Estimation Of Distribution Algorithm Research Articles

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers using fitness landscape analysis (FLA). The spacecraft dynamics is modeled with respect to modified equinoctial elements by considering orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuvers. An adaptive method within the framework of the estimation of distribution algorithms (EDA) is proposed, which aims at conserving the feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and nonperturbed orbit transfer problems are solved. The results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.

Robust information filtering for distributed networks using mixed Gaussian distribution

This paper proposes a robust distributed state estimation algorithm for sensor networks. In a distributed sensor network, sensor nodes may be affected by outliers and thus influence the information fusion results. In this respect, the measurement likelihood and one-step state prediction are modeled by a mixture of Gaussian distributions. In this Gaussian mixture, one Gaussian uses nominal covariance, while the other uses adaptive covariance with larger values and lower probabilities. We build a centralized multi-sensor fusion model in the variational Bayesian framework based on the aforementioned mixture of Gaussian distributions. Then, a consensus strategy is employed to convert the centralized method into a distributed one. Each node completes estimation tasks separately based on the information from itself and nearby nodes. In addition, the weight of sensor information will adaptively update according to the Gaussian distribution that mainly affects the current sensor measurement noise. Finally, simulation experiments demonstrate the effectiveness of the proposed method in handling outlier effects.

The Directed Multi-Objective Estimation Distribution Algorithm (D-MOEDA)

Improvement Direction Mapping (IDM) methods have been applied as a local search strategy to hybridize global search algorithms. A natural question is whether this concept could be applied within a global search scheme, so that the stochastic search operators are directed toward promising regions, promoting a more efficient search. This paper introduces a novel Multi-Objective Evolutionary Algorithm (MOEA) that incorporates the IDM into the reproduction operator of an Estimation of Distribution Algorithm (EDA). In this proposal, the search directions of the IDM based on aggregation functions are used to directly steer the search process of a multi-objective evolutionary algorithm based on decomposition, by orienting a local probability distribution towards a search direction, the proposal intends to steer solutions toward the Pareto front (PF) of the Multi-Objective Optimization Problem (MOP), exploiting the search features of the aggregation functions. The proposal is tested using a set of well-known benchmark MOPs and compared to state of the art MOEAs. Results showed statistical evidence about the importance of the orientation of the search probability distribution to improve the convergence to the Pareto front.

A knowledge-based constructive estimation of distribution algorithm for bi-objective portfolio optimization with cardinality constraints

Portfolio optimization is an essential and practical model for financial decision making. With the consideration of some real-world constraints, especially the cardinality constraints, the problem becomes much more challenging as it converts to a mixed-integer quadratic multi-objective optimization problem. To solve this problem, we propose a knowledge-based constructive estimation of distribution algorithm (KC-EDA) with the following three features. First, a hybrid design of Ant colony optimization (ACO) and Estimation distribution algorithm (EDA) is used to solve this mixed-variable optimization problem based on knowledge information. Second, a knowledge accumulation mechanism is designed to discover the internal relationship among the assets. The mechanism can not only guide the selection of assets effectively but also enable the use of historical information during evolution to direct the allocation of investment proportion. Third, a constructive approach is applied to construct portfolios under the constraints. This hybrid and constructive approach is incorporated into the multi-objective evolutionary framework and the experiment has been performed on the SZ50, SZ180, and SZ380 datasets (from January 2014 to December 2018). The experimental results demonstrate the effectiveness of KC-EDA in solving the portfolio optimization problem with cardinality constraints.

Bivariate estimation-of-distribution algorithms can find an exponential number of optima

Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms typically converge only to a single solution. While this can be counteracted by applying niching strategies, the number of optima is nonetheless trivially bounded by the population size. Estimation-of-distribution algorithms (EDAs) are an alternative, maintaining a probabilistic model of the solution space instead of a population. Such a model is able to implicitly represent a solution set far larger than any realistic population size.To support the study of how optimization algorithms handle large sets of optima, we propose the test function EqualBlocksOneMax (EBOM). It has an easy fitness landscape with exponentially many optima. We show that the bivariate EDA mutual-information-maximizing input clustering, without any problem-specific modification, quickly generates a model that behaves very similarly to a theoretically ideal model for EBOM, which samples each of the exponentially many optima with the same maximal probability. We also prove via mathematical means that no univariate model can come close to having this property: If the probability to sample an optimum is at least inverse-polynomial, there is a Hamming ball of logarithmic radius such that, with high probability, each sample is in this ball.

