This paper studies the assignment problem of multi product assembly jobs to days. The problem aims to minimize the amount of overtime while avoiding assembly delays for jobs that can be fragmented into smaller sub-tasks. When sequence-dependent setup times are negligible, the problem considered transforms into the bin packing problem with restricted item fragmentation where jobs represent items and days stand for bins. We present a mixed integer programming model of the problem by extending earlier formulations in the literature. Computational experiments show that the mathematical model obtained optimal solutions for majority of instances tested within reasonable computation times.
{"title":"Bin packing problem with restricted item fragmentation: Assignment of jobs in multi-product assembly environment with overtime","authors":"Mustafa Ustuncelik, Cagri Koc, Huseyin Tunc","doi":"10.11121/ijocta.1435","DOIUrl":"https://doi.org/10.11121/ijocta.1435","url":null,"abstract":"This paper studies the assignment problem of multi product assembly jobs to days. The problem aims to minimize the amount of overtime while avoiding assembly delays for jobs that can be fragmented into smaller sub-tasks. When sequence-dependent setup times are negligible, the problem considered transforms into the bin packing problem with restricted item fragmentation where jobs represent items and days stand for bins. We present a mixed integer programming model of the problem by extending earlier formulations in the literature. Computational experiments show that the mathematical model obtained optimal solutions for majority of instances tested within reasonable computation times.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"21 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135873073","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}
Additive manufacturing is a rapidly growing technology shaping the future of manufacturing. In an increasingly competitive economy, additive manufacturing can help businesses to remain agile, innovative, and sustainable. This paper introduces the multi-site additive manufacturing (AM) machine scheduling problem considering carbon emissions caused by production and transportation. A mixed-integer linear programming model is developed aiming to optimise two separate objectives addressing economic and environmental sustainability in a multiple unrelated AM machine environment. The former is the total cost caused by production, transportation, set-up and tardiness penalty and the latter is the total amount of carbon emissions caused by production and transportation. The model is coded in Python and solved by Gurobi Optimizer. A numerical example is provided to represent the basic characteristics of the problem and show the necessity of the proposed framework. A comprehensive computational study is conducted under 600s and 1800s time limits for two main scenarios and the results have been elaborated. This article introduces the concept of considering both economic and environmental sustainability caused by production and transportation, proposing the first mathematical model and measuring its performance through a comprehensive experimental study.
{"title":"Scheduling of distributed additive manufacturing machines considering carbon emissions","authors":"Ibrahim Kucukkoc","doi":"10.11121/ijocta.1444","DOIUrl":"https://doi.org/10.11121/ijocta.1444","url":null,"abstract":"Additive manufacturing is a rapidly growing technology shaping the future of manufacturing. In an increasingly competitive economy, additive manufacturing can help businesses to remain agile, innovative, and sustainable. This paper introduces the multi-site additive manufacturing (AM) machine scheduling problem considering carbon emissions caused by production and transportation. A mixed-integer linear programming model is developed aiming to optimise two separate objectives addressing economic and environmental sustainability in a multiple unrelated AM machine environment. The former is the total cost caused by production, transportation, set-up and tardiness penalty and the latter is the total amount of carbon emissions caused by production and transportation. The model is coded in Python and solved by Gurobi Optimizer. A numerical example is provided to represent the basic characteristics of the problem and show the necessity of the proposed framework. A comprehensive computational study is conducted under 600s and 1800s time limits for two main scenarios and the results have been elaborated. This article introduces the concept of considering both economic and environmental sustainability caused by production and transportation, proposing the first mathematical model and measuring its performance through a comprehensive experimental study.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"21 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135873074","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}
Pub Date : 2023-07-29DOI: 10.11121/ijocta.2023.1327
Arumugam Vinodkumar, Sivakumar Harinie, Michal Feckan, J. Alzabut
This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoretical results' effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well.
{"title":"Some stability results on non-linear singular differential systems with random impulsive moments","authors":"Arumugam Vinodkumar, Sivakumar Harinie, Michal Feckan, J. Alzabut","doi":"10.11121/ijocta.2023.1327","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1327","url":null,"abstract":"This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoretical results' effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"23 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90049595","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}
Pub Date : 2023-07-29DOI: 10.11121/ijocta.2023.1326
R. Larhrissi, Mustapha Benoudi
This new research aims to extend the topic of the enlarged controllability of a fractional output linear system. Thus, we characterize the optimal control by two methods, ensuring that the Riemann-Liouville fractional derivative of the final state of the considered system lies between two given functions on a subregion of the evolution domain. Firstly, we transform the considered problem into the saddle point using the Lagrangian multiplier approach. Then, in the second one, we provide the technique of the subdifferential, which allows us to present the cost-explicit formula of the minimum energy control. Moreover, we construct an algorithm of Uzawa type to illustrate the theoretical results obtained through numerical simulations.
