Weight Vector Research Articles

A decomposition-based multi-objective evolutionary algorithm using infinitesimal method

Multi-Objective Evolutionary Algorithm based on decomposition (MOEA/D) has been extensively employed to address a diverse array of real-world challenges and has shown excellent performance. However, the initial collection of aggregate weight vectors proves unsuitable for multi-objective optimization problems (MOPs) featuring intricate Pareto front (PF) structures, and the solving performance will be greatly affected when MOEA/D solves these irregular MOPs. In light of these challenges, a refined MOEA/D algorithm utilizing infinitesimal method is proposed. This algorithm incorporates the notion of global decomposition stemming from infinitesimal method to streamline the feature information of PF, thereby facilitating the adjustment of the weight vector towards optimal distribution. Consequently, enhancements in resource allocation efficiency and algorithmic performance are achieved. In the empirical investigation, the algorithm’s performance is tested on 28 benchmarks from ZDT,DTLZ and WFG test suits.Wilcoxon’s rank-sum test and Fredman’s test were carried out on performance metrics, which proved that the proposed MOEA/D-DKS was superior to other comparison algorithms.

Double Decomposition and Fuzzy Cognitive Graph-Based Prediction of Non-Stationary Time Series.

Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers' trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal's high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models.

A decomposition-based many-objective evolutionary algorithm with Q-learning guide weight vectors update

When dealing with regular, simple Pareto fronts (PFs), the decomposition-based multi-objective optimization algorithm (MOEA/D) performs well by presetting a set of uniformly distributed weight vectors. However, its performance declines when faced with complex and irregular PFs. Many algorithms address this problem by periodically adjusting the distribution of the weight vectors, but these methods do not take into account the performance of the population and are likely to update the weight vectors at the wrong time. In addition, for the SBX crossover operator, the setting of its distribution index will largely affect the exploration and convergence ability of the algorithm, so a single parameter setting will have negative impacts. To tackle these challenges, this paper proposes a method to simultaneously adaptively update weight vectors and optimize SBX parameter via Q-learning(RL-MaOEA/D). In order to make the strategies made by Q-learning more accurate, Two different metrics (CD and NCD) are proposed that capture diversity and convergence of individual and population respectively. RL-MaOEA/D is compared with seven state-of-the-art algorithms on different problems, and the simulation results reflect that the proposed algorithm has better performance.

Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

In order to better balance the convergence and diversity of MOEA/D for many objective optimization problems (MaOPs) with various Pareto fronts (PFs), an adaptive decomposition-based evolutionary algorithm for MaOPs with two-stage dual-density judgment is proposed. To solve the problem that weighted Tchebycheff decomposition may produce weakly Pareto optimal solutions when the solution is not unique or the uniqueness is difficult to guarantee, an augmented weighted Tchebycheff decomposition is adopted. To balance the convergence and diversity of non-dominated solutions in the external archive, different sparsity-level evaluations using vector angles or Euclidean distances are used to measure the distribution of solutions at different stages. To improve the diversity of solution sets obtained by MOEA/D for various PFs, an adaptive weight vector adjustment method based on two-stage dual-density judgment is presented. For weight vector addition, the potential search area is found according to the two-stage density judgment, and then a two-stage sparsity level judgment on the solutions of this area is performed for a second density judgment. For weight vector deletion, the degree of crowding is used to delete the weight vectors with a high crowding degree. Compared with nine advanced multi-objective optimization algorithms on DTLZ and WFG problems, the results demonstrate that the performance of the proposed algorithm is significantly better than other algorithms.

Large Margin Weighted k-Nearest Neighbors Label Distribution Learning for Classification.

Label distribution learning (LDL) helps solve label ambiguity and has found wide applications. However, it may suffer from the challenge of objective inconsistency when adopted to classification problems because the learning objective of LDL is inconsistent with that of classification. Some LDL algorithms have been proposed to solve this issue, but they presume that label distribution can be represented by the maximum entropy model, which may not hold in many real-world problems. In this article, we design two novel LDL methods based on the k -nearest neighbors ( k NNs) approach without assuming any form of label distribution. First, we propose the large margin weighted k NN LDL (LW- k NNLDL). It learns a weight vector for the k NN algorithm to learn label distribution and implement a large margin to address the objective inconsistency. Second, we put forward the large margin distance-weighted k NN LDL (LD k NN-LDL) that learns distance-dependent weight vectors to consider the difference in the neighborhoods of different instances. Theoretical results show that our methods can learn any general-form label distribution. Moreover, extensive experimental studies validate that our methods significantly outperform state-of-the-art LDL approaches.