Initial core loading pattern optimization studies using estimation of distribution algorithm for VVER type cores

Innovative fuel management schemes based on evolutionary algorithms (EAs) now form an integral part of design and operation for nuclear reactors. In the present study, Estimation of Distribution Algorithm (EDA) has been developed for light water reactors (LWRs) and as a case study EDA has been applied to optimize the core loading pattern of VVER X2 benchmark’s initial core. EDA belongs to class of EAs where the optimization solution evolves through progress of generations and in each generation sampling of best candidates of previous generation is done. The main objectives of this study is firstly to develop and test EDA to optimize core loading pattern (LP) for VVER type cores and secondly to generate new optimized LPs having same safety features but with improved fuel utilization with respect to reference benchmark case. The most suitable values for internal parameters for EDA like population size (N), percentage best candidates (M) and weighting factor ‘α’ were evaluated for reaching a reasonable optimized solution in computationally efficient way. During this study, a number of optimized initial core loading patterns were generated, where the target parameters and safety limits are met. A comprehensive analysis for selected LPs has been carried out for full cycle and a comparison has been done for the reported safety and operational characteristics. It is observed that a few of the optimized LPs have better fuel economy than the benchmark LP.

Adaptive-Width Generalized Correntropy Diffusion Algorithm for Secure Distributed Estimation

In this brief, a secure distributed estimation algorithm is devised, based on a generalized correntropy kernel function, which is robust against malicious attacks with false data injection model. An adaptive-width mechanism of generalized correntropy is suggested to reduce the effect of the adversaries in the network by narrowing the width of the generalized correntropy. This makes the proposed distributed algorithm be robust against false data injection attackers. Moreover, some analysis such as updating the parameter width and determining the optimal threshold for adversary detection are provided. Simulation results show the effectiveness of the proposed secure distributed estimation algorithm in comparison with some state-of-the-art algorithms in the literature and also demonstrate the effective detection capability of the adversary.

A Low Complexity Proportionate Generlized Correntropy-Based Diffusion LMS Algorithm With Closed-Form Gain Coefficients

This brief proposes a correntropy-based proportionate diffusion algorithm with low computational complexity. The proportionate diffusion algorithms in the literature suffer from a high computational complexity due to the complicated calculation process of the coefficients of the gain matrix, i.e., by solving an optimization problem or solving a linear system of equations via a matrix inversion. In this brief, by defining a proper correntropy kernel function and suitably assuming a wise constraint, the gain matrix coefficients are derived in a closed-form formula. In fact, the correntropy kernel function is used to determine the gain coefficients. This closed-form formula significantly reduces the computational complexity of the proposed algorithm. Moreover, a condition of uniform convergence for the distributed estimation algorithm at each time instant is obtained analytically. Simulation results show the lower steady-state Normalized Mean Square Deviation (NMSD) and lower computational complexity of the proposed algorithm compared to some other competing algorithms.

Distributed Estimation and Smoothing for Linear Dynamic Systems Over Sensor Networks

This paper focuses on distributed estimation and smoothing for linear dynamic systems monitored by sensors that are organized as a network. To achieve low power consumption of sensors, the system is decomposed into several subsystems based on the observable canonical decomposition method. Each sensor in the network performs state estimation for one subsystem at most, while estimations for the majority of subsystems are obtained from the neighbors of each sensor. The optimal gains of the estimator and the smoother are pre-calculated offline, and a numerical solution is obtained by taking advantage of optimization algorithms. Furthermore, the boundedness of the prediction error covariance is guaranteed resulting from the bounded solution of a Riccati equation, and the performance of the smoother is analyzed. A numerical example is presented to validate the feasibility of the algorithm even if the sensor network suffers from network interruptions. The proposed algorithm is more robust against partial loss of predictions and recovers more rapidly, compared to some consensus-based distributed estimation algorithms.

