Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (30)

Search Parameters:
Keywords = variable neighborhood descent

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 1452 KB  
Article
An Improved Genetic Algorithm for Solving the Semi-Soft Clustered Vehicle Routing Problem
by Yihao Miao and Xiaoguang Bao
Appl. Sci. 2025, 15(9), 4871; https://doi.org/10.3390/app15094871 - 27 Apr 2025
Viewed by 644
Abstract
The Semi-Soft Clustered Vehicle Routing Problem (SemiSoftCluVRP) is a relaxed version of the Clustered Vehicle Routing Problem (CluVRP) and an enhanced variant of the Soft Clustered Vehicle Routing Problem (SoftCluVRP). In the SemiSoftCluVRP, all customers are partitioned into several clusters, and these clusters [...] Read more.
The Semi-Soft Clustered Vehicle Routing Problem (SemiSoftCluVRP) is a relaxed version of the Clustered Vehicle Routing Problem (CluVRP) and an enhanced variant of the Soft Clustered Vehicle Routing Problem (SoftCluVRP). In the SemiSoftCluVRP, all customers are partitioned into several clusters, and these clusters are further divided into two types: hard clusters and soft clusters. Within a hard cluster, customers must be served by the same vehicle without interruption, whereas within a soft cluster, customers must also be served by the same vehicle, but interruptions are permitted. To solve this problem, a mathematical model is first developed, followed by the design of a two-level genetic algorithm that integrates a variable neighborhood descent method. Computational experiments demonstrate that the proposed algorithm produces high-quality solutions and exhibits excellent performance. Compared with the results of CluVRP and SoftCluVRP, the results of SemiSoftCluVRP can reduce and increase logistics costs by up to 6.50% and 7.52%, respectively. In practical applications, by adjusting the hard and soft attributes of clusters, more flexible decision-making references can be provided for relevant decision-makers. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
Show Figures

Figure 1

16 pages, 1380 KB  
Article
Intelligent Scheduling of a Pulsating Assembly Flow Shop Considering a Multifunctional Automated Guided Vehicle
by Hailong Song, Shengluo Yang, Shuoxin Yin, Junyi Wang and Zhigang Xu
Appl. Sci. 2025, 15(5), 2593; https://doi.org/10.3390/app15052593 - 27 Feb 2025
Cited by 1 | Viewed by 797
Abstract
The pulsating assembly line is widely used in modern manufacturing, particularly in high-precision industries such as aerospace, where it greatly enhances production efficiency. To achieve overall optimization, both product scheduling and Automated Guided Vehicle (AGV) scheduling must be simultaneously optimized. However, existing research [...] Read more.
The pulsating assembly line is widely used in modern manufacturing, particularly in high-precision industries such as aerospace, where it greatly enhances production efficiency. To achieve overall optimization, both product scheduling and Automated Guided Vehicle (AGV) scheduling must be simultaneously optimized. However, existing research predominantly focuses on product scheduling, with limited attention given to AGV scheduling. This paper proposes an optimized solution for the pulsating assembly line scheduling problem, incorporating multifunctional AGV scheduling. A mathematical model is developed and three AGV selection strategies and three AGV standby strategies are designed to optimize AGV scheduling and control. To improve scheduling efficiency, nine heuristic strategies are introduced, along with the Variable Neighborhood Descent (VND) algorithm as a metaheuristic method for product scheduling. The VND algorithm refines the solution through multiple neighborhood searches, enhancing both the precision and efficiency of product scheduling. Our experimental results demonstrate that the proposed strategies significantly improve the production efficiency of pulsating assembly workshops, reduce AGV scheduling costs, and optimize overall production workflows. This study offers novel methods for intelligent scheduling in pulsating assembly workshops, contributing to the advancement of manufacturing toward “multiple varieties, small batches, and customization”. Full article
Show Figures