A Kansei engineering-based decision-making method for offline medical service quality evaluation with multidimensional attributes

The evaluation of doctors’ offline medical service quality plays a vital role in evaluating hospital performance. There are two challenges that need to be addressed: (1) Currently, telephone follow-up and questionnaire surveys are the main methods for evaluating the quality of offline (mainly outpatient and inpatient) medical services in hospitals. However, these methods suffer from drawbacks such as low efficiency and resource consumption. (2) There are certain limitations to determining attribute dimensions and weighting patient evaluation attributes based solely on word frequency. To this end, this study proposes a Kansei engineering-based decision-making method for offline medical service quality evaluation with multidimensional attributes. First, this study constructs a medical Kansei lexicon based on speed and cosine similarity. Second, a concept of Kansei utility values is been defined to represent attribute values in medical service quality evaluation. Additionally, this study builds upon the Kano model to obtain the Kano classification of each attribute. On that basis, a novel approach to obtaining the implicit importance of the attributes is proposed. Thus, the weight vector of the attributes can be calculated as the combination of explicit and implicit importance. Finally, the evaluation result is obtained by using the multiattribute decision-making method. The effectiveness of the proposed method is verified through an analysis of online reviews from Haodf.com. The case study reveals that offline patients consider medical ethics and communication skills as the ”must-be” dimension of attributes, medical competence as a one-dimensional attribute, and medical advice and prescriptions as the attractive dimension of attributes. A comparative analysis with the traditional method is conducted to demonstrate the importance of dimensional analysis for offline medical service quality evaluation. The main contributions of this study include the following: (1) A medical Kansei lexicon is constructed based on Kansei engineering, and (2) a novel decision-making framework for medical service evaluation based on both appearance and implicit importance is constructed.

Collaborative Learning and Style-Adaptive Pooling Network for Perceptual Evaluation of Arbitrary Style Transfer.

Although the research of arbitrary style transfer (AST) has achieved great progress in recent years, few studies pay special attention to the perceptual evaluation of AST images that are usually influenced by complicated factors, such as structure-preserving, style similarity, and overall vision (OV). Existing methods rely on elaborately designed hand-crafted features to obtain quality factors and apply a rough pooling strategy to evaluate the final quality. However, the importance weights between the factors and the final quality will lead to unsatisfactory performances by simple quality pooling. In this article, we propose a learnable network, named collaborative learning and style-adaptive pooling network (CLSAP-Net) to better address this issue. The CLSAP-Net contains three parts, i.e., content preservation estimation network (CPE-Net), style resemblance estimation network (SRE-Net), and OV target network (OVT-Net). Specifically, CPE-Net and SRE-Net use the self-attention mechanism and a joint regression strategy to generate reliable quality factors for fusion and weighting vectors for manipulating the importance weights. Then, grounded on the observation that style type can influence human judgment of the importance of different factors, our OVT-Net utilizes a novel style-adaptive pooling strategy guiding the importance weights of factors to collaboratively learn the final quality based on the trained CPE-Net and SRE-Net parameters. In our model, the quality pooling process can be conducted in a self-adaptive manner because the weights are generated after understanding the style type. The effectiveness and robustness of the proposed CLSAP-Net are well validated by extensive experiments on the existing AST image quality assessment (IQA) databases. Our code will be released at https://github.com/Hangwei-Chen/CLSAP-Net.

A graph convolutional neural network model based on fused multi-subgraph as input and fused feature information as output

The graph convolution neural network (GCN)-based node classification model tackles the challenge of classifying nodes in graph data through learned feature representations. However, most existing graph neural networks primarily focus on the same type of edges, which might not accurately reflect the intricate real-world graph structure. This paper introduces a novel graph neural network model, MF-GCN, which integrates subgraphs with various edge types as input and combines feature information from each graph convolutional neural network layer to produce the final output. This model learns node feature representations by separately feeding subgraphs with different edge types into the graph convolutional layer. It then computes the weight vectors for fusing various edge type subgraphs based on the learned node features. Additionally, to efficiently extract feature information, the outputs of each graph convolution layer, without an activation function, are weighted and summed to obtain the final node features. This approach resolves the challenges of determining fusion weights and effectively extracting feature information during subgraph fusion. Experimental results show that the proposed model significantly improves performance on all three datasets, highlighting its effectiveness in node representation learning tasks.

