This paper presents an enhanced and improved particle swarm optimization (PSO) approach to overcome reliability-redundancy allocation problems in series, series-parallel, and complex systems. The problems mentioned above can be solved by increasing the overall system reliability and minimizing the system cost, weight, and volume. To achieve this with these nonlinear constraints, an approach is developed based on PSO. In particular, the inertia and acceleration coefficients of the classical particle swarm algorithm are improved by considering a normal distribution for the coefficients. The new expressions can enhance the global search ability in the initial stage, restrain premature convergence, and enable the algorithm to focus on the local fine search in the later stage, and this can enhance the perfection of the optimization process. Illustrative examples are provided as proof of the efficiency and effectiveness of the proposed approach. Results show that the overall system reliability is far better when compared with that of some approaches developed in previous studies for all three tested cases.
{"title":"Optimization for the Redundancy Allocation Problem of Reliability Using an Improved Particle Swarm Optimization Algorithm","authors":"H. Marouani","doi":"10.1155/2021/6385713","DOIUrl":"https://doi.org/10.1155/2021/6385713","url":null,"abstract":"This paper presents an enhanced and improved particle swarm optimization (PSO) approach to overcome reliability-redundancy allocation problems in series, series-parallel, and complex systems. The problems mentioned above can be solved by increasing the overall system reliability and minimizing the system cost, weight, and volume. To achieve this with these nonlinear constraints, an approach is developed based on PSO. In particular, the inertia and acceleration coefficients of the classical particle swarm algorithm are improved by considering a normal distribution for the coefficients. The new expressions can enhance the global search ability in the initial stage, restrain premature convergence, and enable the algorithm to focus on the local fine search in the later stage, and this can enhance the perfection of the optimization process. Illustrative examples are provided as proof of the efficiency and effectiveness of the proposed approach. Results show that the overall system reliability is far better when compared with that of some approaches developed in previous studies for all three tested cases.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76988372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, the optimum design dimensions and performance analyses of convective-radiative cooling fin subjected to magnetic field are presented using finite element method. The numerical solutions are verified by the exact analytical solution for the linearized models using Laplace transform. The optimum dimensions for the optimum performance of the convection-radiative fin with variable thermal conductivity are investigated and presented graphically. Also, the effects of convective, radiative, and magnetic parameters as well as Biot number on the thermal performance of the cooling fin are analyzed using the numerical solutions. From the results, it is established that the optimum length of the fin and the thermogeometric parameter increases as the nonlinear thermal conductivity term increases. Further analyses also reveal that as the Biot number, convective, radiative, and magnetic parameters, increases, the rate of heat transfer from the fin increases and consequently improves the efficiency of the fin. Additionally, effects of the thermal stability values for the various multiboiling heat transfer modes are established. It is established that, in order to ensure stability and avoid numerical diffusion of the solution by the Galerkin finite element method, the thermogeometric parameter must not exceed some certain values for the different multiboiling heat transfer modes. It is hope that the present study will enhance the understanding of thermal response of solid fin under various factors and fin design considerations.
{"title":"Optimum Design and Performance Analyses of Convective-Radiative Cooling Fin under the Influence of Magnetic Field Using Finite Element Method","authors":"M. Sobamowo","doi":"10.1155/2019/9705792","DOIUrl":"https://doi.org/10.1155/2019/9705792","url":null,"abstract":"In this study, the optimum design dimensions and performance analyses of convective-radiative cooling fin subjected to magnetic field are presented using finite element method. The numerical solutions are verified by the exact analytical solution for the linearized models using Laplace transform. The optimum dimensions for the optimum performance of the convection-radiative fin with variable thermal conductivity are investigated and presented graphically. Also, the effects of convective, radiative, and magnetic parameters as well as Biot number on the thermal performance of the cooling fin are analyzed using the numerical solutions. From the results, it is established that the optimum length of the fin and the thermogeometric parameter increases as the nonlinear thermal conductivity term increases. Further analyses also reveal that as the Biot number, convective, radiative, and magnetic parameters, increases, the rate of heat transfer from the fin increases and consequently improves the efficiency of the fin. Additionally, effects of the thermal stability values for the various multiboiling heat transfer modes are established. It is established that, in order to ensure stability and avoid numerical diffusion of the solution by the Galerkin finite element method, the thermogeometric parameter must not exceed some certain values for the different multiboiling heat transfer modes. It is hope that the present study will enhance the understanding of thermal response of solid fin under various factors and fin design considerations.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2019-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83330932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.