Figure 1

19 pages, 4642 KB  
Article
A Memetic Algorithm Approach for the Job-Shop Scheduling Problem with Variable Machine Efficiency and Maintenance Activities
by David Freud and Amir Elalouf
Appl. Sci. 2025, 15(3), 1431; https://doi.org/10.3390/app15031431 - 30 Jan 2025
Cited by 2 | Viewed by 1878
Abstract
Variable machine efficiency (VME) and maintenance activities (MA) are critical factors often unexplored in job scheduling problems. This paper introduces a new problem termed the job-shop scheduling problem with variable machine efficiency and maintenance activities (JSSP-VME-MT), wherein, unlike the traditional JSSP, machine efficiency [...] Read more.
Variable machine efficiency (VME) and maintenance activities (MA) are critical factors often unexplored in job scheduling problems. This paper introduces a new problem termed the job-shop scheduling problem with variable machine efficiency and maintenance activities (JSSP-VME-MT), wherein, unlike the traditional JSSP, machine efficiency and maintenance activities are explicitly incorporated into the scheduling process. The study proposes a novel memetic algorithm (MA) underpinned by a variable neighborhood descent (VND) local search strategy to address this complex problem. This methodology demonstrates significant improvements, achieving mean makespan reductions ranging from 2.22% to 5.77% across diverse problem instances with varying numbers of machines and jobs. Key contributions include the development of an encoding scheme to model maintenance activities and machine-specific constraints, along with the design of a hybrid metaheuristic framework combining global exploration and local refinement. This work provides a foundation for future comparative studies, algorithm enhancements, and practical industrial applications. The approach offers a scalable and flexible solution to job-shop scheduling challenges involving dynamic efficiency and planned maintenance activities. Full article
Show Figures

Figure 1

30 pages, 3858 KB  
Article
A Decision Support Framework for Aircraft Arrival Scheduling and Trajectory Optimization in Terminal Maneuvering Areas
by Dongdong Gui, Meilong Le, Zhouchun Huang and Andrea D’Ariano
Aerospace 2024, 11(5), 405; https://doi.org/10.3390/aerospace11050405 - 16 May 2024
Cited by 4 | Viewed by 2130
Abstract
This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. [...] Read more.
This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. The first module formulates and solves a trajectory optimization problem, generating a range of candidate descent trajectories for each arriving aircraft. The options for descent operations include step-down descent operation, Continuous Descent Operation (CDO), and CDO with a lateral path stretching strategy. The second module addresses the assignment of conflict-free trajectories to aircraft, determining precise arrival times at each waypoint. This is achieved by solving an aircraft arrival scheduling problem. To overcome computational complexities, a novel variable neighborhood search algorithm is proposed as the solution approach. This algorithm utilizes three neighborhood structures within an extended relaxing and solving framework, and incorporates a tabu search algorithm to enhance the efficiency of the search process in the solution space. The third module focuses on comparing the total cost incurred from flight delays and fuel consumption across the three descent operations, enabling the selection of the most suitable operation for the descent process. The decision support framework is evaluated using real air traffic data from Guangzhou Baiyun International Airport. Experimental results demonstrate that the framework effectively supports air traffic controllers by scheduling more cost-efficient descent operations for arrival aircraft. Full article
Show Figures

Figure 1

32 pages, 9220 KB  
Article
A Multi-Regional Path-Planning Method for Rescue UAVs with Priority Constraints
by Lexu Du, Yankai Fan, Mingzhen Gui and Dangjun Zhao
Drones 2023, 7(12), 692; https://doi.org/10.3390/drones7120692 - 29 Nov 2023
Cited by 10 | Viewed by 3607
Abstract
This study focuses on the path-planning problem of rescue UAVs with regional detection priority. Initially, we propose a mixed-integer programming model that integrates coverage path planning (CPP) and the hierarchical traveling salesman problem (HTSP) to address multi-regional path planning under priority constraints. For [...] Read more.
This study focuses on the path-planning problem of rescue UAVs with regional detection priority. Initially, we propose a mixed-integer programming model that integrates coverage path planning (CPP) and the hierarchical traveling salesman problem (HTSP) to address multi-regional path planning under priority constraints. For intra-regional path planning, we present an enhanced method for acquiring reciprocating flight paths to ensure complete coverage of convex polygonal regions with shorter flight paths when a UAV is equipped with sensors featuring circular sampling ranges. An additional comparison was made for spiral flight paths, and second-order Bezier curves were employed to optimize both sets of paths. This optimization not only reduced the path length but also enhanced the ability to counteract inherent drone jitter. Additionally, we propose a variable neighborhood descent algorithm based on K-nearest neighbors to solve the inter-regional access order path-planning problem with priority. We establish parameters for measuring distance and evaluating the priority order of UAV flight paths. Simulation and experiment results demonstrate that the proposed algorithm can effectively assist UAVs in performing path-planning tasks with priority constraints, enabling faster information collection in important areas and facilitating quick exploration of three-dimensional characteristics in unknown disaster areas by rescue workers. This algorithm significantly enhances the safety of rescue workers and optimizes crucial rescue times in key areas. Full article
(This article belongs to the Special Issue Path Planning, Trajectory Tracking and Guidance for UAVs)
Show Figures