{"title":"Regional enlarged controllability of a fractional derivative of an output linear system","authors":"R. Larhrissi, Mustapha Benoudi","doi":"10.11121/ijocta.2023.1326","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1326","url":null,"abstract":"This new research aims to extend the topic of the enlarged controllability of a fractional output linear system. Thus, we characterize the optimal control by two methods, ensuring that the Riemann-Liouville fractional derivative of the final state of the considered system lies between two given functions on a subregion of the evolution domain. Firstly, we transform the considered problem into the saddle point using the Lagrangian multiplier approach. Then, in the second one, we provide the technique of the subdifferential, which allows us to present the cost-explicit formula of the minimum energy control. Moreover, we construct an algorithm of Uzawa type to illustrate the theoretical results obtained through numerical simulations.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77342875","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}
Pub Date : 2023-07-29DOI: 10.11121/ijocta.2023.1371
N. Yildirim Aksoy, E. Çelik, Muhammed Emin Dadas
In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.
{"title":"The solvability of the optimal control problem for a nonlinear Schrödinger equation","authors":"N. Yildirim Aksoy, E. Çelik, Muhammed Emin Dadas","doi":"10.11121/ijocta.2023.1371","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1371","url":null,"abstract":"In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"56 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77073467","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}
Pub Date : 2023-07-29DOI: 10.11121/ijocta.2023.1278
M. Houas, J. Alzabut, M. Khuddush
In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.
{"title":"Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives","authors":"M. Houas, J. Alzabut, M. Khuddush","doi":"10.11121/ijocta.2023.1278","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1278","url":null,"abstract":"In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82500605","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}
Pub Date : 2023-07-29DOI: 10.11121/ijocta.2023.1366
P. Uzun, Kıvanç Uzun, I. Koca
Academic achievement is very important, as it enables students to be well-equipped for professional and social life and shapes their future. In the case of a possible academic failure, students generally face many cognitive, social, psychological, and behavioral problems. This problem experienced by the students has been addressed with the mathematical model in this study. This mathematical model will be handled with the help of the fractional operator, and the existence, uniqueness, and positivity of the solutions to the model equation system will be examined. In addition, local and global stability analyses of the equilibrium points of the model are planned. Numerical simulations are performed with different values of fractional orders and densities of randomness. This study is very important in terms of its original and multidisciplinary approach to a subject in the field of social sciences.
{"title":"The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors","authors":"P. Uzun, Kıvanç Uzun, I. Koca","doi":"10.11121/ijocta.2023.1366","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1366","url":null,"abstract":"Academic achievement is very important, as it enables students to be well-equipped for professional and social life and shapes their future. In the case of a possible academic failure, students generally face many cognitive, social, psychological, and behavioral problems. This problem experienced by the students has been addressed with the mathematical model in this study. This mathematical model will be handled with the help of the fractional operator, and the existence, uniqueness, and positivity of the solutions to the model equation system will be examined. In addition, local and global stability analyses of the equilibrium points of the model are planned. Numerical simulations are performed with different values of fractional orders and densities of randomness. This study is very important in terms of its original and multidisciplinary approach to a subject in the field of social sciences.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74438712","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}
Pub Date : 2023-07-28DOI: 10.11121/ijocta.2023.1269
Arshed A. Ahmad, K. M. Saffer, Murat Sari, Hande Uslu
Healthcare enables the maintenance of health through some physical and mental care for the prevention, diagnosis and treatment of disease. Diagnosis of anemia, one of the most common health problems of the age, is also very ambitious. Whereas, pathological individuals could be predicted through various biomedical variables using some appropriate methods. In order to estimate these individuals just by taking into account biological data, particle swarm optimization (PSO) and support vector machine (SVM) clustering techniques have been merged (PSO-SVM). In this respect, the dataset provided has been divided into five clusters based on anemia types consisting of 539 subjects in total, and the anemia values of each subject have been recorded according to corresponding biomedical variables taken as independent parameters. The findings of the PSO-SVM method have been compared to the results of the SVM algorithm. The hybrid PSO-SVM method has proven to be quite effective, particularly in terms of the high predictability of clustered disease types. it is possible to lead the successful creation of appropriate treatment programs for diagnosed patients without overlooking or wasting time during treatment.
