Estimation Of Distribution Algorithm Research Articles

An evolutionary fuzzy scheduler for multi-objective resource allocation in fog computing

With rapid development of the Internet of Things (IoT), a vast amount of raw data produced by IoT devices needs to be processed promptly. Compared to cloud computing, fog computing nodes are closer to data resource for decreasing the end-to-end transmission latency. Considering the limited resource of IoT devices, offloading computationally-intensive tasks to the servers with high computing capability is essential in the IoT–fog–cloud system to complete those tasks on time. In this work, we propose a fuzzy logical offloading strategy for IoT applications characterized by uncertain parameters to optimize both agreement index and robustness. A multi-objective Estimation of Distribution Algorithm (EDA) is designed to learn and optimize the fuzzy offloading strategy from a diversity of the applications. The algorithm partitions applications into independent clusters, so that each cluster can be allocated to the corresponding tier for further processing. Thus, system resources are saved by making scheduling decisions in a reduced search space. Simulation studies on benchmark problems and real-world cases are carried out to verify the efficiency of our proposed algorithm. Pareto sets produced by our algorithm outperformed classic heuristic solutions for 88.3% benchmark cases and dominated Pareto sets of two state-of-art multi-objective algorithms for 92.7% and 94.4% cases correspondingly.

Diffusion recursive total least square algorithm over adaptive networks and performance analysis

In most existing distributed estimation algorithms, many scholars adopted the assumption that the output signal of the system is noisy and the input signal is sufficiently accurate. However, in real applications, the filter input vector usually contains noise. In such situations, it has been proved that the adaptive filtering algorithm using total least squares (TLS) method has shown better performance than classical least squares (LS) method. So in this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Then, we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. In addition, to reduce the computational complexity of the DRTLS algorithm,an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. At last, simulation results illustrate the superiority of the proposed algorithms and the validity of the theoretical analysis results.

Improvement of Kriging interpolation with learning kernel in environmental variables study

ABSTRACT Kriging interpolation is a spatial interpolation method widely employed in the field of data analytics and prediction of environmental variables, which provides the best linear unbiased prediction of intermediate values. The core principle of Kriging interpolation is searching for data distribution regularity and predicting regionalised variable value, and it can be transferred into two descriptions of learning process: function fitting problem and coefficient optimisation problem. Although these two problems could be solved by many traditional algorithms like multiple linear regression method, the parameter estimation of variogram model becomes quite difficult when there are drifts or noises in the raw data. The purpose of this paper is to improve the Kriging interpolation algorithm with learning kernels based on Estimation of Distribution Algorithms (EDAs) and Least-Squares Support Vector Machine (LSSVM). The experiments have been carried out based on a real-world case with environmental variables. Compared with other machine learning methods, experimental results verify the effectiveness of the proposed algorithm.

Vine copula-based EDA for dynamic multiobjective optimization

Dynamic Multiobjective Problems cover a set of real-world problems that have many conflicting objectives. These problems are challenging and well known by the dynamic nature of their objective functions, constraint functions, and problem parameters which often change over time. In fact, dealing with these problems has not been investigated in detail using the Estimation of Distribution Algorithms (EDAs). Thus, we propose in this paper an EDA-based on Vine Copulas algorithm to deal with Dynamic Multiobjective Problems (DMOPs). Vines Copulas are graphical models that represent multivariate dependence using bivariate copulas. The proposed Copula-based Estimation of Distribution Algorithm, labeled Dynamic Vine-Copula Estimation of Distribution Algorithm (DynVC-EDA), is used to implement two search strategies. The first strategy is an algorithm that uses the model as a memory to save the status of the best solutions obtained during the current generation. The second strategy is a prediction-based algorithm that uses the history of the best solutions to predict a new population when a change occurs. The proposed algorithms are tested using a set of benchmarks provided with CEC2015 and the Gee-Tan-Abbass. Statistical findings show that the DynVC-EDA is competitive to the state-of-the-art methods in dealing with dynamic multiobjective optimization.