Figure 1

20 pages, 2940 KB  
Article
Planning an Integrated Stockyard–Port System for Smart Iron Ore Supply Chains via VND Optimization
by Álvaro D. O. Lopes, Helder R. O. Rocha, Marcos W. J. Servare Junior, Renato E. N. Moraes, Jair A. L. Silva and José L. F. Salles
Sustainability 2023, 15(11), 8970; https://doi.org/10.3390/su15118970 - 1 Jun 2023
Cited by 4 | Viewed by 3046
Abstract
Stockyard–port planning is a complex combinatorial problem that has been studied primarily through simulation or optimization techniques. However, due to its classification as non-deterministic polynomial-time hard (NP-hard), the generation of optimal or near-optimal solutions in real time requires optimization techniques based on heuristics [...] Read more.
Stockyard–port planning is a complex combinatorial problem that has been studied primarily through simulation or optimization techniques. However, due to its classification as non-deterministic polynomial-time hard (NP-hard), the generation of optimal or near-optimal solutions in real time requires optimization techniques based on heuristics or metaheuristics. This paper proposes a deterministic simulation and a meta-heuristic algorithm to address the stockyard–port planning problem, with the aim of reducing the time that ships spend in berths. The proposed algorithm is based on the ore handling operations in a real stockyard–port terminal, considering the interaction of large physical equipment and information about the production processes. The stockyard–port system is represented by a graph in order to define ship priorities for planning and generation of an initial solution through a deterministic simulation. Subsequently, the Variable Neighborhood Descent (VND) meta-heuristic is used to improve the initial solution. The convergence time of VND ranged from 1 to 190 s, with the total number of ships served in the berths varying from 10 to 1000 units, and the number of stockyards and berths varying from 11 to 15 and 3 to 5, respectively. Simulation results demonstrate the efficiency of the proposed algorithm in determining the best allocation of stockpiles, berths, car-dumpers, and conveyor belts. The results also show that increasing the number of conveyor belts is an important strategy that decreases environmental impacts due to exposure of the raw material to the atmosphere, while also increasing the stockyard–port productivity. This positive impact is greater when the number yards and ship berths increases. The proposed algorithm enables real-time decision-making from small and large instances, and its implementation in an iron ore stockyard–port that uses Industry 4.0 principles is suitable. Full article
(This article belongs to the Collection Operations Research: Optimization, Resilience and Sustainability)
Show Figures

Figure 1

22 pages, 2219 KB  
Article
A Two-Level Variable Neighborhood Descent for a Split Delivery Clustered Vehicle Routing Problem with Soft Cluster Conflicts and Customer-Related Costs
by Rui Xu, Yumiao Huang and Wei Xiao
Sustainability 2023, 15(9), 7639; https://doi.org/10.3390/su15097639 - 6 May 2023
Cited by 3 | Viewed by 2158
Abstract
This paper introduces Split Delivery Clustered Vehicle Routing Problem with Soft cluster conflicts and Customer-related costs (SDCVRPSC) arising in automotive parts of milk-run logistics with supplier cluster distribution in China. In SDCVRPSC, customers are divided into different clusters that can be visited by [...] Read more.
This paper introduces Split Delivery Clustered Vehicle Routing Problem with Soft cluster conflicts and Customer-related costs (SDCVRPSC) arising in automotive parts of milk-run logistics with supplier cluster distribution in China. In SDCVRPSC, customers are divided into different clusters that can be visited by multiple vehicles, but each vehicle can only visit each cluster once. Penalty costs are incurred when traveling between clusters. The transportation cost of a route is calculated as the maximum direct shipment cost between customers on the route plus the total drop costs. The SDCVRPSC aims to minimize the sum of transportation costs and penalty costs by determining the assignment of customers to vehicles and the visiting order of clusters. We propose an integer linear programming model and a two-level variable neighborhood descent algorithm (TLVND) that includes two-stage construction, intensification at cluster and customer levels, and a perturbation mechanism. Experimental results on designed SDCVRPSC benchmark instances demonstrate that TLVND outperforms the Gurobi solver and two adapted algorithms at the business operation level. Moreover, a real case study indicates that TLVND can bring significant economic savings compared to expert experience decisions. TLVND has been integrated into the decision support system of the case company for daily operations. Full article
Show Figures