Research on gas emission quantity prediction model based on EDA-IGA

In order to accurately predict the possible gas emission quantity in coal mines, it is proposed to use the multi-thread calculation of the Immune Genetic Algorithm (IGA) and injection of vaccines to improve the accuracy of prediction and combine the Estimation of Distribution Algorithm (EDA) to the distribution probability of excellent populations. Calculating, and selecting excellent populations for iteration, optimize the population generation process of the Immune Genetic Algorithm, so that the population quality is continuously optimized and improved, and the optimal solution is obtained, thereby establishing a gas emission quantity prediction model based on the Immune Genetic Algorithm and Estimation of Distribution Algorithm. Using the 9136 mining face with gas emission hazards in a coal mine from Shandong Province in China as the prediction object, the absolute gas emission quantity is used to scale the gas emission quantity, and it is found that the model can accurately predict the gas emission quantity, which is consistent with the on-site emission unanimous. In the prediction comparison with IGA, it is found that the accuracy of the prediction results has increased by 9.51%, and the number of iterations to achieve the required goal has been reduced by 67%, indicating that the EDA has a better role in optimizing the population update process such as genetic selection of the IGA. Comparing the prediction results of other models, it is found that the prediction accuracy of the EDA-IGA is 94.93%, which is the highest prediction accuracy, indicating that this prediction model can be used as a new method for the prediction of coal mine gas emission. Accurately predicting the gas emission quantity can provide guidance for safe mining in coal mines. The gas emission quantity can also be used as a safety indicator to reduce the possibility of coal mine accidents, ensure the personal safety of coal miners and reduce economic losses in coal mines.

Using an Estimation of Distribution Algorithm to Achieve Multitasking Semantic Web Service Composition

Web service composition composes existing web services to accommodate users’ requests for required functionalities with the best possible quality of services (QoS). Due to the computational complexity of this problem, evolutionary computation (EC) techniques have been employed to efficiently find composite services with near-optimal functional quality (i.e., quality of semantic matchmaking, QoSM for short) or non-functional quality (i.e., QoS) for each composition request individually. With a rapid increase in composition requests from a growing number of users, solving one composition request at a time can hardly meet the efficiency target anymore. Driven by the idea that the solutions obtained from solving one request can be highly useful for tackling other related requests, multitasking service composition approaches have been proposed to efficiently deal with multiple composition requests concurrently. However, existing attempts have not been effective in learning and sharing knowledge among solutions for multiple requests. In this paper, we model the problem of collectively handling multiple service composition requests as a new multi-tasking service composition problem and propose a new Permutation-based Multi-factorial Evolutionary Algorithm based on an Estimation of Distribution Algorithm (EDA), named PMFEA-EDA, to effectively and efficiently solve this problem. In particular, we introduce a novel method for effective knowledge sharing across different service composition requests. For that, we develop a new sampling mechanism to increase the chance of identifying high-quality service compositions in both the single-tasking and multitasking contexts. Our experiment shows that our proposed approach, PMFEA-EDA, takes much less time than existing approaches that process each service request separately, and also outperforms them in terms of both QoSM and QoS.

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

One particular kind of evolutionary algorithms known as Estimation of Distribution Algorithms (EDAs) has gained the attention of the aerospace industry for its ability to solve nonlinear and complicated problems, particularly in the optimization of space trajectories during on-orbit operations of satellites. This article describes an effective method for optimizing the trajectory of a spacecraft using an evolutionary approach based on EDAs, incorporated with fitness landscape analysis (FLA). The approach utilizes flexible operators that are paired with seeding and selection mechanisms of EDAs. Initially, the orbit transfer problem is mathematically modeled and the objectives and constraints are identified. The landscape feature of the search space is analyzed via the dispersion metric to measure the modality and ruggedness of the search domain. The obtained information are used as feedback in developing adaptive operators for truncation factor and constraints separation threshold of the employed EDA. A framework for spacecraft trajectory optimization has been presented where the dispersion value for a space mission is estimated using a k-nearest neighbors (k-NN) algorithm. The suggested method is used to solve several problems related to low-thrust orbit transfer of satellites in Earth’s orbit. Results demonstrate that the suggested framework for trajectory design and optimization of space transfers is effective enough to offer fuel-efficient and energy-efficient maneuvers for different thrust levels of the propulsion system. Moreover, the performance of the proposed approach is evaluated against non-adaptive EDA and other advanced evolutionary algorithms. The obtained results certify that the proposed adaptive evolutionary approach is superior in identifying feasible minimum-fuel and minimum-energy transfer trajectories.

