music culture in social spiritual and cultural construction.

A roadmap for solving optimization problems with estimation of distribution algorithms

A roadmap for solving optimization problems with estimation of distribution algorithms

How majority-vote crossover and estimation-of-distribution algorithms cope with fitness valleys

The benefits of using crossover in crossing fitness gaps have been studied extensively in evolutionary computation. Recent runtime results show that majority-vote crossover is particularly efficient at optimizing the well-known Jump benchmark function that includes a fitness gap next to the global optimum. Also estimation-of-distribution algorithms (EDAs), which use an implicit crossover, are much more efficient on Jump than typical mutation-based algorithms. However, the allowed gap size for polynomial runtimes with EDAs is at most logarithmic in the problem dimension n.In this paper, we investigate variants of the Jump function where the gap is shifted and appears in the middle of the typical search trajectory. Such gaps can still be overcome efficiently in time O(nlog⁡n) by majority-vote crossover and an estimation-of-distribution algorithm, even for gap sizes almost n. However, if the global optimum is located in the gap instead of the usual all-ones string, majority-vote crossover would nevertheless approach the all-ones string and be highly inefficient. In sharp contrast, an EDA can still find such a shifted optimum efficiently. Thanks to a general property called fair sampling, the EDA will with high probability sample from almost every fitness level of the function, including levels in the gap, and sample the global optimum even though the overall search trajectory points towards the all-ones string. Finally, we derive limits on the gap size allowing efficient runtimes for the EDA.

An EDA-based method for solving electric vehicle charging scheduling problem under limited power and maximum imbalance constraints

Electronic vehicles (EVs) are receiving increasing attention to addressing global warming challenges since fossil fuel is replaced with fuel cell technology. Hence, new challenges arise as demands have increased for using EVs. One of these challenges is the long waiting time of charging EVs spent in queues, especially during peak hours. So, in this study, we aim to propose an efficient method for the electric vehicle charging scheduling problem (EVCSP), which an actual charging station inspires. The most important constraint in this problem is balancing power consumption between charging lines, leading to a limited number of devices that can be charged simultaneously. Also, in this problem, EVs may have interrelationships with each other during the scheduling procedure. So, the estimation of distribution algorithm (EDA) as a competent method in handling the possible relations among decision variables is applied in our proposed hybrid EDA-based solving method. Our proposed method comprises two EDAs, a Markov network-based EDA and a Mallows model-based EDA. It achieves an appropriate schedule and charging line assignment simultaneously while minimizing the total tardiness considering problem constraints. We compared our method with a constraint programming (CP) model and the state-of-art meta-heuristic methods in terms of the objective function value by simulation on a benchmark dataset. Results from the experimental study show significant improvement in solving the introduced EVCSPs.

Novel event‐triggered distributed state estimation algorithm for nonlinear systems over wireless sensor networks

AbstractThis article focuses on the event‐triggered distributed state estimation for nonlinear dynamic systems over wireless sensor networks, where whether measurement should be transmitted from the sensor to the corresponding local estimator depends on a predesigned event‐triggered mechanism. To obtain a better estimation performance while saving the communication energy consumption, a novel event‐triggered nonlinear state estimator is designed by approximating the true posterior probability density function with minimum Kullback–Leibler divergence when the measurement is not transmitted. After local estimation results are produced in every local estimator through applying the cubature rule, according to a communication protocol and covariance intersection fusion strategy, an event‐triggered distributed cubature Kalman filtering (EDCKF) algorithm is developed. Compared with algorithms based on weighted average consensus, the proposed algorithm eliminates the disagreement between local estimators and obtains its best performance within a limited time. Moreover, sufficient conditions are obtained to prove the stability of the EDCKF algorithm. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed estimator and algorithm.

Robust dynamic average consensus with prescribed transient and steady state performance

In this paper, we consider the dynamic average consensus problem for a group of multiple agents that cooperate to estimate the average of locally available time-varying reference signals, under an undirected communication topology. More specifically, we develop a novel robust distributed estimation algorithm, capable of achieving practically zero average tracking error even for fast time-varying reference signals. The proposed scheme is purely distributed, since the estimation algorithm is based solely on local computations and local communication among neighboring agents, and guarantees prescribed performance in the sense that any convergence rate and steady state deviation among the agents’ estimates may be achieved via the appropriate selection of certain design parameters. Moreover, the consensus and average tracking performance are fully decoupled, thus allowing easy tuning of the gains. Additionally, intermittent implementation is proposed via appropriately selected event- and self-triggering mechanisms. Finally, the approach is clarified and verified through various simulation paradigms.

A memetic algorithm based on edge-state learning for max-cut

Max-cut is one of the most classic NP-hard combinatorial optimization problems. The symmetry nature of it leads to special difficulty in extracting meaningful configuration information for learning; none of the state-of-the-art algorithms has employed any learning operators. This paper proposes an original learning method for max-cut, namely post-flip edge-state learning (PF-ESL). Different from previous algorithms, PF-ESL regards edge-states (cut or not cut) rather than vertex-positions as the critical information of a configuration, and extracts their statistics over a population for learning. It is based on following observations. 1) Edges are the only factors considered by the objective function. 2) Edge-states keep invariant when rotating a local configuration to its symmetry position, but vertex-positions do not. These suggest that edge-states contain more meaningful information about a configuration than vertex-positions do. It is impossible to set the state of an edge without influencing some other edges’ states due to their dependencies. Therefore, instead of setting edge-states directly, PF-ESL samples the flips on vertices. Flips on vertices are sampled according to their capacities in increasing the similarity on edge-states between the given solution and a population. PF-ESL is employed in an EDA (Estimation of Distribution Algorithm) perturbation operator and a path-relinking operator. Experimental results show that our algorithm is competitive, and show that edge-state learning is value-added for both the two operators.The main contributions of this paper are as follows. Firstly, previous state-of-the-art evolutionary algorithms for max-cut focus on vertex positions in their evolutionary operation, this paper proposes a new and more reasonable perspective suggesting that edge-states are the critical information of divided graphs rather than vertex positions, and introduces a novel method to measure and utilize their similarities based on it. Such a perspective is fundamental to learning based algorithms design for max-cut and other graph partitioning problems, and can shed lights on future researches. Furthermore, since max-cut is one of the most classic and fundamental NP hard problems, many real-world problems involve dividing graph data into different parts to optimize certain functions, this new perspective may inspire related or similar problems. Secondly, besides the original edge-states based perspective, and the post-flip edge-states learning (PFESL) operator based on it, our memetic algorithm also incorporates a novel evolutionary framework which alternates between EDA based Iterated Tabu search (ITS) and path relinking based genetic algorithm. Finally, the proposed algorithm provides competitive results on two mostly used benchmark sets and improves the best-known results of 6 most challenging instances.