The Runtime of the Compact Genetic Algorithm on Jump Functions

In the first and so far only mathematical runtime analysis of an estimation-of-distribution algorithm (EDA) on a multimodal problem, Hasen\"ohrl and Sutton (GECCO 2018) showed for any $k = o(n)$ that the compact genetic algorithm (cGA) with any hypothetical population size $\mu = \Omega(ne^{4k} + n^{3.5+\varepsilon})$ with high probability finds the optimum of the $n$-dimensional jump function with jump size $k$ in time $O(\mu n^{1.5} \log n)$. We significantly improve this result for small jump sizes $k \le \frac 1 {20} \ln n -1$. In this case, already for $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ the runtime of the cGA with high probability is only $O(\mu \sqrt n)$. For the smallest admissible values of $\mu$, our result gives a runtime of $O(n \log n)$, whereas the previous one only shows $O(n^{5+\varepsilon})$. Since it is known that the cGA with high probability needs at least $\Omega(\mu \sqrt n)$ iterations to optimize the unimodal OneMx function, our result shows that the cGA in contrast to most classic evolutionary algorithms here is able to cross moderate-sized valleys of low fitness at no extra cost. For large $k$, we show that the exponential (in $k$) runtime guarantee of Hasen\"ohrl and Sutton is tight and cannot be improved, also not by using a smaller hypothetical population size. We prove that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size $k$. This result might be the first non-trivial exponential lower bound for EDAs that holds for arbitrary parameter settings.

Cooperative Fault-Tolerant Output Regulation for Multiagent Systems by Distributed Learning Control Approach.

In this article, a new distributed learning control approach is proposed to address the cooperative fault-tolerant output regulation problem for linear multiagent systems with actuator faults. First, a distributed estimation algorithm with an online learning mechanism is presented to identify the system matrix of the exosystem and to estimate the state of the exosystem. In particular, an auxiliary variable is introduced in the distributed estimation algorithm to construct a data matrix, which is used to learn the system matrix of the exosystem for each subsystem. In addition, by resetting the state of the estimator and by using the identified matrix to update the estimator, all subsystems can reconstruct the state of the exosystem at an initial period of time, which is used for the neighbor subsystem to learn the system matrix of the exosystem. Based on the designed estimator, a novel distributed fault-tolerant controller is developed. Compared with the existing cooperative output regulation results, the system matrix of the exosystem considered in this article is unknown for all subsystems. Finally, a simulation example is provided to show the effectiveness of the obtained new design techniques.

An estimation distribution algorithm for wave-picking warehouse management

Recently, market has witnessed a tremendous growth in E-commerce sales, which bring tons of opportunities as well as challenges. Warehouses have to handle unique characteristics of customer orders in the era of E-commerce which consists of small order scales, large items count, unexpected irregular order arrival patterns, seasonality demand peeks, and high service level expectations. Warehouses are adopting wave-picking as an effective policy composed of item-batching, load-assignment and picker-routing problems. In this research, principle combination of load-assignment and picker-routing problems is studied. A mixed integer mathematical model is established based on features of a wave-picking warehouse. In order to conquer the complexity caused by routing decision of the proposed problem, a set of effective modified Estimation Distribution Algorithms is developed. The set of proposed algorithms is proved to have stable gaps (1% on average and maximum less than 2%) compared with Cplex 12.8, while can be solved in much larger scale within quite short time (100 pickers and 350 items in each wave within less than 2 min).

A scheduling decision support model for minimizing the number of drones with dynamic package arrivals and personalized deadlines

Unmanned Aerial Vehicles (UAVs, commonly known as drones) hold great potential to reduce operational costs and guarantee on-time delivery of packages. This paper aims to minimize the number of drones used in a depot, in which each package has its own customized release time, distance to the depot, and personalized deadline. For decision-makers, it is difficult to determine the optimal number of drones to ensure that all packages can be delivered before the corresponding deadline. We propose a mixed integer programming model formulate the problem. Due to the NP-hardness of the problem, a scheduling decision support model with a genetic algorithm (SDSMGA) is developed to address the problem. A fitness function that can determine the minimum number of drones required by a package delivery sequence is proposed. We develop a swap-based correction algorithm to correct unqualified individuals in SDSMGA. Experimental results show that compared with CPLEX for small instances, SDSMGA can obtain solutions of the same quality or sub-optimal solutions. Computational results among SDSMGA, Estimation of Distribution Algorithm (EDA), and Particle Swarm Optimization (PSO) indicate that SDSMGA can effectively and efficiently address the problem. As the number of packages increases, SDSMGA outperforms the other two algorithms. Sensitivity analysis shows that the smaller the dense factor, or the more extensive the service radius, the more drones are needed.