Figure 1

19 pages, 3598 KB  
Article
Technology Upgrade Assessment for Open-Pit Mines through Mine Plan Optimization and Discrete Event Simulation
by Aldo Quelopana, Javier Órdenes, Ryan Wilson and Alessandro Navarra
Minerals 2023, 13(5), 642; https://doi.org/10.3390/min13050642 - 5 May 2023
Cited by 9 | Viewed by 2571
Abstract
Digital technologies are continually gaining traction in the mining and mineral processing industries. Several studies have shown the benefits of their application to help improve various aspects of the mineral value chain. Nevertheless, quantitatively assessing new technologies using a holistic approach is vital [...] Read more.
Digital technologies are continually gaining traction in the mining and mineral processing industries. Several studies have shown the benefits of their application to help improve various aspects of the mineral value chain. Nevertheless, quantitatively assessing new technologies using a holistic approach is vital to evaluate whether the potential localized benefits ultimately translate to an overall increase in project net present value (NPV). This study develops an integrated system-wide methodology for open-pit mines, supporting the technoeconomic assessment of implementing new technology that impacts strategic and operational timeframes. The first part of the framework relies on a state-of-the-art mine plan optimization algorithm that incorporates geological uncertainty. The resulting outputs are then fed into the discrete event simulation portion of the framework (second part) to maximize plant throughput using alternate modes of operation (blending strategy) and operational stockpiles to deal with unexpected changes in ore feed attributes. Sample calculations loosely based on a gold deposit located in the Maricunga belt, Chile, are presented in the context of evaluating different intelligent ore sorting technology options. Full article
Show Figures

Figure 1

14 pages, 1658 KB  
Article
An Iterated Population-Based Metaheuristic for Order Acceptance and Scheduling in Unrelated Parallel Machines with Several Practical Constraints
by Chun-Lung Chen
Mathematics 2023, 11(6), 1433; https://doi.org/10.3390/math11061433 - 16 Mar 2023
Cited by 3 | Viewed by 1617
Abstract
This study considers order acceptance and scheduling problems in unrelated parallel machines with several practical constraints, including order release times, sequence-dependent setup times, machines’ unequal ready times, and preventive maintenance. In a make-to-order production environment, issues with order acceptance and scheduling are mainly [...] Read more.
This study considers order acceptance and scheduling problems in unrelated parallel machines with several practical constraints, including order release times, sequence-dependent setup times, machines’ unequal ready times, and preventive maintenance. In a make-to-order production environment, issues with order acceptance and scheduling are mainly caused by the limited production capacity of a factory, which makes it impossible to accept all orders. Consequently, some orders must be rejected in order to maximize profits and the accepted orders must be completed by the due date or no later than the deadline. An iterated population-based metaheuristic is proposed to solve the problems. The algorithm begins with an efficient initial solution generator to generate an initial solution, and then uses the destruction and construction procedure to generate a population with multiple solutions. Then, a solution is selected from the population, and a variable neighborhood descent search algorithm with several new reduced-size neighborhood structures is applied to improve the selected solution. Following the completion of the local search, a method for updating the members of the population was devised to enhance its diversity. Finally, the metaheuristic allows the populations to evolve for several generations until the termination condition is satisfied. To evaluate the performance of the proposed metaheuristic, a heuristic rule and an iterated local search algorithm are examined and compared. The computational experimental results indicate that the presented metaheuristic outperforms the other heuristics. Full article
Show Figures

Figure 1

19 pages, 3556 KB  
Article
Geometallurgical Detailing of Plant Operation within Open-Pit Strategic Mine Planning
by Aldo Quelopana, Javier Órdenes, Rodrigo Araya and Alessandro Navarra
Processes 2023, 11(2), 381; https://doi.org/10.3390/pr11020381 - 26 Jan 2023
Cited by 8 | Viewed by 2548
Abstract
Mineral and metallurgical processing are crucial within the mineral value chain. These processes involve several stages wherein comminution is arguably the most important due to its high energy consumption, and its impact on subsequent extractive processes. Several geological properties of the orebody impact [...] Read more.
Mineral and metallurgical processing are crucial within the mineral value chain. These processes involve several stages wherein comminution is arguably the most important due to its high energy consumption, and its impact on subsequent extractive processes. Several geological properties of the orebody impact the efficiency of mineral processing and extractive metallurgy; scholars have therefore proposed to deal with the uncertain ore feed in terms of grades and rock types, incorporating operational modes that represent different plant configurations that provide coordinated system-wide responses. Even though these studies offer insights into how mine planning impacts the ore fed into the plant, the simultaneous optimization of mine plan and metallurgical plant design has been limited by the existing stochastic mine planning algorithms, which have only limited support for detailing operational modes. The present work offers to fill this gap for open-pit mines through a computationally efficient adaptation of a strategic mine planning algorithm. The adaptation incorporates a linear programming representation of the operational modes which forms a Dantzig-Wolfe decomposition, nested within a high-performing stochastic mine planning algorithm based on a variable neighborhood descent metaheuristic. Sample calculations are presented, loosely based on the Mount Isa deposit in Australia, in which a metallurgical plant upgrade is evaluated, showing that the upgraded design significantly decreases the requirement on the mining equipment, without significantly affecting the NPV. Full article
(This article belongs to the Special Issue Process Analysis and Simulation in Extractive Metallurgy)
Show Figures

