Objective Function Value Research Articles

Multilingual Information Retrieval Using Graph Neural Networks: Practical Applications in English Translation

Multilingual information retrieval using graph neural networks offers practical applications in English translation by leveraging advanced computational models to enhance the efficiency and accuracy of cross-lingual search and translation tasks. By representing textual data as graphs and utilizing graph neural networks (GNNs), this approach captures intricate relationships between words and phrases across different languages, enabling more effective language understanding and translation. GNNs can learn complex linguistic structures and semantic similarities from multilingual corpora, facilitating the development of more robust translation systems that are capable of handling diverse language pairs and domains. The paper introduces a novel approach termed the Multilingual Ant Bee Optimization Graph Neural Network (MABO-GNN) for addressing optimization, classification, and multilingual translation tasks. MABO-GNN integrates ant bee optimization algorithms with graph neural networks to provide a versatile framework capable of optimizing objective functions, improving classification accuracy iteratively, and facilitating high-quality translations across multiple languages. Through comprehensive experimentation, the efficacy of MABO-GNN is demonstrated across various tasks, languages, and datasets. in optimization experiments, MABO-GNN achieves objective function values of 0.012, 0.015, 0.011, and 0.013 in Experiment 1, Experiment 2, Experiment 3, and Experiment 4, respectively, with convergence times ranging from 90 to 150 seconds. In classification tasks, the model exhibits notable performance improvements over iterations, with BLEU scores reaching 0.84 and METEOR scores reaching 0.78 in the fifth iteration. The translation results showcase BLEU scores of 0.85 for English, 0.82 for French, 0.79 for German, 0.81 for Spanish, and 0.75 for Chinese, indicating the model's proficiency in generating high-quality translations across diverse languages.

A risk‐averse strategy based on information gap decision theory for optimal placement of service transformers in distribution networks

AbstractIn distribution networks, among the planning problems, optimal placement of medium voltage to low voltage (MV/LV) transformers is a vital and challenging issue. Electrical load uncertainty is an important factor that affects the result of this planning problem. This paper investigates optimal allocation of service transformers with respect to the load uncertainty modelled by information gap decision theory (IGDT). For this aim, the planning problem is solved in risk‐neutral (RN) and risk‐averse (RA) frameworks. In RN strategy, objective function is defined to minimize the cost of service transformers and low voltage feeders as well as the cost of power losses. On the other hand, in RA strategy, objective function is defined to maximize the radius of the uncertainty in such a way that any deviation of the uncertain parameter results in an objective function value that is not worse than the critical limit. The optimization problem is solved by crow search algorithm (CSA) and particle swarm optimization (PSO) and the results are compared. In mid‐term planning, with respect to the deviation factors of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3, optimal values of the uncertainty radius are 5.89%, 13.64%, 21.37%, 28.97%, 34.39% and 43.46%, respectively. In long‐term planning, with respect to the deviation factors of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3, optimal values of the uncertainty radius are 6.92%, 13.33%, 20.39%, 27.03%, 34% and 40.46%, respectively. Moreover, on average, CSA finds more promising results than PSO.

Optimization Model of Emergency Evacuation Network Based on Genetic Algorithm

Aggregation and dispersion are the normal states. In economic production and social life, the evacuation of people and materials deserves extensive attention. From the perspective of mathematics and economics, arranging a thoughtful evacuation is essential for the best balance between personal satisfaction and cost. In this paper, evacuation is deeply studied by a genetic algorithm; the balance, cost, and willingness (satisfaction) priority models, which consider both satisfaction and cost, are established. In this paper, based on the field investigation and questionnaire survey conducted by Oriental Sports Center, overall satisfaction is inferred by the satisfaction of each person in the tested sample, and the time cost from the evacuation point to different reception points is inferred through actual investigation. Based on these data, a balance model is established, and the calculation is performed. The ratio of the total willingness value of the evacuated individuals to the total cost is taken as the function of the optimization objective. When the optimization objective function is complex, the genetic algorithm is used to search for the optimal solution by simulating the process of natural evolution. At the same time, the cost priority and willingness priority models are established to compare the advantages and disadvantages of different evacuation schemes and their applicable situations. The evacuation of Oriental Sports Center is studied using a genetic algorithm. The objective function value of equilibrium model optimization is 0.2155 (optimal solution), significantly different from willingness priority model optimization (0.0300). After calculating the optimization objective function value and cost value under the conditions of cost priority and willingness priority, a “People-oriented and cost-balanced” suggestion is put forward for a large crowd evacuation scheme.