A selective LVQ algorithm for improving instance reduction techniques and its application for text classification

Instance-Based Learning, such as the k Nearest Neighbor (kNN), offers a straightforward and effective solution for text classification. However, as a lazy learner, kNN’s performance heavily relies on the quality and quantity of training instances, often leading to time and space inefficiencies. This challenge has spurred the development of instance-reduction techniques aimed at retaining essential instances and discarding redundant ones. While such trimming optimizes computational demands, it might adversely affect classification accuracy. This study introduces the novel Selective Learning Vector Quantization (SLVQ) algorithm, specifically designed to enhance the performance of datasets reduced through such techniques. Unlike traditional LVQ algorithms that employ random vector weights (codebook vectors), SLVQ utilizes instances selected by the reduction algorithm as the initial weight vectors. Importantly, as these instances often contain nominal values, SLVQ modifies the distances between these nominal values, rather than modifying the values themselves, aiming to improve their representation of the training set. This approach is crucial because nominal attributes are common in real-world datasets and require effective distance measures, such as the Value Difference Measure (VDM), to handle them properly. Therefore, SLVQ adjusts the VDM distances between nominal values, instead of altering the attribute values of the codebook vectors. Hence, the innovation of the SLVQ approach lies in its integration of instance reduction techniques for selecting initial codebook vectors and its effective handling of nominal attributes. Our experiments, conducted on 17 text classification datasets with four different instance reduction algorithms, confirm SLVQ’s effectiveness. It significantly enhances the kNN’s classification accuracy of reduced datasets. In our empirical study, the SLVQ method improved the performance of these datasets, achieving average classification accuracies of 82.55%, 84.07%, 78.54%, and 83.18%, compared to the average accuracies of 76.25%, 79.62%, 66.54%, and 78.19% achieved by non-fine-tuned datasets, respectively.

A Decision-Making Model with Cloud Model, Z-Numbers, and Interval-Valued Linguistic Neutrosophic Sets.

Interval-valued linguistic neutrosophic sets (IVLNSs), Z-numbers, and the trapezium cloud model are powerful tools for expressing uncertainty and randomness. This paper aims to combine these methodologies. First, we review relevant concepts and operators, introducing a novel combination of IVLNSs and Z-numbers, which establishes a new form of expression. Subsequently, we propose the Z-interval-valued linguistic neutrosophic set-trapezium-trapezium cloud (Z-IVLNS-TTC) model, designed to minimize information loss and distortion during quantification. A novel method for calculating the objective weight vector is then developed using multi-objective programming (MOP). Drawing inspiration from the TOPSIS method, we propose a new approach for calculating the distance between Z-IVLNS-TTCs based on the p-norm. Finally, a group decision-making problem is presented to demonstrate the practical application of the proposed method. To validate the effectiveness and feasibility of the method, sensitivity analysis and comparisons with existing approaches are conducted.

Optimization of Interference Suppression Algorithm for Polarization Sensitive Conformal Array in Complex Electromagnetic Environment

With the development of modern electronic technology, the electromagnetic environment is becoming increasingly complex, which poses a severe challenge to the normal work of radar, communication and other systems. Polarization sensitive array can more effectively distinguish and suppress interference signals by using polarization information of electromagnetic waves, and improve the signal-to-noise ratio (SNR) and anti-interference ability of the system. Conformal array can be closely attached to the carrier surface, reducing space occupation and improving signal receiving efficiency and accuracy. However, at present, polarization-sensitive conformal arrays still face technical problems in interference suppression, especially in complex electromagnetic environment, how to optimize interference suppression algorithms to improve system performance has become the research focus. In this paper, an adaptive interference suppression algorithm combining spatial-polarization domain processing is proposed. The algorithm digitally processes the received signal, extracts spatial and polarization domain information, constructs the joint feature vector of the signal in spatial and polarization domain, and designs a joint filter in spatial and polarization domain. The minimum mean square error (MMSE) criterion and the least mean square (LMS) algorithm are used to update the weight vector of the filter in real time, enabling the filter to automatically adapt to changes in the electromagnetic environment and achieve optimal interference suppression. Simulation experiments show that the algorithm exhibits good stability and adaptability under different electromagnetic environments, effectively suppressing interference and extracting the desired signal. Compared with traditional interference suppression algorithms based solely on spatial domain, the joint spatial-polarization domain adaptive interference suppression algorithm significantly improves the interference suppression ratio (ISR) and signal-to-interference-plus-noise ratio (SINR) performance indicators, verifying that the introduction of polarization domain information can enhance the effect of interference suppression.