{"title":"Theoretical Analysis of an Imprecise Prey-Predator Model with Harvesting and Optimal Control","authors":"Anjana P. Das, M. Pal","doi":"10.1155/2019/9512879","DOIUrl":"https://doi.org/10.1155/2019/9512879","url":null,"abstract":"In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73196514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Caballero-Morales, Erika Barojas-Payán, Diana Sánchez-Partida, J. Martínez-Flores
Mexico is located within the so-called Fire Belt which makes it susceptible to earthquakes. In fact, two-thirds of the Mexican territory have a significant seismic risk. On the other hand, the country’s location in the tropical zone makes it susceptible to hurricanes which are generated in both the Pacific and Atlantic Oceans. Due to these situations, each year many communities are affected by diverse natural disasters in Mexico and efficient logistic systems are required to provide prompt support. This work is aimed at providing an efficient metaheuristic to determine the most appropriate location for support centers in the State of Veracruz, which is one of the most affected regions in Mexico. The metaheuristic is based on the K-Means Clustering (KMC) algorithm which is extended to integrate (a) the associated capacity restrictions of the support centers, (b) a micro Genetic Algorithm μGA to estimate a search interval for the most suitable number of support centers, (c) variable number of assigned elements to centers in order to add flexibility to the assignation task, and (d) random-based decision model to further improve the final assignments. These extensions on the KMC algorithm led to the GRASP-Capacitated K-Means Clustering (GRASP-CKMC) algorithm which was able to provide very suitable solutions for the establishment of 260 support centers for 3837 communities at risk in Veracruz, Mexico. Validation of the GRASP-CKMC algorithm was performed with well-known test instances and metaheuristics. The validation supported its suitability as alternative to standard metaheuristics such as Capacitated K-Means (CKM), Genetic Algorithms (GA), and Variable Neighborhood Search (VNS).
{"title":"Extended GRASP-Capacitated K-Means Clustering Algorithm to Establish Humanitarian Support Centers in Large Regions at Risk in Mexico","authors":"S. Caballero-Morales, Erika Barojas-Payán, Diana Sánchez-Partida, J. Martínez-Flores","doi":"10.1155/2018/3605298","DOIUrl":"https://doi.org/10.1155/2018/3605298","url":null,"abstract":"Mexico is located within the so-called Fire Belt which makes it susceptible to earthquakes. In fact, two-thirds of the Mexican territory have a significant seismic risk. On the other hand, the country’s location in the tropical zone makes it susceptible to hurricanes which are generated in both the Pacific and Atlantic Oceans. Due to these situations, each year many communities are affected by diverse natural disasters in Mexico and efficient logistic systems are required to provide prompt support. This work is aimed at providing an efficient metaheuristic to determine the most appropriate location for support centers in the State of Veracruz, which is one of the most affected regions in Mexico. The metaheuristic is based on the K-Means Clustering (KMC) algorithm which is extended to integrate (a) the associated capacity restrictions of the support centers, (b) a micro Genetic Algorithm μGA to estimate a search interval for the most suitable number of support centers, (c) variable number of assigned elements to centers in order to add flexibility to the assignation task, and (d) random-based decision model to further improve the final assignments. These extensions on the KMC algorithm led to the GRASP-Capacitated K-Means Clustering (GRASP-CKMC) algorithm which was able to provide very suitable solutions for the establishment of 260 support centers for 3837 communities at risk in Veracruz, Mexico. Validation of the GRASP-CKMC algorithm was performed with well-known test instances and metaheuristics. The validation supported its suitability as alternative to standard metaheuristics such as Capacitated K-Means (CKM), Genetic Algorithms (GA), and Variable Neighborhood Search (VNS).","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84316975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the topology-aware two-phase I/O (TATP), which optimizes the most popular collective MPI-IO implementation of ROMIO. In order to improve the hop-bytes metric during the file access, topology-aware two-phase I/O employs the Linear Assignment Problem (LAP) for finding an optimal assignment of file domain to aggregators, an aspect which is not considered in most two-phase I/O implementations. The distribution is based on the local data stored by each process, and its main purpose is to reduce the total hop-bytes of the I/O collective operation. Therefore, the global execution time can be improved. In most of the considered scenarios, topology-aware two-phase I/O obtains important improvements when compared with the original two-phase I/O implementations.
