Evolutionary Multi/Many-Objective Optimisation via Bilevel Decomposition

Decomposition of a complex multi-objective optimisation problem(MOP)to multiple simple subMOPs,known as M2M for short,is an effective approach to multi-objective optimisation.However,M2M facilitates little communication/collaboration between subMOPs,which limits its use in complex optimisation scenarios.This paper extends the M2M framework to develop a unified algorithm for both multi-objective and manyobjective optimisation.Through bilevel decomposition,an MOP is divided into multiple subMOPs at upper level,each of which is further divided into a number of single-objective subproblems at lower level.Neighbouring subMOPs are allowed to share some subproblems so that the knowledge gained from solving one subMOP can be transferred to another,and eventually to all the subMOPs.The bilevel decomposition is readily combined with some new mating selection and population update strategies,leading to a high-performance algorithm that competes effectively against a number of state-of-the-arts studied in this paper for both multiand many-objective optimisation.Parameter analysis and component analysis have been also carried out to further justify the proposed algorithm.

Tourism Route Recommendation Based on A Multi-Objective Evolutionary Algorithm Using Two-Stage Decomposition and Pareto Layering

Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.

Research on Modulation Signal Denoising Method Based on Improved Variational Mode Decomposition

In order to further analyze the micro-motion modulation signals generated by rotating components and extract micro-motion features,a modulation signal denoising algorithm based on improved variational mode decomposition(VMD)is proposed.To improve the time-frequency performance,this method decomposes the data into narrowband signals and analyzes the internal energy and frequency variations within the signal.Genetic algorithms are used to adaptively optimize the mode number and bandwidth control parameters in the process of VMD.This approach aims to obtain the optimal parameter combination and perform mode decomposition on the micro-motion modulation signal.The optimal mode number and quadratic penalty factor for VMD are determined.Based on the optimal values of the mode number and quadratic penalty factor,the original signal is decomposed using VMD,resulting in optimal mode number intrinsic mode function(IMF)components.The effective modes are then reconstructed with the denoised modes,achieving signal denoising.Through experimental data verification,the proposed algorithm demonstrates effective denoising of modulation signals.In simulation data validation,the algorithm achieves the highest signal-to-noise ratio(SNR)and exhibits the best performance.

An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition.This paper proposes a new randomized fixed-precision algorithm which for a given third-order tensor and a prescribed approximation error bound,it automatically finds the tubal rank and corresponding low tubal rank approximation.The algorithm is based on the random projection technique and equipped with the power iteration method for achieving better accuracy.We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.

Robot coverage algorithm under rectangular decomposition environment

The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into individual square sub-areas. Each sub-area is orientated by the central point of the sub-areas called a node. The rectangular map based on the square map can enlarge the square area side size to increase the coverage efficiency in the case of there being an adjacent obstacle. Based on this algorithm, a new coverage algorithm, which includes global path planning and local path planning, is introduced. In the global path planning, uncovered subspaces are found by using a special rule. A one-dimensional array P, which is used to obtain the searching priority of node in every direction, is defined as the search rule. The array P includes the condition of coverage towards the adjacent cells, the condition of connectivity and the priorities defined by the user in all eight directions. In the local path planning, every sub-area is covered by using template models according to the shape of the environment. The simulation experiments show that the coverage algorithm is simple, efficient and adapted for complex two- dimensional environments.

A Parallel Global-Local Mixed Evolutionary Algorithm for Multimodal Function Optimization Based on Domain Decomposition

This paper presents a parallel two-level evolutionary algorithm based on domain decomposition for solving function optimization problem containing multiple solutions. By combining the characteristics of the global search and local search in each sub-domain, the former enables individual to draw closer to each optima and keeps the diversity of individuals, while the latter selects local optimal solutions known as latent solutions in sub-domain. In the end, by selecting the global optimal solutions from latent solutions in each sub-domain, we can discover all the optimal solutions easily and quickly.

Wind speed forecasting based on wavelet decomposition and wavelet neural networks optimized by the Cuckoo search algorithm

Wind speed forecasting is of great importance for wind farm management and plays an important role in grid integration. Wind speed is volatile in nature and therefore it is difficult to predict with a single model. In this study, three hybrid multi-step wind speed forecasting models are developed and compared — with each other and with earlier proposed wind speed forecasting models. The three models are based on wavelet decomposition(WD), the Cuckoo search(CS) optimization algorithm, and a wavelet neural network(WNN). They are referred to as CS-WD-ANN(artificial neural network), CS-WNN, and CS-WD-WNN, respectively. Wind speed data from two wind farms located in Shandong, eastern China, are used in this study. The simulation result indicates that CS-WD-WNN outperforms the other two models, with minimum statistical errors. Comparison with earlier models shows that CS-WD-WNN still performs best, with the smallest statistical errors. The employment of the CS optimization algorithm in the models shows improvement compared with the earlier models.

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm （MCRDA）, is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.

ANALYSIS OF WAVEGUIDE PROBLEMS USING A RELAXED ITERATIVE DOMAIN DECOMPOSITION METHOD COMBINED WITH MULTIFRONTAL ALGORITHM

In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.

