Function Optimization Problems Research Articles

An Optimization Numerical Spiking Neural Membrane System with Adaptive Multi-Mutation Operators for Brain Tumor Segmentation.

Magnetic Resonance Imaging (MRI) is an important diagnostic technique for brain tumors due to its ability to generate images without tissue damage or skull artifacts. Therefore, MRI images are widely used to achieve the segmentation of brain tumors. This paper is the first attempt to discuss the use of optimization spiking neural P systems to improve the threshold segmentation of brain tumor images. To be specific, a threshold segmentation approach based on optimization numerical spiking neural P systems with adaptive multi-mutation operators (ONSNPSamos) is proposed to segment brain tumor images. More specifically, an ONSNPSamo with a multi-mutation strategy is introduced to balance exploration and exploitation abilities. At the same time, an approach combining the ONSNPSamo and connectivity algorithms is proposed to address the brain tumor segmentation problem. Our experimental results from CEC 2017 benchmarks (basic, shifted and rotated, hybrid, and composition function optimization problems) demonstrate that the ONSNPSamo is better than or close to 12 optimization algorithms. Furthermore, case studies from BraTS 2019 show that the approach combining the ONSNPSamo and connectivity algorithms can more effectively segment brain tumor images than most algorithms involved.

Quantum particle swarm optimization algorithm based on diversity migration strategy

Particle swarm optimization algorithm has been successfully applied to solve practical optimization problems due to its simplicity and efficiency. However, the traditional particle swarm optimization algorithm has inferior search performance in complicated high-dimensional optimization issues and is prone to falling into local optima. To address these problems, a new migration mechanism is introduced and a quantum particle swarm optimization method based on diversity migration is proposed. The strategy can capture different ranges of particles in the population, and the selection of migrating individuals depends not only on their fitness values but is also influenced by the positions within the population. The individual with the minimal average Hamming distance in the population can indicate the direction of iterative population optimization. After comparing the fitness values and the average Hamming distance between particles, the particles deviating from the central range of the population are replaced. The performance of the proposed algorithm is investigated under seven different sets of benchmark function optimization problems in the CEC2020 single-objective boundary-constrained optimization competition, and is compared with those of several other representative optimization algorithms. The quantum particle swarm optimization algorithm based on diversity migration strategy outperforms other typical optimization algorithms. Moreover, the proposed algorithm is convergent and stable.

基于EMSDBO算法农业植保无人机三维航迹多目标优化研究

Both cruising ability and safety should be considered in the 3D inspection path planning of agricultural unmanned aerial vehicles (UAVs). Specific to a complex working environment, the 3D inspection environment of agricultural UAVs was simulated through terrain modeling and threat modeling. First, the dynamic constraints of flight approaching rate and response time were added to the threat cost, and the 3D mission space model and flight path cost function were constructed considering the influence of UAVs’ turning performance. Second, the offset estimation strategy, variable spiral search strategy, quasi-reverse learning strategy and dimension-by-dimension mutation strategy were introduced into the dung beetle optimizer (DBO) algorithm to improve the global optimization ability and convergence rate of the algorithm. By establishing a three-dimensional trajectory planning model for unmanned aerial vehicles, the trajectory planning is transformed into a multi-objective function optimization problem, and an improved algorithm is used to solve the three-dimensional trajectory planning of unmanned aerial vehicles. The fitness is evaluated by considering the objective function of trajectory cost, terrain cost, and danger level, and the trajectory planning is iteratively optimized. The results indicate that the proposed improved dung beetle algorithm for trajectory planning has lower overall cost and stability in adapting to different complex terrain environments.

