Multimodal Problems Research Articles

Integration of preferences in multimodal multi-objective optimization

Various existing multimodal multi-objective evolutionary algorithms (MMEAs) efficiently search for an approximation to the Pareto optimal front (PF), which consists of multiple equivalent Pareto optimal sets (PSs), when tackling multimodal multi-objective optimization problems (MMOPs). However, in practical applications, the Decision-maker (DM) often seeks specific portions of the PF, known as the Region of Interest (ROI), corresponding to particular instances rather than the whole PF. Existing MMEAs only focus on the whole PF and lack exploration of the ROI. Consequently, we propose an innovative MMEA that incorporates the DM’s preferences and local convergence quality (MMEA-PLC). The proposed algorithm integrates the DM’s preferences into the traditional Pareto-dominance relationship, enabling the search for multiple equivalent Pareto optimal set subsets (PSSs) within the ROI. Due to the influence of local PFs, accurately representing the ROI can be challenging when expressed across different PFs. Therefore, we design a preference-based Pareto-dominance relationship to accurately convey the preferences on different PFs by mapping solutions onto a hyperplane in the objective space. Then, we further develop a scheme for assessing local convergence quality (LCQ) to ensure that the algorithm can identify multiple equivalent PSSs within the same ROI. To verify the effectiveness of the proposed algorithm, MMEA-PLC was experimentally compared with eight state-of-the-art MMEAs on 28 benchmark functions and a real-life application problem. Experimental results show that MMEA-PLC has significant competitive advantages in different preference scenarios.

Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm

Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material’s fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values.

On the optimization of green multimodal transportation: a case study of the West German canal system

AbstractIn this study, we address a biobjective multimodal routing problem that consists of selecting transportation modes and their respective quantities, optimizing transshipment locations, and allocating port orders. In the objective functions, we minimize total transportation costs and use the EcoTransit methodology to minimize total greenhouse gas emissions. The optimization model selects the transportation mode and transshipment port where quantities are transshipped from one mode to another. We compare inland waterway transportation and trucks encountering infrastructure failures that require rerouting or modal shifting in a real-life case study on the supply of goods for the chemical industry in the West German canal system. We propose a population-based heuristic to solve large instances in a reasonable computation time. A sensitivity analysis of demand, of varying lock times, and of infrastructure failure scenarios was conducted. We show that compared with inland waterway transportation, multimodal transportation reduces costs by 23% because of longer lock times. Our analysis shows that the use of inland waterway transportation only during infrastructure failures imposes nearly 28% higher costs per day depending on the failure location compared to that of the case of no failures. We also show that the use of a multimodal transportation system helps to reduce this cost increase in lock failure scenarios.

Multi‐strategy Grey Wolf Optimizer for Engineering Problems and Sewage Treatment Prediction

Grey wolf optimizer (GWO) is a highly valued heuristic algorithm in many fields. However, for some complex problems, especially high‐dimensional and multimodal problems, the basic algorithm has limited computational power and cannot get a satisfactory answer. In order to find a better solution, an improved algorithm based on GWO is proposed herein. Gaussian barebone, random selection and chaotic game mechanisms are introduced into the GWO algorithm to enhance the global search ability. The GWO enhanced by three mechanisms is called CBRGWO. To verify the performance of CBRGWO, using IEEE CEC 2017 as a test function, CBRGWO is compared to five GWO variants, five basic algorithms, six advanced algorithms, and four champion algorithms. CBRGWO is evaluated using the Friedman test and Wilcoxon signed‐rank test. Then, the stability of CBRGWO is analyzed. To verify that CBRGWO is still effective in practical application, CBRGWO is applied to five engineering problems and a water quality prediction problem. The experimental findings indicate that CBRGWO maintains excellent optimization ability in practical engineering problems.