NCG-TSM: A Noncooperative Game for the Taxi Sharing Model in Urban Road Networks

Taxi sharing is a promising method to save resource consumption and alleviate traffic congestion while satisfying people’s commuting needs. Existing research methods include taxi dispatching methods based on intelligent algorithms, single vehicle route recommendation algorithms, and route recommendation algorithms based on vehicle traffic history. However, these studies either focus on how to efficiently dispatch satisfactory vehicles for passengers, ignoring the effect of efficient routes on vehicle travel efficiency, or let vehicles follow the shortest detour distance recommended by the system, ignoring the traffic congestion caused by the influx of vehicles into the same road. To address the abovementioned problems, a noncooperative game for a taxi sharing model (NCG-TSM) in urban road networks is proposed in this paper combined with the traffic conditions of the optional routes, and a distribution estimation algorithm for the shared taxi game is designed to make multivehicle route selections reach Nash equilibrium. The effectiveness of NCG-TSM is verified through simulation experiments. When the number of vehicles reaches the congestion capacity of the road segment, compared to the three common frameworks, the travel time cost and fuel consumption cost can be reduced by 5.8% to 9.1% and 3.5% to 8.9%, respectively. Besides, the occupancy rate has been improved, especially compared to the BMP framework, by 5.5% to 40%.

Surrogate-Assisted Hybrid-Model Estimation of Distribution Algorithm for Mixed-Variable Hyperparameters Optimization in Convolutional Neural Networks.

The performance of a convolutional neural network (CNN) heavily depends on its hyperparameters. However, finding a suitable hyperparameters configuration is difficult, challenging, and computationally expensive due to three issues, which are 1) the mixed-variable problem of different types of hyperparameters; 2) the large-scale search space of finding optimal hyperparameters; and 3) the expensive computational cost for evaluating candidate hyperparameters configuration. Therefore, this article focuses on these three issues and proposes a novel estimation of distribution algorithm (EDA) for efficient hyperparameters optimization, with three major contributions in the algorithm design. First, a hybrid-model EDA is proposed to efficiently deal with the mixed-variable difficulty. The proposed algorithm uses a mixed-variable encoding scheme to encode the mixed-variable hyperparameters and adopts an adaptive hybrid-model learning (AHL) strategy to efficiently optimize the mixed-variables. Second, an orthogonal initialization (OI) strategy is proposed to efficiently deal with the challenge of large-scale search space. Third, a surrogate-assisted multi-level evaluation (SME) method is proposed to reduce the expensive computational cost. Based on the above, the proposed algorithm is named s urrogate-assisted hybrid-model EDA (SHEDA). For experimental studies, the proposed SHEDA is verified on widely used classification benchmark problems, and is compared with various state-of-the-art methods. Moreover, a case study on aortic dissection (AD) diagnosis is carried out to evaluate its performance. Experimental results show that the proposed SHEDA is very effective and efficient for hyperparameters optimization, which can find a satisfactory hyperparameters configuration for the CIFAR10, CIFAR100, and AD diagnosis with only 0.58, 0.97, and 1.18 GPU days, respectively.

Distributed Maximum Correntropy Cubature Information Filtering for Tracking Unmanned Aerial Vehicle

Aiming at improving the performance of tracking unmanned aerial vehicle in the battlefield, this paper focuses on the algorithm involving tracking the maneuvering target with a distributed sensor network under non-Gaussian measurement noise. A novel distributed maximum correntropy cubature information filtering based on interactive multiple model is proposed. Taking advantage of the correntropy, we design a maximum correntropy cubature information filtering for each node to estimate the target state under non-Gaussian measurement noise. Then, distributed information fusion based on weighted average consensus is conducted to improve the stability of the sensor network. After that, the information pair is changed, so that a distributed state estimation algorithm based on interactive multiple model is developed to increase the accuracy of maneuvering target tracking. Simulation results and comparison with other algorithms in three typical non-Gaussian measurement noise scenarios are given to evaluate the effectiveness of the proposed algorithm.

2-D distributed pose estimation of multi-agent systems using bearing measurements

This article studies distributed pose (orientation and position) estimation of leader–follower multi-agent systems over κ-layer graphs in 2-D plane. Only the leaders have access to their orientations and positions, while the followers can measure the relative bearings or (angular and linear) velocities in their unknown local coordinate frames. For the orientation estimation, the local relative bearings are used to obtain the relative orientations among the agents, based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation. For the position estimation, the local relative bearings are used to obtain the position constraints among the agents, and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints. Both the orientation and position estimation errors converge to zero asymptotically. A simulation example is given to verify the theoretical results.