Multi-strategy boosted Aquila optimizer for function optimization and engineering design problems

Multi-strategy boosted Aquila optimizer for function optimization and engineering design problems

Symmetry-Enhanced, Improved Pathfinder Algorithm-Based Multi-Strategy Fusion for Engineering Optimization Problems

The pathfinder algorithm (PFA) starts with a random search for the initial population, which is then partitioned into only a pathfinder phase and a follower phase. This approach often results in issues like poor solution accuracy, slow convergence, and susceptibility to local optima in the PFA. To address these challenges, a multi-strategy fusion approach is proposed in the symmetry-enhanced, improved pathfinder algorithm-based multi-strategy fusion for engineering optimization problems (IPFA) for function optimization problems. First, the elite opposition-based learning mechanism is incorporated to improve the population diversity and population quality, to enhance the solution accuracy of the algorithm; second, to enhance the convergence speed of the algorithm, the escape energy factor is embedded into the prey-hunting phase of the GWO and replaces the follower phase in the PFA, which increases the diversity of the algorithm and improves the search efficiency of the algorithm; lastly, to solve the problem of easily falling into the local optimum, the optimal individual position is perturbed using the dimension-by-dimension mutation method of t-distribution, which helps the individual to jump out of the local optimum rapidly and advance toward other regions. The IPFA is used for testing on 16 classical benchmark test functions and 29 complex CEC2017 function sets. The final optimization results of PFA and IPFA in pressure vessels are 5984.8222 and 5948.3597, respectively. The final optimization results in tension springs are 0.012719 and 0.012699, respectively, which are comparable with the original algorithm and other algorithms. A comparison between the original algorithm and other algorithms shows that the IPFA algorithm is significantly enhanced in terms of solution accuracy, and the lower engineering cost further verifies the robustness of the IPFA algorithm.

Development and Practical Applications of Computational Intelligence Technology

Computational intelligence (CI) uses applied computational methods for problem-solving inspired by the behavior of humans and animals. Biological systems are used to construct software to solve complex problems, and one type of such system is an artificial immune system (AIS), which imitates the immune system of a living body. AISs have been used to solve problems that require identification and learning, such as computer virus identification and removal, image identification, and function optimization problems. In the body’s immune system, a wide variety of cells work together to distinguish between the self and non-self and to eliminate the non-self. AISs enable learning and discrimination by imitating part or all of the mechanisms of a living body’s immune system. Certainly, some deep neural networks have exceptional performance that far surpasses that of humans in certain tasks, but to build such a network, a huge amount of data is first required. These networks are used in a wide range of applications, such as extracting knowledge from a large amount of data, learning from past actions, and creating the optimal solution (the optimization problem). A new technique for pre-training natural language processing (NLP) software ver.9.1by using transformers called Bidirectional Encoder Representations (BERT) builds on recent research in pre-training contextual representations, including Semi-Supervised Sequence Learning, Generative Pre-Training, ELMo (Embeddings from Language Models), which is a method for obtaining distributed representations that consider context, and ULMFit (Universal Language Model Fine-Tuning). BERT is a method that can address the issue of the need for large amounts of data, which is inherent in large-scale models, by using pre-learning with unlabeled data. An optimization problem involves “finding a solution that maximizes or minimizes an objective function under given constraints”. In recent years, machine learning approaches that consider pattern recognition as an optimization problem have become popular. This pattern recognition is an operation that associates patterns observed as spatial and temporal changes in signals with classes to which they belong. It involves identifying and retrieving predetermined features and rules from data; however, the features and rules here are not logical information, but are found in images, sounds, etc. Therefore, pattern recognition is generally conducted by supervised learning. Based on a new theory that deals with the process by which the immune system learns from past infection experiences, the clonal selection of immune cells can be viewed as a learning rule of reinforcement learning.