A novel robust evaluation approach to improve systematic behavior of failure safety in water supply system under various ellipsoid uncertainties

This study proposes a novel robust optimization approach for an integrated water supply system, wherein the decision-makers attempt to improve failure safety of system under various uncertainty strategies. To cope with uncertainty, the ellipsoid uncertainty set is assumed to evaluate the best feasible solution in the direction of water supply under various strategies. We assessed the case of Hamoun watershed, a water-stressed watershed in southeastern of Iran, to evaluate the developed robust optimization model. In the following, the comparative feasibility under uncertainty levels is conducted to analyze the impacts of simulation strategies on the status of robust model. Based on the final results, the reliability of the model's objective functions experienced an increasing trend (58.3%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$58.3\\%$$\\end{document}), and the objective function values under the uncertainty strategies is greatly improved. The findings of the analysis show that the robust strategies in response to the failure safety achieve outstanding optimal objectives under uncertainty.

Multiscale topology optimization of structures by using isogeometrical level set approach

This study aims to optimize topology of structures at macro and micro scales, simultaneously, by using a level set method in an isogeometric analysis (IGA) framework. To achieve this, equilibrium and homogenization equations in the model are solved by IGA method. The level set functions are defined over a grid in parameter space of associating b-splines of the IGA model. Therefore, control net of the model and level set grid are separated and there is no need to refine the control net for having smooth boundaries. Sensitivity analyses for both scales are performed to calculate the velocity of boundary points and the level set functions are updated by solving reaction-diffusion equations. Finally, several 2D and 3D examples with different geometry and boundary conditions are provided to show performance and efficiency of the method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function. Also, by using IGA level set method, smooth boundaries are achieved in the final topology of micro and macro structures.

Sustainable cold supply chain design for livestock and perishable products using data-driven robust optimization

ABSTRACT Food products are a critical part of everyday life. To increase the efficiency of the food supply chain, designing a comprehensive mathematical is necessary. This study tries to optimize a protein supply chain. This supply chain is divided into livestock and perishable products. The integration of these two supply chain echelons has been applied to create an extensive model. Moreover, sustainability has been considered as a competitive advantage in the chain. Perishable products are temperature-sensitive. Hence, a cold supply chain has been considered. The model has three objective functions: maximizing the total profit, minimizing the storage cost in the cold chain, minimizing the health risk. In dealing with uncertainty, a data-driven robust optimization method has been used. Therefore, this paper used machine learning to construct the uncertainty sets from historical data. The Torabi-Hassini method has been implemented to solve the multi-objective model. Finally, to show the applicability and efficiency of the proposed approach, a real-world case study on the poultry supply chain, including abattoirs, breeding centers, slaughtering, and selling branches, has been applied. The result shows that this methodology significantly influences total profits and improves the environmental criteria in a real-world case study. Moreover, different sensitivity analyses have been prepared to help managers make a trade-off between the robustness of the model and objective function value with various weights and calculate the influence of supply chain integration on objective functions.

ABC-WOA Optimization Strategy for UPQC Fuzzy PI Tuning

Growing numbers of power electronics-based non-linear loads have raised worries about power quality (PQ) problems, which include equipment failures, overheating, and unplanned shutdowns. Power filters have traditionally been used for harmonics elimination, but their limitations in dynamic compensation and size present challenges. The present research presents a new methodology using the Artificial Bee Colony - Whale Optimizations Algorithm (ABC-WOA) to optimize the Unified Power Quality Conditioner (UPQC) controller. Assignment aims to tackle obstacles that come with it. The suggested algorithm's efficacy is clear, as shown from the stabilization of objective function values. Highlighting the expertise of the Proportional-Integral (PI) controller in effectively regulating the DC-link voltage, this study successfully addresses power quality concerns. The analysis of voltage injection emphasizes the significant influence of the controller on the power system, showcasing seamless integration and enhanced power quality. This research provides valuable insights into the application of advanced control algorithms in power systems, specifically in addressing challenges related to non-linear loads and transient conditions.