Manufacturing rescheduling after crisis or disaster-caused supply chain disruption

In this paper, we study the problems a repair shop has with rescheduling after major supply disruptions. The repair shop provides repair and maintenance services to its customers. After a major disruption to production, the repair shop faces delays in production and order delivery due to shortages in materials and/or labor, which requires rescheduling of all the unfinished parts. We observe that the finished parts incur high holding costs until the entire order is completed, while any unfinished parts (in the form of raw material or work-in-progress) incur low holding costs until production starts. Moreover, the repair shop incurs a setup cost when switching between different types of parts. Considering these new features, we formulate the rescheduling problem for the repair shop under a coordinated supply chain as an integer program to minimize the total tardiness, setup cost, and holding cost. To solve the model, we propose an innovative two-stage genetic algorithm, which utilizes the estimation of distribution algorithm (EDA) to improve the search process of the optimal solution. We test the performance of this algorithm on a dataset generated from the order data of a heavy machinery maintenance provider. The numerical results show that our model generates solutions that outperform the initial schedule, which was obtained by minimizing holding and setup costs without disruption. In addition, using other closely-related genetic algorithms as benchmarks, we show that our algorithm outperforms the benchmarks without sacrificing the computational time. We also discuss an extension of the main model by considering the recovery of productivity in terms of processing time.

Distributed Localization Estimation for Dynamic Multiagent Systems

This article investigates the real-time localization problem of dynamic multiagent systems with repetitive operation characteristics under directed graph. A distributed localization estimation algorithm based on iterative learning is proposed. The barycentric coordinates calculated based on the relative distance are used to estimate the real coordinates of the agent. Different from the traditional estimation methods along the time axis, the proposed method utilizes the information of iteration axis simultaneously. In this method, the current estimation coordinates are updated by using the estimation coordinates of the same sampling time in previous iteration, the estimation accuracy is improved, and the velocity constraint is removed. Additionally, the real-time localization problem of dynamic multiagent systems under arbitrary deployment is concerned. An improved distributed localization estimation algorithm with signed coefficients based on iterative learning is proposed. Meanwhile, the results are also extended to the localization estimation of multiagent systems with arbitrary deployment in 3-D space. By introducing Richardson iteration and infinite norm, the global asymptotic convergence of the proposed methods is guaranteed. Finally, numerical simulations and the Qbot-2e robot experiment are provided to show the effectiveness and validity of the obtained results.

Distributed Estimation With Iterative Inverse Covariance Intersection

For distributed estimation in sensor network systems, intractable correlation among local estimates has a great impact on the accuracy and consistency of the fused estimate. An inconsistent or over conservative estimate would lead to degradation of estimation performance or even estimation divergence. In this brief, a distributed iterative diffusion estimation algorithm based on inverse covariance intersection (ICI) technique is proposed to address the unknown correlation and yield an estimate with uncertainty close to the true mean square error. The proposed algorithm is referred to as iterative ICI (It-ICI), which leverages the iteration of fusions that is only executed locally. Every sensor node only combines estimates from its neighbors. By iterations, the local information can be propagated to the entire sensor network and the accuracy can be incrementally improved. The fused estimate is proved to be unbiased with bounded covariance provided that the local filters’ estimates are unbiased and bounded. The performance of the proposed distributed estimation algorithm is illustrated by a collaborative target tracking problem in terms of enhanced tracking accuracy and consistency.

Distributed Estimation of Stochastic Multiagent Systems for Cooperative Control With a Virtual Network

This article proposes a distributed estimation algorithm that uses local information about the neighbors through sensing or communication to design an estimation-based cooperative control of the stochastic multiagent system (MAS). The proposed distributed estimation algorithm solely relies on local sensing information rather than exchanging estimated state information from other agents, as is commonly required in conventional distributed estimation methods, reducing communication overhead. Furthermore, the proposed method allows interactions between all agents, including non-neighboring agents, by establishing a virtual fully connected network with the MAS state information independently estimated by each agent. The stability of the proposed distributed estimation algorithm is theoretically verified. Numerical simulations demonstrate the enhanced performance of the estimation-based linear and nonlinear control. In particular, using the virtual fully connected network concept in the MAS with the sensing/communication range, the flock configuration can be tightly controlled within the desired boundary, which cannot be achieved through the conventional flocking methods.