A real-time integrated optimization of the aircraft holding time and rerouting under risk area

Fight on-time rate is one of the key air transport industry’s service quality indicators, often affected by adverse weather. In order to improve flight punctuality and reduce the impact of adverse weather on flights, a Real-time Integrated Optimization of the Aircraft Holding Time and Rerouting under Risk Area (RIOAHTR-RA) model is proposed at minimizing the total flight duration from the start point of rerouting to the end point of rerouting under adverse weather condition. In this model, the update cycle based on radar data is generally 6 min, and the position relationship between risk area and the aircraft is available and described in real time. The RIOAHTR-RA model is then solved by the distribution estimation algorithm with improved artificial potential field (IAPF) by introducing intermediate target point, relative position and relative velocity factors. Then, the optimal holding time and rerouting path for aircraft were allocated. The results are compared with the single rerouting strategy, and the effectiveness of the optimization solver with improved IAPF is evaluated. Compared with the data of the Hong Kong Observatory’s forecast system, the results show that appropriate holding time before rerouting can reduce flight delays. The proposed RIOAHTR-RA model is suitable for real-time air traffic flow management.

Cooperative Path Planning of UAVs & UGVs for a Persistent Surveillance Task in Urban Environments

There have been many applications of drones in urban environments, such as delivery, rescue, and surveillance. In a persistent surveillance task, the drones sometimes cannot complete it independently when some regions are required to be covered on the ground. For this purpose, unmanned aerial vehicles and unmanned ground vehicles (UAVs & UGVs) system is introduced to perform such a task in this article, and the goal is to generate the circular paths for the drones and the UGVs, respectively, to minimize their travel time of realizing a complete coverage. First, the cooperative path planning problem of UAVs & UGVs is formulated into a large-scale 0-1 optimization problem, in which the on-off states of the discrete points are to be optimized. Second, a hybrid algorithm integrating the estimation of distribution algorithm (EDA) and the genetic algorithm (GA) algorithm is proposed to solve the problem. The advantages of EDA and GA in the global and local search are fully taken considering the demands in different phases of the iterative process. A simple sweep-based approach is employed to determine the optimal sequence of passing the open points. Then, an online local adjustment strategy is also applied to address the changes of the requirements on covering the ground area. Simulation results demonstrate that the UAVs & UGVs system can enhance the efficiency of the task. The hybrid EDA-GA algorithm can greatly improve the performance of EDA and GA in terms of the quality and the stability of solutions. The online adjustment strategy is effective to maintain a complete coverage while minimizing the impact on the circular paths.

Estimation of Distribution Algorithms with Fuzzy Sampling for Stochastic Programming Problems

Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problems is to combine sampling methods with optimal search methods. Sampling techniques have a serious problem when the sample size is small, so estimating the objective function values with noise is not accurate in this case. In this research, a new sampling technique is proposed based on fuzzy logic to deal with small sample sizes. Then, simulation-based optimization methods are designed by combining the estimation of distribution algorithms with the proposed sampling technique and other sampling techniques to solve the stochastic programming problems. Moreover, additive versions of the proposed methods are developed to optimize functions without noise in order to evaluate different efficiency levels of the proposed methods. In order to test the performance of the proposed methods, different numerical experiments were carried out using several benchmark test functions. Finally, three real-world applications are considered to assess the performance of the proposed methods.