A Kepler optimization algorithm improved using a novel Lévy-Normal mechanism for optimal parameters selection of proton exchange membrane fuel cells: A comparative study

Proton exchange membrane fuel cells (PEMFCs) are considered a promising renewable energy source and have sparked a lot of interest over the last few years due to their robust efficiency, low operating temperature, and longevity. The PEMFC's electrochemical model has seven unknown parameters, which are not given in the manufacturer's datasheets and need to be accurately estimated to present a more accurate model, leading to improved efficiency and performance of the PEMFC systems. The estimation of those unknown parameters has been dealt with as a complex and non-linear optimization problem that needs a powerful optimization algorithm to solve it. The existing optimization algorithms still have some disadvantages, such as falling into local minima and low convergence speed, which make them ineligible to solve this complicated problem with acceptable accuracy and low computational cost. Therefore, this study presents a new parameter estimation technique for estimating the unknown parameters of the PEMFC model more accurately, thereby achieving precise modeling of PEMFCs. This technique called IKOA is based on integrating the Kepler optimization algorithm (KOA) with a novel Lévy-Normal (LN) mechanism to strengthen its exploration and exploitation capabilities against this multimodal optimization problem. The Lévy flight in this mechanism aims to improve the KOA's exploitation operator to accelerate the convergence speed toward the near-optimal solution, thus minimizing the computational cost; meanwhile, the normal distribution is used to strengthen its exploration operator, thereby aiding in the escape of local minima. The proposed IKOA and KOA are herein evaluated against several rival algorithms using six well-known commercial PEMFC stacks to highlight their efficiency and effectiveness. Key performance metrics such as computational cost, fitness measures, and statistical validation through the Wilcoxon rank-sum test are herein used to highlight IKOA's effective performance in enhancing the predictive accuracy and operational efficiency of PEMFCs. The numerical findings show the high superiority of IKOA against all rival optimizers on all solved benchmarks.

A Hybrid Equilibrium Optimizer Based on Moth Flame Optimization Algorithm to Solve Global Optimization Problems

Abstract Equilibrium optimizer (EO) is a novel metaheuristic algorithm that exhibits superior performance in solving global optimization problems, but it may encounter drawbacks such as imbalance between exploration and exploitation capabilities, and tendency to fall into local optimization in tricky multimodal problems. In order to address these problems, this study proposes a novel ensemble algorithm called hybrid moth equilibrium optimizer (HMEO), leveraging both the moth flame optimization (MFO) and EO. The proposed approach first integrates the exploitation potential of EO and then introduces the exploration capability of MFO to help enhance global search, local fine-tuning, and an appropriate balance during the search process. To verify the performance of the proposed hybrid algorithm, the suggested HMEO is applied on 29 test functions of the CEC 2017 benchmark test suite. The test results of the developed method are compared with several well-known metaheuristics, including the basic EO, the basic MFO, and some popular EO and MFO variants. Friedman rank test is employed to measure the performance of the newly proposed algorithm statistically. Moreover, the introduced method has been applied to address the mobile robot path planning (MRPP) problem to investigate its problem-solving ability of real-world problems. The experimental results show that the reported HMEO algorithm is superior to the comparative approaches.

Multimodality in teaching a foreign language to students of philological and pedagogical disciplines

Relevance. The era of digital technologies necessitates the exploration of new avenues in various domains, including education. In the modern world, multimodality is an essential aspect, encompassing diverse modes of information transmission and all types of communication. The relevance of this study lies in its examination of how multimodality can be effectively utilized in the pedagogy of foreign languages, particularly for students in philological and pedagogical disciplines. Purpose. The primary aim of this research was to investigate the concept of multimodality and its application in teaching foreign languages. The study focused on identifying how multimodal methods can enhance the educational process and meet the set learning objectives. Methodology. This theoretical research employed methods such as induction and deduction for constructing and presenting scientific reasoning. It also utilized various techniques for collecting and systematizing information from previous studies. The methodology was designed to explore the fundamental aspects of multimodality and its pedagogical implications. Results. The study first examined the concept of multimodality and its connection with pedagogy. It identified the conditions under which multimodal methods could be applied in foreign language lessons. The research found that multimodal techniques engage students more effectively, making the learning process more exciting and interesting. Conclusions. The research concluded that the use of multimodal methods in teaching foreign languages offers significant pedagogical benefits. It enhances student engagement and supports comprehensive learning. The practical significance of this study lies in its contribution to the development of multimodality problems, suggesting that these methods can broadly realize educational objectives in foreign language education. Keywords: means of expression; verbalism; teaching methodology; education