Figure 1

27 pages, 5058 KB  
Article
Energy-Efficient Hybrid Flowshop Scheduling with Consistent Sublots Using an Improved Cooperative Coevolutionary Algorithm
by Chengshuai Li, Biao Zhang, Yuyan Han, Yuting Wang, Junqing Li and Kaizhou Gao
Mathematics 2023, 11(1), 77; https://doi.org/10.3390/math11010077 - 25 Dec 2022
Cited by 14 | Viewed by 2073
Abstract
Energy conservation, emission reduction, and green and low carbon are of great significance to sustainable development, and are also the theme of the transformation and upgrading of the manufacturing industry. This paper concentrates on studying the energy-efficient hybrid flowshop scheduling problem with consistent [...] Read more.
Energy conservation, emission reduction, and green and low carbon are of great significance to sustainable development, and are also the theme of the transformation and upgrading of the manufacturing industry. This paper concentrates on studying the energy-efficient hybrid flowshop scheduling problem with consistent sublots (HFSP_ECS) with the objective of minimizing the energy consumption. To solve the problem, the HFSP_ECS is decomposed by the idea of “divide-and-conquer”, resulting in three coupled subproblems, i.e., lot sequence, machine assignment, and lot split, which can be solved by using a cooperative methodology. Thus, an improved cooperative coevolutionary algorithm (vCCEA) is proposed by integrating the variable neighborhood descent (VND) strategy. In the vCCEA, considering the problem-specific characteristics, a two-layer encoding strategy is designed to represent the essential information, and a novel collaborative model is proposed to realize the interaction between subproblems. In addition, special neighborhood structures are designed for different subproblems, and two kinds of enhanced neighborhood structures are proposed to search for potential promising solutions. A collaborative population restart mechanism is established to ensure the population diversity. The computational results show that vCCEA can coordinate and solve each subproblem of HFSP_ECS effectively, and outperform the mathematical programming and the other state-of-the-art algorithms. Full article
Show Figures

Figure 1

28 pages, 4153 KB  
Article
Reliability Analysis of Survivable Networks under the Hostile Model
by Sebastián Laborde, Franco Robledo and Sergio Nesmachnow
Symmetry 2022, 14(12), 2523; https://doi.org/10.3390/sym14122523 - 29 Nov 2022
Viewed by 1978
Abstract
This article studies the Generalized Steiner Problem with Node-Connectivity Constraints and Hostile Reliability and introduces a metaheuristic resolution approach based on Greedy Randomized Adaptive Search Procedure and Variable Neighborhood Descent. Under the hostile model, nodes and links are subject to probabilistic failures. The [...] Read more.
This article studies the Generalized Steiner Problem with Node-Connectivity Constraints and Hostile Reliability and introduces a metaheuristic resolution approach based on Greedy Randomized Adaptive Search Procedure and Variable Neighborhood Descent. Under the hostile model, nodes and links are subject to probabilistic failures. The research focuses on studying the relationship between the optimization and the reliability evaluation in a symmetric network design problem. Relevant research questions are addressed, linking the number of feasible networks for the full probabilistic model, the sensitivity with respect to elementary probabilities of operation for both edges and nodes, and the sensitivity of the model with respect to the symmetric connectivity constraints defined for terminal nodes. The main result indicates that, for the hostile model, it is better at improving the elementary probabilities of operation of links than improving the elementary probabilities of Steiner nodes, to meet a required reliability threshold for the designed network. Full article
(This article belongs to the Section Computer)
Show Figures