Machine learning-driven polygenic risk scores for bipolar disorder, depression, and panic disorder

Polygenic Risk Score (PRS) is a computational tech- nique that uses various genomic data to simultaneously analyze an individ- ual’s genetic risk for particular illnesses or traits. However, the traditional PRS computation has a few weaknesses, including its limited capacity to account for just a portion of trait variance, susceptibility to overfitting, and insufficient ability to discriminate among the larger population. Machine Learning (ML) methods offer a promising alternative to the traditional method by avoiding the problem of overfitting and improving accuracy. This study aims to develop an ML model for improved PRS calculation. We used the summary statistics for three mentals diseases, bipolar, depression, and panic disorder, from the Psychiatric Genomics Consortium (PGC) as a disease reference. We also obtained actual genotype data of individuals from OpenSNP, which includes both case and control samples. This data is used for predicting scores. The suggested approach, called Polygenic Risk Score Neural Network (PRSNN), calculates the PRS using weight vectors that estimate the relevance of each single nucleotide polymorphism (SNP) with a particular phenotype by deep learning model as an alternative to the traditional method. This study aims to develop a machine learning model, called PRSNN, for improved calculation of Polygenic Risk Scores (PRS). The PRSNN method outperforms the conventional method in identifying individuals at risk of mental disease. A novel deep-learning approach, named as PRSNN, is proposed for generating PRSs. The results demonstrate that it outperforms the traditional method of computing PRS for complex diseases. Further upgrades for this tool are required to overcome the current limitations, including lack of validation with external data from different ancestries, which may limit the applicability of the PRSNN method across diverse populations, and the small sample size, which may affect the results.

On value efficiency analysis and cone-ratio data envelopment analysis models

AbstractIn this paper we relate the Value Efficiency Analysis (VEA) efficiency scores with those of three different Cone-Ratio Data Envelopment Analysis (CR-DEA) models, when the chosen model Decision Making Units (DMUs) in CR-DEA jointly comprise the Most Preferred Solution (MPS) in VEA. In particular, we consider the cases where the set of feasible weight vectors is given respectively by (i) the weight vectors that are jointly optimal in DEA for all the model DMUs, (ii) every weight vector that is optimal in DEA for at least one of the model DMUs, and (iii) only those weight vectors with strictly positive input and output weights, each of which is jointly optimal in DEA for all the model DMUs. In each of these cases we show that the CR-DEA efficiency scores can be obtained or approximated by estimating either a VEA model or a series of VEA models, without the need of identifying a priori the set of feasible weight vectors. We illustrate the usefulness of our results by means of an empirical application using data on Japanese regional banks.

Algorithm for solving multi-objective hybrid flow shop scheduling problem

Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem, a multi-objective mathematical model is established with the goal of minimizing the maximum completion time, total machine energy consumption and machine processing cost. An improved multi-objective evolution algorithm based on decomposition (IMOEAD) is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. Normal distribution crossover and adaptive Gaussian mutation are used to improve the global and local search capabilities of the algorithm. Individuals are selected in the neighborhood of the weight vector to generate new solutions. The non-dominated rank and crowding distance are used to update the external archive. The inverse generation distance, generation distance and number of non-dominated solutions are used as performance indicators. Through a large number of case simulations, the algorithm is compared with the non-dominated sorting genetic algorithm II and the multi-objective evolution algorithm based on decomposition. The results verify the effectiveness of the algorithm.