Deadlock-Free Scheduling of Flexible Assembly Systems Based on Petri Nets and Local Search

Deadlock-free scheduling and control is critical for optimizing the performance of flexible assembly systems (FASs). Based on the Petri net models of FASs, this paper integrates a deadlock prevention policy with local search and develops a novel deadlock-free scheduling algorithm. A solution of the scheduling problem is coded as a chromosome representation that is a permutation with repetition of parts. By using the deadlock prevention policy, a repairing algorithm (RA) is developed to repair unfeasible chromosomes. A perturbation strategy based on estimation of distribution algorithm is developed to escape from local optima. Moreover, to improve population diversity, an acceptance criterion (AC) based on Pareto dominance is proposed. The chromosome representation, RA, perturbation strategy, and AC together support the cooperative aspect of local search for scheduling problems strongly.

Re-sampled inheritance compact optimization

Compact optimization is an alternative paradigm in the field of metaheuristics requiring a modest use of memory to optimize a problem. As opposed to population-based algorithms, which conduct the search by employing a set of candidate solutions, compact algorithms use a probabilistic model to describe how solutions are distributed over the search space. Compared to other Estimation of Distribution Algorithms, peculiar features such as the use of simple probabilistic models, in which variables are treated independently, and the need for a minimal number of solutions to be sampled to perform the search, make these algorithms suitable for those applications plagued by memory limitations. Compact algorithms show good results on different kinds of optimization problems but often prematurely converge and perform poorly on non-separable. In this paper, we attempt to overcome these limitations by combining compact algorithms with a restart mechanism named Re-Sampled Inheritance (RI) whose purpose is to avoid premature convergence while also inheriting parts of the variables from the best solution found so far. To assess the effect of the RI mechanism, we extensively test various existing compact algorithms, with and without RI, and compare the best RI-based compact algorithm against several competing algorithms on several optimization problems at different dimensionalities. We also evaluate the effect of the RI parameters on the overall algorithmic performance. Our numerical results not only show that RI consistently enhances the performances of compact algorithms, but also shed some light on the effectiveness of different compact logics at handling problems at different dimensionalities.

Cooperative hybrid evolutionary algorithm for large scale multi-stage multi-product batch plants scheduling problem

As an important part of batch chemical industry scheduling problems, the multi-stage multi-product batch plant scheduling problem (MMSP) has been widely studied for decades. This problem is characterized by multiple stages with non-identical parallel units and operate based on customer orders. In this paper, we focus on the large scale MMSP and treat the minimization of make-span as the objective function. An efficient cooperative hybrid evolutionary algorithm is proposed based on the framework of cooperative co-evolution. First, a novel two-line encoding scheme is developed to represent the unit assignment and sequencing for orders respectively. Second, modified estimation of distribution algorithm (EDA) and differential evolutionary (DE) operations are proposed according to the feature of MMSP. EDA operation with a novel population-based incremental learning strategy is applied to handle the unit assignment variables. And novel DE operation based on a novel encoding method is adopted to deal with sequence variables. Then, two selection strategies are applied to preserve optimal and sub-optimal solutions for the proposed algorithm. The critical path based local search algorithm is adopted to further improve the efficiency of local optimization. The proposed algorithm has been tested by several instances with different sizes and characteristics. The numerical results and comparisons show that the proposed work is very competitive in solving large scale MMSP.

Distributed Data-Driven Intrusion Detection for Sparse Stealthy FDI Attacks in Smart Grids

The stealthy false data injection (FDI) attacks in smart grids can bypass the bad data detection, and thus make an incorrect state estimate in the control center. In this brief, a distributed data-driven intrusion detection approach is proposed to reveal the existence of the sparse stealthy FDI attack in a multi-area interconnected power system. The proposed distributed intrusion detection approach avoids the over-fitting issue that is extensively seen when implementing machine learning algorithms for large-scale systems. Firstly, each area estimates the entire system state based on a distributed state estimation algorithm. Then, the state of each local area is used as trained neural network input to detect the stealthy FDI attacks. Simulation results on the IEEE 118-bus system verify that the proposed method not only reduces the risk of over-fitting, but also can locate the areas which have been attacked.