A Multi-strategy Enhanced Arithmetic Optimization Algorithm and Its Application in Path Planning of Mobile Robots

A multi-strategy enhanced arithmetic optimization algorithm called MSEAOA is proposed to address the issues of low population diversity, imbalanced exploration and exploitation capabilities, and low accuracy of optimal solution in the Arithmetic Optimization Algorithm. Firstly, using the good point set strategy for population initialization to improve population diversity and thus accelerate convergence speed. Secondly, we integrate the exploration and exploition capabilities of differential self-learning strategy, best example learning strategy, and second-order differential perturbation strategy balancing algorithm. Finally, the introduction of somersault foraging strategy improves the accuracy of the optimal solution. We select 14 classical benchmark test functions and the CEC2019 function test set to test the optimization ability of MSEAOA, and apply MSEAOA to the path planning problem of mobile robots. MSEAOA is compared with other meta-heuristic optimization algorithms, and the experimental results are statistically analyzed by the Wilcoxon rank-sum test. The simulation experimental results show that MSEAOA performs the best among 14 benchmark functions, but for 10 CEC2019 functions, MSEAOA has the best optimization performance among 5 of them (50%). In the path optimization problem of mobile robots, the path obtained by MSEAOA is also the best among all algorithms, its path shortening rate exceeds 8.8% in 83% of environments. The results indicate that MSEAOA is a reliable algorithm suitable for function optimization and practical optimization problems.

Constrained Nonnegative Matrix Factorization Based on Label Propagation for Data Representation

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nonnegative matrix factorization</i> (NMF) algorithms are a series of dimensional reduction techniques widely used in data preprocessing. To improve the performance of clustering and the discrimination of the low-dimensional representation in NMF, we proposed a novel semi-supervised <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained nonnegative matrix factorization based on label propagation</i> (LpCNMF). Specifically, the proposed LpCNMF adopts graph and label propagation as regularization terms, then makes use of a small amount of labeled data to predict the label information of the unlabeled data and finally obtains a predictive membership matrix with more label information. At the same time, we introduce an efficient alternating iterative algorithm to solve the optimization problem of the objective function in the LpCNMF. Unlike other NMF algorithms that only update the basis and coefficient matrices, the LpCNMF algorithm increases the update of the predictive membership matrix obtained by label propagation. Experimental results on various benchmark datasets demonstrate the superiority of our algorithm over existing state-of-the-art NMF algorithms. The code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/ycwang-libra/LpCNMF_github.git.</uri>

Improved moth-flame algorithm based on cat chaotic and dynamic cosine factor.

The moth-flame algorithm shows some shortcomings in solving the complex problem of optimization, such as insufficient population diversity and unbalanced search ability. In this paper, an IMFO (Improved Moth-Flame Optimization) algorithm is proposed to be applied in solving the optimization problem of function. First, cat chaotic mapping is used to generate the initial position of moth to improve the population diversity. Second, cosine inertia weight is introduced to balance the global and local search abilities of the algorithm. Third, the memory information in the particle swarm algorithm is introduced into the iterative process of the algorithm to speed up the convergence of the population. Finally, Gaussian mutation strategy is used in the current optimal solution to avoid the algorithm from falling into the local optimum. Simulation experiments are conducted on 11 benchmark test functions, compared with other improved MFO (Moth-Flame Optimization) algorithms and classical optimization algorithms. The results show that the IMFO has higher accuracy and stability in solving the above-mentioned test functions. The proposed algorithm is experimented and verified by optimizing the KELM (Kernel Extreme Learning Machine) in an engineering example and exhibits a better optimization performance.

Optimization modeling of vegetable pricing replenishment strategy based on machine learning