Uncertainty estimation and evaluation of deformation image registration based convolutional neural networks

Objective. Fast and accurate deformable image registration (DIR), including DIR uncertainty estimation, is essential for safe and reliable clinical deployment. While recent deep learning models have shown promise in predicting DIR with its uncertainty, challenges persist in proper uncertainty evaluation and hyperparameter optimization for these methods. This work aims to develop and evaluate a model that can perform fast DIR and predict its uncertainty in seconds. Approach. This study introduces a novel probabilistic multi-resolution image registration model utilizing convolutional neural networks to estimate a multivariate normal distributed dense displacement field (DDF) in a multimodal image registration problem. To assess the quality of the DDF distribution predicted by the model, we propose a new metric based on the Kullback–Leibler divergence. The performance of our approach was evaluated against three other DIR algorithms (VoxelMorph, Monte Carlo dropout, and Monte Carlo B-spline) capable of predicting uncertainty. The evaluation of the models included not only the quality of the deformation but also the reliability of the estimated uncertainty. Our application investigated the registration of a treatment planning computed tomography (CT) to follow-up cone beam CT for daily adaptive radiotherapy. Main results. The hyperparameter tuning of the models showed a trade-off between the estimated uncertainty’s reliability and the deformation’s accuracy. In the optimal trade-off, our model excelled in contour propagation and uncertainty estimation (p <0.05) compared to existing uncertainty estimation models. We obtained an average dice similarity coefficient of 0.89 and a KL-divergence of 0.15. Significance. By addressing challenges in DIR uncertainty estimation and evaluation, our work showed that both the DIR and its uncertainty can be reliably predicted, paving the way for safe deployment in a clinical environment.

Applying the Sine-Cosine Optimization Algorithm to the Parametric Estimation Problem in Three-Phase Induction Motors

The steady-state analysis of electrical machines requires a detailed characterization of their equivalent electrical circuit, which adequately represents the transformation and interaction between electrical and mechanical energy. This research aims to characterize the equivalent circuit of three-phase induction motors by minimizing the mean square error between the measured and calculated torque variables. These torques are obtained from data provided by the manufacturer, including starting, peak, and full-load torques. A metaheuristic optimization technique is applied to solve the resulting nonlinear programming model based on the interactions between the sine and cosine functions. The numerical results obtained with this algorithm demonstrate its efficiency in terms of response quality, reaching objective function values of less than \(1\times10^{-8}\) with regard to the measured and calculated variables. Simulation results in two test systems allow concluding that the parametric estimation problem in three-phase induction motors is a multimodal optimization problem. This implies a potentially infinite set of solutions that minimize the root mean square error and adequately represent the behavior of the motor's output torque under various probable operating conditions.

A dual-population coevolutionary algorithm for balancing convergence and diversity in the decision space in multimodal multi-objective optimization

Many multimodal multi-objective evolutionary algorithms (MMEAs) are effective in solving multimodal multi-objective problems (MMOPs), which have multiple equivalent Pareto optimal sets (PSs) mapping to the same Pareto optimal front (PF). Due to the existence of the global convergence-first mechanism, these MMEAs will remove the solutions that can improve the diversity of the decision space but have poor convergence and even lead to the loss of PS when encountering MMOPs with an imbalance between convergence and diversity in the decision space (MMOP-ICD) or an MMOP with a local PS (MMOPL). We propose a new dual-population coevolutionary algorithm to address these issues. The auxiliary population helps the main population locate areas where equivalent PSs may exist, and the main population focuses on balancing convergence and diversity in the decision space. When updating the auxiliary population, a strength local convergence quality (SLCQ) is used to explore the distribution of the equivalent PSs. When updating the main population, the new niche-based truncation strategy first deletes the solutions that contribute less to convergence. Then, a distance-based subset selection method balances the diversity between the decision and objective spaces. The comparison results show the overall performance of the proposed algorithm is significantly better than other state-of-the-art algorithms.