A Multi‐Objective Evolutionary Algorithm Based on Bilayered Decomposition for Constrained Multi‐Objective Optimization

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Robust model averaging approach by Mallows-type criterion.

Model averaging is an important tool for treating uncertainty from model selection process and fusing information from different models, and has been widely used in various fields. However, the most existing model averaging criteria are proposed based on the methods of ordinary least squares or maximum likelihood, which possess high sensitivity to outliers or violation of certain model assumption. For the mean regression, no optimal robust methods are developed. To fill this gap, in our paper, we propose an outlier-robust model averaging approach by Mallows-type criterion. The idea is that we first construct a generalized M (GM) estimator for each candidate model, and then build robust weighting schemes by the asymptotic expansion of the final prediction error based on the GM-type loss function. So, we can still achieve a trustworthy result even if the dataset is contaminated by outliers in response and/or covariates. Asymptotic properties of the proposed robust model averaging estimators are established under some regularity conditions. The consistency of our weight estimators tending to the theoretically optimal weight vectors is also derived. We prove that our model averaging estimator is robust in terms of having bounded influence function. Further, we define the empirical prediction influence function to evaluate the quantitative robustness of the model averaging estimator. A simulation study and a real data analysis are conducted to demonstrate the finite sample performance of our estimators and compare them with other commonly used model selection and averaging methods.

Approximation algorithm for generalized budgeted assignment problems and applications in transportation systems

Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves L bins and P items. Each bin l has a utilization cost cl and an nl-dimensional capacity vector. Each item p has an nl-dimensional binary weight vector rlp, where the 1s in rlp (if any) appear in consecutive positions, and its assignment to bin l yields a reward vlp. The objective is to maximize total rewards through an assignment that satisfies three constraints: (i) the total weights of assigned items do not violate any bin’s capacity; (ii) each item is assigned to at most one open bin; and (iii) the overall utilization costs remain within a total budget B.We propose the first randomized rounding algorithm with a constant approximation ratio for this problem. We then apply our framework to the motivating transit line planning problem, presenting corresponding models and conducting numerical experiments using real-world data. Our results demonstrate significant improvements over previous approaches in addressing this critical transportation challenge.

Free superfermions construction for the coupled super KP and super modified KP hierarchies

In this paper, the Kac–van de Leur version of the coupled super KP (SKP) and super modified KP (SmKP) hierarchies are constructed. We define the tau functions as the orbit of a new group G(g) acting on the weight vectors, where G(g) is generated by elements in the even part of the tensor product of Clifford superalgebra and Grassmann algebra. The super Hirota bilinear equations of the coupled SKP and SmKP hierarchies are obtained by super boson-fermion correspondence of type A, and the bilinear identities with respect to the super Baker functions and tau functions in superbosonic Fock space are also constructed. Finally, the Miura transformation in terms of superfermions is also discussed.

Highest Weight Vectors in Plethysms, II

Highest Weight Vectors in Plethysms, II

A Relative Projection-Based Multiattribute Group Decision-Making Model With Noncooperative Behavior Management and Application to NEV Supplier Selection.

This article reports a novel consensus model where a group of internal and external experts evaluate alternatives under multiple attributes and provide mutual evaluations. First, different from previous studies, the cognitive and interest conflicts of internal and external experts are considered simultaneously. But interest conflict is emphasized for internal experts, and cognitive conflict is mainly considered for external experts. Second, we explore the categorization and management methods of noncooperative behaviors (NCBs) of experts. The relative projection-based indexes are proposed for the first time to measure the degrees of cognitive and interest conflicts by using multiattribute preference matrices (MAPMs) and the weight vectors of attributes. A group of experts are divided into three categories and the corresponding management strategies are developed. Third, we investigate the consensus mechanism among experts with cognitive and interest conflicts. For reaching an acceptable consensus level, an adjustment process is proposed to revise some local entries in MAPMs and mutual evaluation matrix (MEM). A penalty mechanism is further established to dynamically update the weights of experts. An algorithm is designed to capture the consensus reaching process in multiattribute group decision making, where internal and external experts are distinguished by proposing a parameter. Finally, the high-performance battery supplier selection of new energy vehicle is studied to illustrate the proposed model. The results reveal that the efficiency of reaching consensus can be enhanced by using the developed model with effective management of NCBs.