Figure 1

1 pages, 149 KB  
Correction
Correction: Bruni, M.E.; Khodaparasti, S. A Variable Neighborhood Descent Matheuristic for the Drone Routing Problem with Beehives Sharing. Sustainability 2022, 14, 9978
by Maria Elena Bruni and Sara Khodaparasti
Sustainability 2022, 14(23), 15623; https://doi.org/10.3390/su142315623 - 24 Nov 2022
Cited by 1 | Viewed by 1018
Abstract
There was an error in the original publication [...] Full article
(This article belongs to the Special Issue Women’s Special Issue Series: Sustainable Energy)
11 pages, 2237 KB  
Article
Multiple Mitochondrial Dysfunction Syndrome Type 3: A Likely Pathogenic Homozygous Variant Affecting a Patient of Cuban Descent and Literature Review
by Steven H. Lang, Francesca Camponeschi, Evan de Joya, Paulo Borjas-Mendoza, Mustafa Tekin and Willa Thorson
Genes 2022, 13(11), 2044; https://doi.org/10.3390/genes13112044 - 6 Nov 2022
Cited by 6 | Viewed by 2101
Abstract
Multiple mitochondrial dysfunction syndrome type 3 (MMDS3) is a rare mitochondrial leukoencephalopathy caused by biallelic pathogenic variants in IBA57. Here, we describe a homozygous variant in IBA57, (NM_001010867.2): c.310G>T (p.Gly104Cys), in a 2-month-old infant of Cuban descent who presented with a [...] Read more.
Multiple mitochondrial dysfunction syndrome type 3 (MMDS3) is a rare mitochondrial leukoencephalopathy caused by biallelic pathogenic variants in IBA57. Here, we describe a homozygous variant in IBA57, (NM_001010867.2): c.310G>T (p.Gly104Cys), in a 2-month-old infant of Cuban descent who presented with a one-month history of progressive hypotonia, weakness, and episodes of upgaze deviation. This is the first report of a patient homozygous for this variant and the first report of MMDS3 in a patient of Hispanic descent described to our knowledge. Using in silico tools, we found that the variant resides in a putative mutational hotspot located in the neighborhood of a key active ligand required for iron-sulfur cluster coordination. In addition, while previous case reports/series have reported the variable phenotypic features of the disease, the incidence of these features across the literature has not been well described. In order to construct a clearer global picture of the typical presentation of MMDS3, we reviewed 52 cases across the literature with respect to their clinical, biochemical, genotypic, and neuroradiographic features. Full article
(This article belongs to the Section Human Genomics and Genetic Diseases)
Show Figures

Figure 1

33 pages, 530 KB  
Article
Relaxation Subgradient Algorithms with Machine Learning Procedures
by Vladimir Krutikov, Svetlana Gutova, Elena Tovbis, Lev Kazakovtsev and Eugene Semenkin
Mathematics 2022, 10(21), 3959; https://doi.org/10.3390/math10213959 - 25 Oct 2022
Cited by 9 | Viewed by 2336
Abstract
In the modern digital economy, optimal decision support systems, as well as machine learning systems, are becoming an integral part of production processes. Artificial neural network training as well as other engineering problems generate such problems of high dimension that are difficult to [...] Read more.
In the modern digital economy, optimal decision support systems, as well as machine learning systems, are becoming an integral part of production processes. Artificial neural network training as well as other engineering problems generate such problems of high dimension that are difficult to solve with traditional gradient or conjugate gradient methods. Relaxation subgradient minimization methods (RSMMs) construct a descent direction that forms an obtuse angle with all subgradients of the current minimum neighborhood, which reduces to the problem of solving systems of inequalities. Having formalized the model and taking into account the specific features of subgradient sets, we reduced the problem of solving a system of inequalities to an approximation problem and obtained an efficient rapidly converging iterative learning algorithm for finding the direction of descent, conceptually similar to the iterative least squares method. The new algorithm is theoretically substantiated, and an estimate of its convergence rate is obtained depending on the parameters of the subgradient set. On this basis, we have developed and substantiated a new RSMM, which has the properties of the conjugate gradient method on quadratic functions. We have developed a practically realizable version of the minimization algorithm that uses a rough one-dimensional search. A computational experiment on complex functions in a space of high dimension confirms the effectiveness of the proposed algorithm. In the problems of training neural network models, where it is required to remove insignificant variables or neurons using methods such as the Tibshirani LASSO, our new algorithm outperforms known methods. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
Show Figures

Figure 1

Back to TopTop