An autoencoder-based self-supervised learning for multimodal sentiment analysis

Representation learning is a crucial and challenging task within multimodal sentiment analysis. Effective multimodal sentiment representations contain two key aspects: consistency and difference. However, the state-of-the-art multimodal sentiment analysis approaches failed to capture the difference and consistency of sentiment information across diverse modalities. To address the multimodal sentiment representation problem, we propose an autoencoder-based self-supervised learning framework. In the pre-training stage, an autoencoder is designed for each modality, leveraging unlabeled data to learn richer sentiment representations for each modality through sample reconstruction and modality consistency detection tasks. In the fine-tuning stage, the pre-trained autoencoder is injected into MulT (AE-MT) and enhance the model's ability to extract deep sentiment information by incorporating a contrastive learning auxiliary task. Our experiments on the popular Chinese sentiment analysis benchmark (CH-SIMS v2.0) and English sentiment analysis benchmark (MOSEI) demonstrate significant gains over baseline models.

Teaching–Learning-Based Optimization Algorithm with Stochastic Crossover Self-Learning and Blended Learning Model and Its Application

This paper presents a novel variant of the teaching–learning-based optimization algorithm, termed BLTLBO, which draws inspiration from the blended learning model, specifically designed to tackle high-dimensional multimodal complex optimization problems. Firstly, the perturbation conditions in the “teaching” and “learning” stages of the original TLBO algorithm are interpreted geometrically, based on which the search capability of the TLBO is enhanced by adjusting the range of values of random numbers. Second, a strategic restructuring has been ingeniously implemented, dividing the algorithm into three distinct phases: pre-course self-study, classroom blended learning, and post-course consolidation; this structural reorganization and the random crossover strategy in the self-learning phase effectively enhance the global optimization capability of TLBO. To evaluate its performance, the BLTLBO algorithm was tested alongside seven distinguished variants of the TLBO algorithm on thirteen multimodal functions from the CEC2014 suite. Furthermore, two excellent high-dimensional optimization algorithms were added to the comparison algorithm and tested in high-dimensional mode on five scalable multimodal functions from the CEC2008 suite. The empirical results illustrate the BLTLBO algorithm’s superior efficacy in handling high-dimensional multimodal challenges. Finally, a high-dimensional portfolio optimization problem was successfully addressed using the BLTLBO algorithm, thereby validating the practicality and effectiveness of the proposed method.

A comprehensive survey of convergence analysis of beetle antennae search algorithm and its applications

In recent years, swarm intelligence optimization algorithms have been proven to have significant effects in solving combinatorial optimization problems. Introducing the concept of evolutionary computing, which is currently a hot research topic, into swarm intelligence optimization algorithms to form novel swarm intelligence optimization algorithms has proposed a new research direction for better solving combinatorial optimization problems. The longhorn beetle whisker search algorithm is an emerging heuristic algorithm, which originates from the simulation of longhorn beetle foraging behavior. This algorithm simulates the touch strategy required by longhorn beetles during foraging, and achieves efficient search in complex problem spaces through bioheuristic methods. This article reviews the research progress on the search algorithm for longhorn beetles from 2017 to present. Firstly, the basic principle and model structure of the beetle whisker search algorithm were introduced, and its differences and connections with other heuristic algorithms were analyzed. Secondly, this paper summarizes the research achievements of scholars in recent years on the improvement of longhorn whisker search algorithms. Then, the application of the beetle whisker search algorithm in various fields was explored, including function optimization, engineering design, and path planning. Finally, this paper summarizes the research achievements of scholars in recent years on the improvement of the longhorn whisker search algorithm, and proposes future research directions, including algorithm deep learning fusion, processing of multimodal problems, etc. Through this review, readers will have a comprehensive understanding of the research status and prospects of the longhorn whisker search algorithm, providing useful guidance for its application in practical problems.