A machine learning framework for explainable knowledge mining and production, maintenance, and quality control optimization in flexible circular manufacturing systems

In the present study, we employed multiple decision tree algorithms to categorize cases and reflect the most efficient policies constructed by a reinforcement learning algorithm. These approaches treated a complex production, maintenance, and quality control optimization problem within a degrading manufacturing and remanufacturing system. The decision trees’ nodes represent the independent variables, while the trees’ leaves represent the set of function values. The reinforcement learning method revealed all optimization parameters and best policies, which were employed as the training sample for the tree algorithms. After constructing every decision tree, each resulting decision rule was used to solve the optimization problem, and its performance was assessed. Additionally, we performed a sensitivity analysis to determine if the pruning level impacts the objective function value and, generally, the effectiveness of the proposed approach.

Extending oscars-ii to generally constrained global optimization

AbstractA derivative free method for generally constrained global optimization is described. A non-smooth merit function with one parameter is used. When this parameter equals the optimal objective function value $$f^*$$ f ∗ , the merit function becomes an exact penalty function. The method estimates $$f^*$$ f ∗ , avoiding the need for it to be supplied. The method randomly samples the region satisfying the simple bounds from time to time, ensuring convergence almost surely. Other samples are drawn randomly from smaller regions considered promising. Numerical testing is done using a variety of bound constrained problems and generally constrained problems from the G-suite and elsewhere. Results show the method is competitive in practice. They also show that the method performs better when it estimates the optimal objective function value than when the actual value is used.

A sample average approximation-based heuristic for the stochastic production routing problem

AbstractThe Production Routing Problem under demand uncertainty is an integrated problem containing production, inventory, and distribution decisions. At the planning level, the aim is to meet retailers demand, when only the demand distribution is known in advance, while minimizing the corresponding costs. In this study, a two-stage formulation is presented in which the routing can be adjusted at short notice. In the first stage, only production decisions are made, while delivery and inventory quantities and retailer visit schedules are determined in the second stage. To handle a large number of scenarios, two solution methods based on Sample Average Approximation are introduced. Furthermore, the impact of the routing quality is explored by applying a simple heuristic and an effective metaheuristic on the routing part. It is shown that, on average, the simple heuristic within an adjustable Sample Average Approximation approach provides better objective function values than the metaheuristic within a non-adjustable approach. Also all solution approaches outperform an expected value based approach in terms of runtime and objective function value.

A [formula omitted]-power neurodynamic approach to distributed nonconvex optimization

In this paper, a neurodynamic optimization approach based on a p-power transformation Lagrangian function is developed for distributed nonconvex optimization. A new Lagrangian function is proposed to eliminate dual gaps of nonconvex problems, and a distributed average tracking approach is developed for estimating global objective function value. Based on the Lagrangian function and the distributed average tracking approach, a neurodynamic model is developed for distributed nonconvex optimization, and its convergence to a local minimum is proven. Two numerical examples are provided to demonstrate the validity and effectiveness of the proposed approach.

The sampling method for optimal precursors of El Niño–Southern Oscillation events

Abstract. The El Niño–Southern Oscillation (ENSO) is a significant climate phenomenon that appears periodically in the tropical Pacific. The intermediate coupled ocean–atmosphere Zebiak–Cane (ZC) model is the first and classical one designed to numerically forecast the ENSO events. Traditionally, the conditional nonlinear optimal perturbation (CNOP) approach has been used to capture optimal precursors in practice. In this paper, based on state-of-the-art statistical machine learning techniques1, we investigate the sampling algorithm proposed in Shi and Sun (2023) to obtain optimal precursors via the CNOP approach in the ZC model. For the ZC model, or more generally, the numerical models with a large number O(104−105) of degrees of freedom, the numerical performance, regardless of the statically spatial patterns and the dynamical nonlinear time evolution behaviors as well as the corresponding quantities and indices, shows the high efficiency of the sampling method compared to the traditional adjoint method. The sampling algorithm does not only reduce the gradient (first-order information) to the objective function value (zeroth-order information) but also avoids the use of the adjoint model, which is hard to develop in the coupled ocean–atmosphere models and the parameterization models. In addition, based on the key characteristic that the samples are independently and identically distributed, we can implement the sampling algorithm by parallel computation to shorten the computation time. Meanwhile, we also show in the numerical experiments that the important features of optimal precursors can still be captured even when the number of samples is reduced sharply.