Fresh supermarkets are affected by commodity attributes and transaction time, and usually need to be replenished every day. It is of great significance to study the distribution law of sales volume of each category and single product, and to give replenishment and pricing strategies for the commercial supermarket to maximize its revenue. Based on the machine learning method, this paper analyzes the sales flow records of a supermarket in the past three years, obtains the sales rules of each category, and establishes a dynamic optimization model for subsequent pricing and replenishment decisions. The steps are as follows: Firstly, data preprocessing is carried out. Secondly, the kernel density estimation method is used to analyze the distribution law of the total sales volume of each category. With the help of correlation coefficient Screening feature selection method, neural network method and regression tree method, the first 33 single vegetable variables that have an important impact on the total sales volume of vegetables and meet the given constraints are comprehensively selected. Based on these 33 variables, the revenue function of single product sales, single product pricing, single product replenishment and single product wholesale price is constructed, so that the optimization problem of the revenue function is transformed into a constrained optimization problem of a quadratic function of the cost markup rate, and the specific pricing and replenishment strategy on July 1,2023 is obtained. The model established in this study can provide some new solutions to the vegetable pricing and replenishment strategy of supermarket.

A high-resolution handheld millimeter-wave imaging system with phase error estimation and compensation

Despite the enormous potential of millimeter-wave (mmWave) imaging, the high cost of large-scale antenna arrays or stringent prerequisites of the synthetic aperture radar (SAR) principle impedes its widespread application. Here, we report a portable, affordable, and high-resolution 3D mmWave imaging system by overcoming the destructive motion error of handheld SAR imaging. This is achieved by revealing two important phenomenons: spatial asymmetry of motion errors in different directions, and local similarity of phase errors exhibited by different targets, based on which we formulate the challenging phase error estimation problem as a tractable point spread function optimization problem. Experiments demonstrate that our approach can recover high-fidelity 3D mmWave images from severely distorted signals and augment the aperture size by over 50 times. Since our system does not rely on costly massive antennas or bulky motion controllers, it can be applied for diverse applications including security inspection, autonomous driving, and medical monitoring.

First- and Second-Order Maximum Principles for Discrete-Time Stochastic Optimal Control With Recursive Utilities

This paper deals with the discrete-time stochastic optimal control problems with recursive utilities under weakened convexity assumption. A new stochastic maximum principle is established. Moreover, by constructing two new adjoint equations and two new variational equations for the backward stochastic difference equation (BS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula> E), we obtain the second-order necessary optimality condition of quasi-singular control. Finally, as an illustration, a discrete-time mean-variance portfolio selection mixed with a recursive utility functional optimization problem is solved.

Fuzzy logic applied to mutation size in evolutionary strategies

Tuning of algorithm parameters is a complex but very important issue in the design of Evolutionary Algorithms. This paper discusses a new concept of mutation size tuning in Evolutionary Strategies. The proposed algorithm uses data on evolutionary history in earlier generations to tune the mutation size. A Fuzzy Logic Part examines this historical data and tunes the mutation size of individuals to improve the algorithm’s convergence and its resistance to getting stuck in a local optimum. The Fuzzy Logic Part tunes the mutation size and keeps an appropriate relation of algorithm’s exploration and exploitation. The proposed concept is discussed, and several tests on Function Optimization Problems are performed. In tests, we use a set of data and functions with different difficulties recommended in the commonly used benchmarks. The results of experiments suggest that the proposed method is more efficient and resistant to getting stuck in suboptimal solutions. The proposed algorithm has been used in recognizing the type of ultra-high energy cosmic ray particle that initiates the Extensive Air Showers when hit the Earth atmosphere. It could be used for a wide range of similar problems. It is possible that the proposed method could be adapted to other types of optimization methods, inspired by natural evolution, for example, Evolutionary Algorithms.

A Deep Learning Neural Network Method Using Linear Eigenvalue Statistics for Schizophrenic EEG Data Classification