Eigenspectrum regularisation reverse neighbourhood discriminative learning

AbstractLinear discriminant analysis is a classical method for solving problems of dimensional reduction and pattern classification. Although it has been extensively developed, however, it still suffers from various common problems, such as the Small Sample Size (SSS) and the multimodal problem. Neighbourhood linear discriminant analysis (nLDA) was recently proposed to solve the problem of multimodal class caused by the contravention of independently and identically distributed samples. However, due to the existence of many small‐scale practical applications, nLDA still has to face the SSS problem, which leads to instability and poor generalisation caused by the singularity of the within‐neighbourhood scatter matrix. The authors exploit the eigenspectrum regularisation techniques to circumvent the singularity of the within‐neighbourhood scatter matrix of nLDA, which is called Eigenspectrum Regularisation Reverse Neighbourhood Discriminative Learning (ERRNDL). The algorithm of nLDA is reformulated as a framework by searching two projection matrices. Three eigenspectrum regularisation models are introduced to our framework to evaluate the performance. Experiments are conducted on the University of California, Irvine machine learning repository and six image classification datasets. The proposed ERRNDL‐based methods achieve considerable performance.

Two-echelon multi-commodity multimodal vehicle routing problem considering user heterogeneity in city logistics

The considerable increase in parcel deliveries has negatively impacted the accessibility and livability of cities. One solution strategy is to decouple short-distance from long-distance shipping so that last-mile transport can be performed with low-footprint vehicles. Such solutions are referred to in the literature as multi-echelon distribution systems. This study introduced a new variant of the two-echelon vehicle routing problem that considers multiple alternative transport modes as well as multiple commodities over a multi-period time horizon, where customers can obtain their commodities from any store. We referred to this problem as the two-echelon multi-commodity multimodal vehicle routing problem (MCM-2E-VRP). The objective of service providers is to minimize total generalized costs while satisfying customer requirements. We formulated this as a mathematical model based on a space–time network and introduced a random utility discrete choice model to capture variations in performance and preferences. We developed an adaptive large-neighborhood search (ALNS) algorithm to provide solutions for newly generated MCM-2E-VRP instances based on the Beijing Yizhuang transportation network. Extensive numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. A sensitivity analysis revealed some policy-relevant findings regarding the effects of store distribution and vehicle capacity.

Path Optimization of Container Multimodal Transportation Considering Differences in Cargo Time Sensitivity

To optimize the container multimodal transportation path selection problem with differences in cargo time sensitivity, this paper introduces the concept of mixed time windows and establishes an integer programming model from the perspective of carriers. The objective is to minimize the total transportation cost while meeting the customer’s on-time delivery requirements. The model imposes hard time window constraints on cargoes with on-time delivery requirements and soft time window constraints on general cargoes. A bi-level genetic algorithm is employed to solve the model. A case study is conducted to demonstrate the effectiveness of the proposed approach. Experimental results show that the bi-level genetic algorithm’s convergence ability, efficiency, stability, and global search capabilities are far superior to those of traditional single-level genetic algorithms. This indicates that the use of multi-stage solution approaches can mitigate the shortcomings of genetic algorithms in dealing with high-dimensional problems. In addition, when analyzing the effects of time penalty intensity and time window on decision-making results, it is found that the more time-sensitive cargoes are more likely to be affected by the time window setting, and will tend to sacrifice costs to ensure that the time demand is met. At the same time an increase in demand for time-sensitive services is accompanied by an increase in operating costs. Accurate assessment and classification of time sensitivity of cargoes can effectively prevent wasting resources in unnecessary areas, and ultimately maximize decision outcomes and ensure the most efficient use of resources.