Developing a tactical decision-making framework for a sustainable egg supply chain considering switchable parallel machines

ABSTRACT The increasing world population has increased food supply needs in recent years. Despite the numerous studies in the field of food supply chains, there are few articles on optimizing a sustainable egg supply chain. A fuzzy multi-objective mathematical model is presented to optimize a sustainable egg supply chain in a tactical decision structure. Switchable green packaging and labeling machines in parallel production lines, suppliers with different reliability rates and the provision of raw materials with different qualities have been studied in this article. Despite the significant reduction of the total costs while using switchable machines, the majority of the costs are still related to raw materials so that an increase of 2 to 4 times in the amount of input materials can change the values of objective functions by 23% to 60%. By using the unused capacity of the packaging and labeling machines, the total costs can be reduced significantly.

Comparison of New and Old Optimization Algorithms for Traveling Salesman Problem on Small, Medium, and Large-scale Benchmark Instances

The Traveling Salesman Problem (TSP), a prominent combinatorial optimization issue, is the subject of this study's evaluation of the performance of new and old optimization techniques. This paper seeks to expand knowledge of optimization techniques and how they might be applied to solve TSP challenges. The goal of the research is to compare various algorithms' scalability, convergence, and computation times on benchmark instances of several sizes. To achieve this goal, this paper carried out extensive testing using the Artificial Bee Colony (ABC), Grey Wolf Optimization (GWO), and Salp Swarm Algorithm (SSA) as new optimization algorithms and the Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Simulated Annealing (SA) as old optimization algorithms. On small, medium, and large-scale benchmark cases, these algorithms were examined. The findings of this investigation show that the new optimization techniques are more convergent and scalable than the old ones, especially for medium-scale scenarios. They perform better performance in terms of solution quality by applying objective function values. The new methods also exhibit improved scalability, successfully adjusting to medium-scale instances. However, there were no discernible changes between the smaller and larger instances. This study makes an impact by offering insightful information about how well optimization methods perform while solving the TSP. Each algorithm's strengths and downsides have been reported, and these details offer useful guidance for choosing an algorithm for a certain scenario. The results also show the practical ramifications of applying novel optimization techniques, especially in medium-scale instances..

Optimal Transport with Cyclic Symmetry

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph processing. Our main idea is to reduce OT to a small optimization problem that has significantly fewer variables by utilizing cyclic symmetry and various optimization techniques. On the basis of this reduction, our algorithms solve the small optimization problem instead of the original OT. As a result, our algorithms obtain the optimal solution and the objective function value of the original OT faster than solving the original OT directly. In this paper, our focus is on two crucial OT formulations: the linear programming OT (LOT) and the strongly convex-regularized OT, which includes the well-known entropy-regularized OT (EROT). Experiments show the effectiveness of our algorithms for LOT and EROT in synthetic/real-world data that has a strict/approximate cyclic symmetry structure. Through theoretical and experimental results, this paper successfully introduces the concept of symmetry into the OT research field for the first time.

Calibrating Agro-Hydrological Model under Grazing Activities and Its Challenges and Implications

Recently, the Agricultural Policy Extender (APEX) model was enhanced with a grazing module, and the modified grazing database, APEXgraze, recommends sustainable livestock farming practices. This study developed a combinatorial deterministic approach to calibrate runoff-related parameters, assuming a normal probability distribution for each parameter. Using the calibrated APEXgraze model, the impact of grazing operations on native prairie and cropland planted with winter wheat and oats in central Oklahoma was assessed. The existing performance criteria produced four solutions with very close values for calibrating runoff at the farm outlet, exhibiting equifinality. The calibrated results showed that runoff representations had coefficients of determination and Nash–Sutcliffe efficiencies >0.6 in both watersheds, irrespective of grazing operations. Because of non-unique solutions, the key parameter settings revealed different metrics yielding different response variables. Based on the least objective function value, the behavior of watersheds under different management and grazing intensities was compared. Model simulations indicated significantly reduced water yield, deep percolation, sediment yield, phosphorus and nitrogen loadings, and plant temperature stress after imposing grazing, particularly in native prairies, as compared to croplands. Differences in response variables were attributed to the intensity of tillage and grazing activities. As expected, grazing reduced forage yields in native prairies and increased crop grain yields in cropland. The use of a combinatorial deterministic approach to calibrating parameters offers several new research benefits when developing farm management models and quantifying sensitive parameters and uncertainties that recommend optimal farm management strategies under different climate and management conditions.