Electroencephalography (EEG) signals can be used as a neuroimaging indicator to analyze brain-related diseases and mental states, such as schizophrenia, which is a common and serious mental disorder. However, the main limiting factor of using EEG data to support clinical schizophrenia diagnosis lies in the inadequacy of both objective characteristics and effective data analysis techniques. Random matrix theory (RMT) and its linear eigenvalue statistics (LES) can provide an effective mathematical modeling method for exploring the statistical properties of non-stationary nonlinear systems, such as EEG signals. To obtain an accurate classification and diagnosis of schizophrenia, this paper proposes a LES-based deep learning network scheme in which a series of random matrixes, consisting of EEG data sliding window sampling and their eigenvalues, are employed as features for deep learning. Due to the fact that the performance of the LES-based scheme is sensitive to the LES’s test function, the proposed LES-based deep learning network is embedded with two ways of combining LES’s test functions with learning techniques: the first is to have the LES’s test function assigned, while, using the second way, the optimal LES’s test function should be solved in a functional optimization problem. In this paper, various test functions and different optimal learning methods were coupled in experiments. Our results revealed a binary classification accuracy of nearly 90% in distinguishing between healthy controls (HC) and patients experiencing the first episode of schizophrenia (FES). Additionally, we achieved a ternary classification accuracy of approximately 70% by including clinical high risk for psychosis (CHR). The LES-embedded approach yielded notably higher classification accuracy compared to conventional machine learning methods and standard convolutional neural networks. As the performance of schizophrenia classification is strongly influenced by test functions, a functional optimization problem was proposed to identify an optimized test function, and an approximated parameter optimization problem was introduced to limit the search area of suitable basis functions. Furthermore, the parameterization test function optimization problem and the deep learning network were coupled to be synchronously optimized during the training process. The proposal approach achieved higher classification accuracy rates of 96.87% between HC and FES, with an additional 89.06% accuracy when CHR was included. The experimental studies demonstrated that the proposed LES-based method was significantly effective for schizophrenic EEG data classification.

Research on function optimization problem based on Newtons method

Optimization is important because it helps improve efficiency, reduce waste, and achieve better outcomes in various fields such as business, engineering, and science. It enables organizations and individuals to make the most of their resources and capabilities, ultimately leading to increased productivity, cost savings, and better overall performance. The main focus of this paper is on studying how to optimize results when solving mathematical problems. We use optimization in mathematical problems to achieve the best possible solution or outcome by efficiently utilizing available resources and constraints. This helps us make informed decisions, save time, and find solutions that are both effective and efficient. The main focus of this article is to explore what Newton's method is, its fundamental principles, and its practical applications in solving mathematical problems. It delves into how Newton's method can be employed to achieve optimization within mathematical problem-solving contexts. The article discovers that utilizing Newton's method to solve mathematical problems for computational optimization is a favorable choice.

Multi-view unsupervised complementary feature selection with multi-order similarity learning

Graph construction, an open and challenging problem, is of great significance for multi-view unsupervised feature selection. So far, many graph construction methods, such as distance-based (the local structure) and self-reconstruction-based (the global structure), have been devised to serve the feature selection task. Although these methods have achieved some improvements, they fail to utilize high-order neighbor information, let alone exploit the neighbor information of different orders, to improve the feature selection task. In this paper, we propose a new insight to construct graphs that can accommodate multi-order neighbor information for selecting the relevant features. Besides, we observe that existing methods adopts the general information fusion strategy in multi-view learning, e.g. fusing graphs, without taking into account the unique characteristics of the feature selection task. Therefore, the proposed method seeks to project multi-view data onto a shared latent representation, which explores the complementarity tailored to the feature selection task at the feature level. A simple yet effective algorithm is designed to solve the optimization problem of the objective function. Extensive clustering experiments demonstrate the superiority of our method over state-of-the-art ones.