Nature-inspired optimization algorithms based feature selection: Application in credit scoring

Nature-inspired algorithms as problem-solving methodologies are extremely effective in discovery of optimized solutions in multi-dimensional and multi-modal problems. Because of qualities like “self-optimization”, “flexibility” and etc., nature-inspired algorithms for problem solving are effectively optimal. Feature selection is an approach to find approximate optimal subset of the features which are more relevant towards the particular outcome. In this study, we focused on how feature selection may improve the credit scoring model’s performance for prediction. Nature-inspired algorithms are applied for feature selection to improve the predictive performance of the credit scoring model. Additionally, four benchmark credit scoring datasets collected from the UCI repository are used to test feature selection by several Nature-inspired algorithms aggregated with “Random Forest (RF)”, “Logistic Regression (LR),” and “Multi-layer Perceptron (MLP)” for classification and results are compared in terms of classification accuracy and G-measures.

A discrepancy-aware self-distillation method for multi-modal glioma grading

Gliomas are the most common intracranial primary tumors. Accurate grading of gliomas is crucial in determining treatment options and prognosis. Clinicians conventionally rely on multiple Magnetic Resonance Imaging (MRI) sequences for accurate glioma assessment. Traditional deep learning methods typically utilize the individual MRI sequence with the annotations of Region of Interest (ROIs), incurring substantial manual effort while losing the complementary information provided by other sequences. This task is inherently a standard multi-modal problem. However, existing methods often adopt complex multi-stream networks for feature extraction and fusion, leading to high resource demands and potential feature redundancy. To address the above challenge, a discrepancy-aware self-distillation method is proposed for multi-modal glioma grading, which requires only a single-stream network to concurrently analyze multiple MRI sequences without auxiliary ROIs. The first Modality Discrepancy-aware Fusion (MDF) module considers the MRI imaging differentiation and widens the inter-modal contrasts, allowing the modality-specific features to be highlighted and the modality-invariant features to be diminished. Furthermore, the proposed Class Activation Self-Distillation (CASD) strategy leverages the generated Class Activation Maps (CAMs) as dark knowledge for the distillation process. This guides shallow layers to focus on the category discriminative features specifically within the lesion region. Extensive experiments were conducted on the BraTS2018 and BraTS2019 datasets to evaluate the effectiveness of our method. The results show that our method outperforms other relevant glioma grading and multi-modal fusion methods on both datasets.

Differential evolution based on strategy adaptation and deep reinforcement learning for multimodal optimization problems

Multimodal optimization problems (MMOPs) include multiple optima, which are common in practical fields. However, the success of solving MMOPs requires the algorithm to have both exploration and exploitation performance. How to select a reasonable search strategy is a difficult problem facing MMOPs. In this research, a differential evolution based on strategy adaptation and deep reinforcement learning, termed SA-DQN-DE, is proposed to select mutation strategies reasonably and search the optima effectively, which mainly includes three aspects. First, strategy adaptation, which calculates selection probability based on the feedback of different mutation operators in previous evolution, and assigns mutation operations to each individual to provide guidance for the next stage of evolution is developed. Secondly, a new historical individual preservation method is designed to improve search efficiency. Thirdly, deep reinforcement learning is applied to select multiple local search operators to refine the accuracy of potential optimal solutions. The performance of SA-DQN-DE is tested on publicly acknowledged CEC2013 benchmark MMOP set. The experimental results demonstrate that the proposed SA-DQN-DE has competitive performance compared with some of its peer multimodal optimization algorithms.

A multi-role steered artificial bee colony algorithm with variable dimensionality perturbation for multimodal optimization problems

A multi-role steered artificial bee colony algorithm with variable dimensionality perturbation for multimodal optimization problems