Automatic calculation of step size and inertia parameter for convolutional dictionary learning

The convergent methods available for convolutional dictionary learning (CDL) are the proximal gradient method (PGM) and the inertial proximal gradient method (IPGM). However, it is not trivial and heuristic for IPGM to set the step size and inertia parameter, and IPGM produces local minima and oscillating solutions. To address these issues, in this paper, we introduce a dry friction, which has an oscillation-alleviating property. Specifically, the proposed IPGM with dry friction (IPGM-DF) generates the composite proximal mappings, whose construction and optimization solver are two challenges. An auxiliary function is designed to construct the composite proximal mappings, whose optimization problem is solved by the alternating direction method of multipliers. Fortunately, IPGM-DF obtains the formulas of the step size and inertia parameter. The finite convergence of IPGM-DF is proved. Experimental results of image reconstruction, separation, and fusion demonstrate the superiority of IPGM-DF over IPGM and the state-of-the-art methods. For image reconstruction, the objective function value of IPGM-DF is reduced by about 38.708% than that of IPGM. Throughout alleviating oscillations, IPGM-DF obtains a much lower value of the objective function than IPGM, which indicates that IPGM-DF jumps out of the local minima of IPGM. In addition, the average PSNR of IPGM-DF is about 3.5 dB larger than that of IPGM and the state-of-the-art methods. The code is available.

A Pareto dominance relation based on reference vectors for evolutionary many-objective optimization

Pareto dominance based approach is a classical method for solving multi-objective optimization problems (MOPs). However, as the number of objectives increases, the selection pressure drops sharply. Solutions with good convergence and diversity are hardly obtained. To tackle these issues, this paper proposes a Pareto dominance relation based on reference vectors (called PRV-dominance) for evolutionary many-objective optimization. In PRV-dominance, solutions in the population are divided into several subregions according to a set of uniform reference vectors. To enhance the convergence, a new convergence metric based on the ranking of objective function values is designed to determine the dominance relationship between two solutions. Then, the density in different subregions is considered to maintain the diversity. In order to verify the performance of our approach, WFG and MaF benchmark problems with 3, 5, 8, and 15 objectives are utilized. Experimental results demonstrate that the proposed PRV-dominance outperforms eight existing dominance relations in balancing convergence and diversity. An improved NSGA-II is suggested based on the proposed PRV-dominance, which shows the competitive performance when compared with six other state-of-the-art algorithms in solving many-objective optimization problems (MaOPs). The effectiveness of the proposed PRV-dominance is also verified on two other existing many-objective evolutionary algorithms.

Multi-objective optimization design of power pack structures based on floating projection topology optimization

Battery packs are vital components for storing and releasing energy. However, during driving, the intensity of heat emission and mechanical performance of electric vehicles are interrelated but conflicting indicators. To address this problem, this study topologically optimizes the power pack support structure with multiple objectives of minimizing compliance and heat dissipation, aiming to achieve a comprehensive and integrated design scheme. A floating projection topology optimization (FPTO) method is proposed, which normalizes the objectives of structural compliance and heat dissipation and derives the sensitivity. FPTO demonstrates superior objective function values and smoother topology configuration compared to the solid isotropic material with penalization (SIMP) method. Finally, the proposed method is applied to the power pack support structure. The results demonstrate that the method obtains a design solution with excellent mechanical performance and high heat dissipation performance with a suitable trade-off. The lightweight design of the overall structure of the battery pack is achieved.

Global convergence properties of a Dai-Liao-type CGM for unconstrained optimization

A popular optimization technique called the conjugate gradient method (CGM) is renowned for its effectiveness in addressing problems involving unconstrained optimization. Several conjugate gradient (CG) techniques have been proven to possess global convergence properties both theoretically and numerically. The Dai-Liao-type CGM is a variant that incorporates certain modifications to enhance its convergence properties. This paper examines the global convergence properties of a Dai-Liao-type CGM for unconstrained optimization problems. Theoretically, this study investigates the conditions under which the method ensures convergence to the global minimum of the objective function, focusing on the algorithm’s descent directions, the necessary reduction in objective function values, and termination criteria. A numerical experiment is conducted on a set of unconstrained optimization problems to validate the theoretical results obtained in this work. The numerical findings of this study demonstrate the robustness and reliability of the Dai-Liao-type CGM, showing its ability to find the global optimal solution in a wide range of unconstrained optimization problems.