{"title":"Topology-Aware Strategy for MPI-IO Operations in Clusters","authors":"Weifeng Liu, Jie Zhou, Meng Guo","doi":"10.1155/2018/2068490","DOIUrl":"https://doi.org/10.1155/2018/2068490","url":null,"abstract":"This paper presents the topology-aware two-phase I/O (TATP), which optimizes the most popular collective MPI-IO implementation of ROMIO. In order to improve the hop-bytes metric during the file access, topology-aware two-phase I/O employs the Linear Assignment Problem (LAP) for finding an optimal assignment of file domain to aggregators, an aspect which is not considered in most two-phase I/O implementations. The distribution is based on the local data stored by each process, and its main purpose is to reduce the total hop-bytes of the I/O collective operation. Therefore, the global execution time can be improved. In most of the considered scenarios, topology-aware two-phase I/O obtains important improvements when compared with the original two-phase I/O implementations.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89049204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Brain abnormality is a cause for the chief risk factors in human society with larger morbidity rate. Identification of tumor in its early stage is essential to provide necessary treatment procedure to save the patient. In this work, Jaya Algorithm (JA) and Otsu’s Function (OF) guided method is presented to mine the irregular section of brain MRI recorded with Flair and T2 modality. This work implements a two-step process to examine the brain tumor from the axial, sagittal, and coronal views of the two-dimensional (2D) MRI slices. This paper presents a detailed evaluation of thresholding procedure with varied threshold levels (Th=2,3,4,5), skull stripping process before/after the thresholding practice, and the tumor extraction based on the Chan-Vese approach. Superiority of JA is confirmed among other prominent heuristic approaches found in literature. The outcome of implemented study confirms that Jaya Algorithm guided method is capable of presenting superior values of Jaccard-Index, Dice-Coefficient, sensitivity, specificity, accuracy, and precision on the BRATS 2015 dataset.
脑异常是造成人类社会主要危险因素之一，发病率较高。早期发现肿瘤对于提供必要的治疗程序以挽救患者至关重要。本文采用Jaya算法(JA)和Otsu 's Function (OF)引导方法对Flair和T2模态记录的脑MRI不规则切片进行挖掘。这项工作实现了两步的过程，从二维(2D) MRI切片的轴向，矢状面和冠状面检查脑肿瘤。本文详细评价了不同阈值水平(Th=2,3,4,5)的阈值分割过程，阈值分割前后的颅骨剥离过程，以及基于Chan-Vese方法的肿瘤提取。在文献中发现的其他突出的启发式方法中，JA的优越性得到了证实。实施的研究结果证实，Jaya算法指导方法能够在BRATS 2015数据集上呈现优越的Jaccard-Index、Dice-Coefficient、灵敏度、特异性、准确度和精密度值。
{"title":"Jaya Algorithm Guided Procedure to Segment Tumor from Brain MRI","authors":"S. Satapathy, V. Rajinikanth","doi":"10.1155/2018/3738049","DOIUrl":"https://doi.org/10.1155/2018/3738049","url":null,"abstract":"Brain abnormality is a cause for the chief risk factors in human society with larger morbidity rate. Identification of tumor in its early stage is essential to provide necessary treatment procedure to save the patient. In this work, Jaya Algorithm (JA) and Otsu’s Function (OF) guided method is presented to mine the irregular section of brain MRI recorded with Flair and T2 modality. This work implements a two-step process to examine the brain tumor from the axial, sagittal, and coronal views of the two-dimensional (2D) MRI slices. This paper presents a detailed evaluation of thresholding procedure with varied threshold levels (Th=2,3,4,5), skull stripping process before/after the thresholding practice, and the tumor extraction based on the Chan-Vese approach. Superiority of JA is confirmed among other prominent heuristic approaches found in literature. The outcome of implemented study confirms that Jaya Algorithm guided method is capable of presenting superior values of Jaccard-Index, Dice-Coefficient, sensitivity, specificity, accuracy, and precision on the BRATS 2015 dataset.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84505886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hamiltonian Cycle Problem is one of the most explored combinatorial problems. Being an NP-complete problem, heuristic approaches are found to be more powerful than exponential time exact algorithms. This paper presents an efficient hybrid heuristic that sits in between the complex reliable approaches and simple faster approaches. The proposed algorithm is a combination of greedy, rotational transformation and unreachable vertex heuristics that works in three phases. In the first phase, an initial path is created by using greedy depth first search. This initial path is then extended to a Hamiltonian path in second phase by using rotational transformation and greedy depth first search. Third phase converts the Hamiltonian path into a Hamiltonian cycle by using rotational transformation. The proposed approach could find Hamiltonian cycles from a set of hard graphs collected from the literature, all the Hamiltonian instances (1000 to 5000 vertices) given in TSPLIB, and some instances of FHCP Challenge Set. Moreover, the algorithm has O(n3) worst case time complexity. The performance of the algorithm has been compared with the state-of-the-art algorithms and it was found that HybridHAM outperforms others in terms of running time.