Distributed Multi-Area State Estimation for Power Systems With Switching Communication Graphs

We consider distributed multi-area state estimation algorithms for power systems with switching communication graphs. The power system is partitioned into multiple geographically non-overlapping areas and each area is assigned with an estimator to give a local estimate of the entire power system's state. The inter-area communication networks are assumed to switch among a finite set of digraphs. Each area runs a distributed estimation algorithm based on consensus+innovations strategies. By the binomial expansion of matrix products, time-varying system and algebraic graph theories, we prove that all area's local estimates converge to the global least square estimate with probability 1 if the measurement system is jointly observable and the communication graphs are balanced and jointly strongly connected. Finally, we demonstrate the theoretical results by an IEEE 118-bus system.

A novel strategy for power sources management in connected plug-in hybrid electric vehicles based on mobile edge computation framework

This paper proposes a novel control framework and the corresponding strategy for power sources management in connected plug-in hybrid electric vehicles (cPHEVs). A mobile edge computation (MEC) based control framework is developed first, evolving the conventional on-board vehicle control unit (VCU) into the hierarchically asynchronous controller that is partly located in cloud. Elaborately contrastive analysis on the performance of processing capacity, communication frequency and communication delay manifests dramatic potential of the proposed framework in sustaining development of the cooperative control strategy for cPHEVs. On the basis of MEC based control framework, a specific cooperative strategy is constructed. The novel strategy accomplishes energy flow management between different power sources with incorporation of the active energy consumption plan and adaptive energy consumption management. The method to generate the reference battery state-of-charge (SOC) trajectories in energy consumption plan stage is emphatically investigated, fast outputting reference trajectories that are tightly close to results by global optimization methods. The estimation of distribution algorithm (EDA) is employed to output reference control policies under the specific terminal conditions assigned via the machine learning based method. Finally, simulation results highlight that the novel strategy attains superior performance in real-time application that is close to the offline global optimization solutions.

Distributed secure estimation for cyber-physical systems with fading measurements and false data injection attacks

This paper is concerned with the distributed secure estimation problem for a cyber-physical system (CPS) with fading measurements and false data injection (FDI) attacks, where the fading probability of measurements is assumed to be individual for each sensor, and the FDI attacks occur at the physical system layer to intensively modify the system's state. For improving security of the system, an attack detection mechanism is proposed based on an FDI attack observer constructed by minimising the upper bound of observation error covariance. Then a complete distributed state estimation algorithm is given to provide locally reliable estimation. A sufficient condition is provided to guarantee boundedness of the estimation error covariance. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and practical example simulation.

Kernels of Mallows Models under the Hamming Distance for solving the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it has captured the attention of the optimization community for decades. As a result, a large number of algorithms have been proposed to tackle this problem. Among these, exact methods are only able to solve instances of size $n<40$. To overcome this limitation, many metaheuristic methods have been applied to the QAP. In this work, we follow this direction by approaching the QAP through Estimation of Distribution Algorithms (EDAs). Particularly, a non-parametric distance-based exponential probabilistic model is used. Based on the analysis of the characteristics of the QAP, and previous work in the area, we introduce Kernels of Mallows Model under the Hamming distance to the context of EDAs. Conducted experiments point out that the performance of the proposed algorithm in the QAP is superior to (i) the classical EDAs adapted to deal with the QAP, and also (ii) to the specific EDAs proposed in the literature to deal with permutation problems.

Distributed weighted least-squares estimation for networked systems with edge measurements

This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes, and edge measurements for the connecting nodes. Each node in the network carries out distributed estimation by using its own measurement and information transmitted from its neighbours. We study two distributed estimation algorithms: a recently proposed distributed WLS algorithm and the so-called Gaussian Belief Propagation (BP) algorithm. We first establish the equivalence of the two algorithms. We then prove a key result which shows that the information matrix is always generalized diagonally dominant, under some very mild condition. Using these two results and some known convergence properties of the Gaussian BP algorithm, we show that the aforementioned distributed WLS algorithm computes the exact WLS solution asymptotically. A bound on its convergence rate is also presented.