{"title":"Prediction of anemia with a particle swarm optimization-based approach","authors":"Arshed A. Ahmad, K. M. Saffer, Murat Sari, Hande Uslu","doi":"10.11121/ijocta.2023.1269","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1269","url":null,"abstract":"Healthcare enables the maintenance of health through some physical and mental care for the prevention, diagnosis and treatment of disease. Diagnosis of anemia, one of the most common health problems of the age, is also very ambitious. Whereas, pathological individuals could be predicted through various biomedical variables using some appropriate methods. In order to estimate these individuals just by taking into account biological data, particle swarm optimization (PSO) and support vector machine (SVM) clustering techniques have been merged (PSO-SVM). In this respect, the dataset provided has been divided into five clusters based on anemia types consisting of 539 subjects in total, and the anemia values of each subject have been recorded according to corresponding biomedical variables taken as independent parameters. The findings of the PSO-SVM method have been compared to the results of the SVM algorithm. The hybrid PSO-SVM method has proven to be quite effective, particularly in terms of the high predictability of clustered disease types. it is possible to lead the successful creation of appropriate treatment programs for diagnosed patients without overlooking or wasting time during treatment.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"107 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83550874","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}
Pub Date : 2023-07-27DOI: 10.11121/ijocta.2023.1260
M. Demirtas, Farhan Ahmad
The power circuit of AC voltage controller capable of operating at a leading, lagging, and unity power factor is studied by a lot of researchers in the literature. Circuits working with high switching frequency are known as power factor correctors (PFCs). The single-phase boost converter has become the most popular topology for power factor correction (PFC) in general purpose power supplies. Power factor correction circuit provides conventional benefits to electric power systems. The benefits are the reduction of power factor penalty and utility bill and power loss. Therefore, a boost converter power factor correction scheme is presented in this paper. A PI, fuzzy logic PI and fractional order PI (FOPI) controllers are used to fix an active shaping of input current of the circuit and to improve the power factor. The controller parameters (coefficients) are optimized using the Particle Swarm Optimization (PSO) algorithm. Average current mode control (ACMC) method is used in the circuit. The converter circuit consists of a single-phase bridge rectifier, boost converter, transformer and load. A mathematical model of the plant is required to design the PI controller. A model for power factor correction circuit is formed in MATLAB/Simulink toolbox and a filter is designed to reduce THD value. The proposed model is simulated using a combination of PI, fuzzy logic and FOPI controllers. The control scheme is applied to 600 Watt PFC boost converter to get 400 Volt DC output voltage and 0.99 power factor. The input voltage is 230 VRMS with 50 Hz. The combination of FOPI and PI controller has the best solution to control the power factor according to PI and fuzzy controllers.
{"title":"Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter","authors":"M. Demirtas, Farhan Ahmad","doi":"10.11121/ijocta.2023.1260","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1260","url":null,"abstract":"The power circuit of AC voltage controller capable of operating at a leading, lagging, and unity power factor is studied by a lot of researchers in the literature. Circuits working with high switching frequency are known as power factor correctors (PFCs). The single-phase boost converter has become the most popular topology for power factor correction (PFC) in general purpose power supplies. Power factor correction circuit provides conventional benefits to electric power systems. The benefits are the reduction of power factor penalty and utility bill and power loss. Therefore, a boost converter power factor correction scheme is presented in this paper. A PI, fuzzy logic PI and fractional order PI (FOPI) controllers are used to fix an active shaping of input current of the circuit and to improve the power factor. The controller parameters (coefficients) are optimized using the Particle Swarm Optimization (PSO) algorithm. Average current mode control (ACMC) method is used in the circuit. The converter circuit consists of a single-phase bridge rectifier, boost converter, transformer and load. A mathematical model of the plant is required to design the PI controller. A model for power factor correction circuit is formed in MATLAB/Simulink toolbox and a filter is designed to reduce THD value. The proposed model is simulated using a combination of PI, fuzzy logic and FOPI controllers. The control scheme is applied to 600 Watt PFC boost converter to get 400 Volt DC output voltage and 0.99 power factor. The input voltage is 230 VRMS with 50 Hz. The combination of FOPI and PI controller has the best solution to control the power factor according to PI and fuzzy controllers.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"7 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78691595","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}
Pub Date : 2023-07-19DOI: 10.11121/ijocta.2023.1398
I. Koca, A. Atangana
A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.
{"title":"Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators","authors":"I. Koca, A. Atangana","doi":"10.11121/ijocta.2023.1398","DOIUrl":"https://doi.org/10.11121/ijocta.2023.1398","url":null,"abstract":"A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"104 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86199184","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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