An improved cut-based recursive decomposition algorithm for reliability analysis of networks

In this paper, an improved cut-based recursive decomposition algorithm is proposed for lifeline networks. First, a complementary structural function is established and three theorems are presented as a premise of the proposed algorithm. Taking the minimal cut of a network as decomposition policy, the proposed algorithm constructs a recursive decomposition process. During the decomposition, both the disjoint minimal cut set and the disjoint minimal path set are simultaneously enumerated. Therefore, in addition to obtaining an accurate value after decomposing all disjoint minimal cuts and disjoint minimal paths, the algorithm provides approximate results which satisfy a prescribed error bound using a probabilistic inequality. Two example networks, including a large urban gas system, are analyzed using the proposed algorithm. Meanwhile, a part of the results are compared with the results obtained by a path-based recursive decomposition algorithm. These results show that the proposed algorithm provides a useful probabilistic analysis method for the reliability evaluation of lifeline networks and may be more suitable for networks where the edges have low reliabilities.

Automatic target recognition of moving target based on empirical mode decomposition and genetic algorithm support vector machine

In order to improve measurement accuracy of moving target signals, an automatic target recognition model of moving target signals was established based on empirical mode decomposition(EMD) and support vector machine(SVM). Automatic target recognition process on the nonlinear and non-stationary of Doppler signals of military target by using automatic target recognition model can be expressed as follows. Firstly, the nonlinearity and non-stationary of Doppler signals were decomposed into a set of intrinsic mode functions(IMFs) using EMD. After the Hilbert transform of IMF, the energy ratio of each IMF to the total IMFs can be extracted as the features of military target. Then, the SVM was trained through using the energy ratio to classify the military targets, and genetic algorithm(GA) was used to optimize SVM parameters in the solution space. The experimental results show that this algorithm can achieve the recognition accuracies of 86.15%, 87.93%, and 82.28% for tank, vehicle and soldier, respectively.

A novel decomposition and coordination algorithm for complex networks and its application to power grids

To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algorithm is made up of two parts: the first part decomposes the network into several independent areas based on community structure and decouples the information flow and control power among areas; the second part selects the center nodes from each area with the help of the control centrality index. As long as the status of center nodes is kept on a satisfactory level in each area, the whole system is under effective control. Finally, the algorithm is applied to power grids, and the simulations prove its effectiveness.

AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

A novel trilinear decomposition algorithm:Three-dimension non-negative matrix factorization

Non-negative matrix factorization （NMF） is a technique for dimensionality reduction by placing non-negativity constraints on the matrix. Based on the PARAFAC model, NMF was extended for three-dimension data decomposition. The three-dimension nonnegative matrix factorization （NMF3） algorithm, which was concise and easy to implement, was given in this paper. The NMF3 algorithm implementation was based on elements but not on vectors. It could decompose a data array directly without unfolding, which was not similar to that the traditional algorithms do, It has been applied to the simulated data array decomposition and obtained reasonable results. It showed that NMF3 could be introduced for curve resolution in chemometrics.

Algorithmic tangent modulus at finite strains based on multiplicative decomposition

The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.

STATE SPACE TREE METHOD AND EXACT DECOMPOSITION ALGORITHM FOR FINDING NETWORK OVERALL RELIABILITY

First,the state space tree method for finding communication network overall re-liability is presented.It directly generates one disjoint tree multilevel polynomial of a networkgraph.Its advantages are smaller computational effort(its computing time complexity is O(en_l),where e is the number of edges and n_l is the number of leaves)and shorter resulting expression.Second,based on it an exact decomposition algorithm for finding communication network overallreliability is presented by applying the hypergraph theory.If we use it to carry out the m-timedecomposition of a network graph,the communication network scale which can be analyzed by acomputer can be extended to m-fold.

Segmented second algorithm of empirical mode decomposition

A new algorithm, named segmented second empirical mode decomposition （EMD） algorithm, is proposed in this paper in order to reduce the computing time of EMD and make EMD algorithm available to online time-frequency analysis. The original data is divided into some segments with the same length. Each segment data is processed based on the principle of the first-level EMD decomposition. The algorithm is compared with the traditional EMD and results show that it is more useful and effective for analyzing nonlinear and non-stationary signals.

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.

AN ACCELERATION FOR THE EIGENSYSTEM REALIZATION ALGORITHM WITH PARTIAL SINGULAR VALUES DECOMPOSITION

The real-time identification of dynamic parameters is importantfor the control system of spacecraft. The eigensystme realizationalgorithm (ERA) is currently the typical method for such applica-tion. In order to identify the dynamic parameter of spacecraftrapidly and accurately, an accelerated ERA with a partial singularvalues decomposition (PSVD) algorithm is presented. In the PSVD, theHankel matrix is reduced to dual diagonal form first, and thentransformed into a tridiagonal matrix.

An Evolutionary Algorithm Based on a New Decomposition Scheme for Nonlinear Bilevel Programming Problems

In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.