Joint sparse latent representation learning and dual manifold regularization for unsupervised feature selection

As an effective dimensionality reduction method, unsupervised feature selection (UFS) focuses on the mutual correlations between high-dimensional data features but often overlooks the intrinsic relationships between instances. We also utilize pseudo-labels learned from the data to guide feature selection in UFS. However, the raw data space may contain noise and outliers, leading to a lower accuracy of the learned pseudo-label matrix. We propose a minimum-redundant UFS approach to tackle these problems through jointing sparse latent representation learning with dual manifold regularization (SLRDR). Firstly, SLRDR learns a subspace of latent representation by exploring the interconnection of original data. To enhance subspace sparsity, ℓ2,1-norm is applied to the residual matrix of latent representation learning. Pseudo-label matrix learning is then carried out in the high-quality latent space, resulting in effective pseudo-label information that can provide more useful guidance for sparse regression. Secondly, based on the manifold learning hypothesis, SLRDR exploits features’ local structural properties in feature space and explores the association between data and labels, allowing the model to learn richer and more accurate structural information. In addition, ℓ2,1/2-norm is imposed on the weight matrix to obtain a minimum-redundant solution and select more discriminative features. Finally, an alternating iterative method is used for SLRDR to solve the optimization problem of the objective function, and the convergence of the model is theoretically analyzed. Besides, a series of comparative experiments with ten existing algorithms on nine benchmark datasets are used to verify the model’s effectiveness.

Analysis of improved particle swarm algorithm in wireless sensor network localization

Abstract Among the various WSN technologies, node localization technology is one of the core parts of WSN applications and an important component and key technology, which is also a hot spot and focus of research at this stage. In this paper, firstly, we propose a classical ion swarm localization algorithm for wireless sensor network localization, randomly assigning appropriate velocity and position to each particle in the population in order to find the global optimum in the iterative process. Based on this, a network node localization model is established to convert the functional optimization problem with constraints into an unconstrained optimization problem to solve. At the same time, the space is searched using a chaotic search strategy, which greatly improves the search efficiency. Next, the particle swarm algorithm is further optimized, and simulation experiments are set up using MATLAB software to do comparison experiments on the PSOAPF algorithm and other algorithms. The experimental results show that when the density of beacon nodes is 40%, the average localization error of the PSOAPF algorithm is 14.26%, with the smoothest decreasing trend. When the percentage of anchor nodes is 10%, the localization error is reduced by 6.89%, and the localization accuracy of the PSOAPF algorithm is also higher than other models. This study shows that the improved particle swarm algorithm can effectively improve the localization accuracy, reduce error and accelerate the convergence speed in wireless sensing network localization.

The Multiple Frequency Conversion Sinusoidal Chaotic Neural Network and Its Application

Aiming at the problem that the global search performance of a transiently chaotic neural network is not ideal, a multiple frequency conversion sinusoidal chaotic neural network (MFCSCNN) model is proposed based on the biological mechanism of the brain, including multiple functional modules and sinusoidal signals of different frequencies. In this model, multiple FCS functions and Sigmoid functions with different phase angles were used to construct the excitation function of neurons in the form of weighted sum. In this paper, the inverted bifurcation diagram, Lyapunov exponential diagram and parameter range of the model are given. The dynamic characteristics of the model are analyzed and applied to function optimization and combinatorial optimization problems. Experimental results show that the multiple frequency conversion sinusoidal chaotic neural network has better global search performance than the transient chaotic neural network and other related models.

Ensemble clustering via fusing global and local structure information

Ensemble clustering is aimed at obtaining a robust consensus result from a set of weak base clusterings. Most existing methods rely on a co-association (CA) matrix that describes the frequency at which pairs of samples are clustered into the same class and exhibits a symmetrical property. However, these methods typically focus on either the global or local structure of the CA matrix and do not consider using both types of information simultaneously to improve ensemble clustering performance. To address this issue, we propose a novel scheme to Fuse both the global Structure and the local structure information for Ensemble Clustering, namely FSEC, in this paper. Specifically, FSEC integrates both global structural information and local structural information into a learning framework by self-expressive and CA matrix self-enhancement models respectively. Moreover, FSEC embeds a Hadamard product fusion term to maximize the commonalities between global structure and local structure. The objective function optimization problem is solved by using the alternating direction method of multipliers (ADMM). Experimental results demonstrate that the proposed FSEC outperforms many state-of-the-art methods of ensemble clustering.