{"title":"HybridHAM: A Novel Hybrid Heuristic for Finding Hamiltonian Cycle","authors":"K. R. Seeja","doi":"10.1155/2018/9328103","DOIUrl":"https://doi.org/10.1155/2018/9328103","url":null,"abstract":"Hamiltonian Cycle Problem is one of the most explored combinatorial problems. Being an NP-complete problem, heuristic approaches are found to be more powerful than exponential time exact algorithms. This paper presents an efficient hybrid heuristic that sits in between the complex reliable approaches and simple faster approaches. The proposed algorithm is a combination of greedy, rotational transformation and unreachable vertex heuristics that works in three phases. In the first phase, an initial path is created by using greedy depth first search. This initial path is then extended to a Hamiltonian path in second phase by using rotational transformation and greedy depth first search. Third phase converts the Hamiltonian path into a Hamiltonian cycle by using rotational transformation. The proposed approach could find Hamiltonian cycles from a set of hard graphs collected from the literature, all the Hamiltonian instances (1000 to 5000 vertices) given in TSPLIB, and some instances of FHCP Challenge Set. Moreover, the algorithm has O(n3) worst case time complexity. The performance of the algorithm has been compared with the state-of-the-art algorithms and it was found that HybridHAM outperforms others in terms of running time.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87716686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in L∞Ω, with Ω⊂Rd, using spectral theory. An elegant way to model the problem using a time asymptotic observability constant is presented. For certain small potentials, we demonstrate the existence of a nonzero asymptotic observability constant under given conditions and describe its explicit properties and optimal values. Moreover, we give a precise description of numerical models to analyze the properties of important examples of potentials wells, including that of the modified harmonic oscillator.
{"title":"Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential","authors":"Alden Waters, Ekaterina Merkurjev","doi":"10.1155/2018/8162845","DOIUrl":"https://doi.org/10.1155/2018/8162845","url":null,"abstract":"We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in L∞Ω, with Ω⊂Rd, using spectral theory. An elegant way to model the problem using a time asymptotic observability constant is presented. For certain small potentials, we demonstrate the existence of a nonzero asymptotic observability constant under given conditions and describe its explicit properties and optimal values. Moreover, we give a precise description of numerical models to analyze the properties of important examples of potentials wells, including that of the modified harmonic oscillator.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90984381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the management of software testing, testing-recourse allocation is one of the most important problems due to the tradeoff between development cost and reliability of released software. This paper presents the model-based approach to design the testing-resource allocation. In particular, we employ the architecture-based software reliability model with operational profile to estimate the quantitative software reliability in operation phase and formulate the multiobjective optimization problems with respect to cost, testing effort, and software reliability. In numerical experiment, we investigate the difference of the presented optimization problem from the existing testing-resource allocation model.
{"title":"Optimizing Testing-Resource Allocation Using Architecture-Based Software Reliability Model","authors":"H. Okamura, T. Dohi","doi":"10.1155/2018/6948656","DOIUrl":"https://doi.org/10.1155/2018/6948656","url":null,"abstract":"In the management of software testing, testing-recourse allocation is one of the most important problems due to the tradeoff between development cost and reliability of released software. This paper presents the model-based approach to design the testing-resource allocation. In particular, we employ the architecture-based software reliability model with operational profile to estimate the quantitative software reliability in operation phase and formulate the multiobjective optimization problems with respect to cost, testing effort, and software reliability. In numerical experiment, we investigate the difference of the presented optimization problem from the existing testing-resource allocation model.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75648586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.
{"title":"A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence","authors":"B. Baluch, Z. Salleh, Ahmad Alhawarat","doi":"10.1155/2018/5057096","DOIUrl":"https://doi.org/10.1155/2018/5057096","url":null,"abstract":"This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.","PeriodicalId":42964,"journal":{"name":"Journal of Optimization","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2018-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89274856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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