Pub Date : 2021-08-12DOI: 10.4236/ojop.2021.103005
Bingzhuang Liu
We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.
{"title":"A New Unified Path to Smoothing Nonsmooth Exact Penalty Function for the Constrained Optimization","authors":"Bingzhuang Liu","doi":"10.4236/ojop.2021.103005","DOIUrl":"https://doi.org/10.4236/ojop.2021.103005","url":null,"abstract":"We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47969137","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 : 2021-08-12DOI: 10.4236/ojop.2021.103007
Bi-Foua Tanguy Emmanuel Lorou, P. Muchiri, P. Kuloba, J. Kimotho
Due to global completion in the automotive industry, productivity improvement is vital in these industries. In automotive assembly lines, productivity loses are attributed to bottlenecks, long processing time in workstations and underutilization of resources. The purpose of this research is to evaluate the performance of the production system, analyze the bottlenecks in different parts of the workstation, their capacity and constraints. Also, develop different scenarios for improvement. To achieve this objective, a simulation model was developed using Arena Software to analyze bottlenecks in each workstation. The analysis was based on the queue in the system to identify the longest queue in workstations. After analysis of the assembly line, the result showed that the longest waiting time observed is cab preparation and drop, bumper, engine subassembly fitment of soundproof with respective numbers 14.4, 13.97, 13.00, 13.70 minutes, with respective average number waiting of 24.87%, 17.57%, 25.91% and 23.39%. Using different scenarios for the improvement of the production line showed that the waiting time observed in-cab preparation and drop, bumper, engine subassembly, fitment of soundproof has greatly reduced for the two workstations added and three operators respectively from 14.4 to 3.97 and 3.1, from 13.97 to 3.77 and 2.48, from 13.00 to 4.21 and 3.83, from 13.70 to 0.00 and 2.37 minutes, with respective average number waiting from 24.87% to 5% and 2%, from 17.57% to 5% and 0.9%, from 25.91% to 5% and 4%, and from 23.39% to 0.00% and 3%. To conclude the research study was able to demonstrate the modelling approach using simulation for analysis of a production line assembly. The contribution of this research was so enormous, this study has improved the output production up to 144%.
{"title":"Performance Improvement of Truck Assembly Line through Modeling and Simulation Using Arena Software","authors":"Bi-Foua Tanguy Emmanuel Lorou, P. Muchiri, P. Kuloba, J. Kimotho","doi":"10.4236/ojop.2021.103007","DOIUrl":"https://doi.org/10.4236/ojop.2021.103007","url":null,"abstract":"Due to global completion in the automotive industry, productivity improvement is vital in these industries. In automotive assembly lines, productivity loses are attributed to bottlenecks, long processing time in workstations and underutilization of resources. The purpose of this research is to evaluate the performance of the production system, analyze the bottlenecks in different parts of the workstation, their capacity and constraints. Also, develop different scenarios for improvement. To achieve this objective, a simulation model was developed using Arena Software to analyze bottlenecks in each workstation. The analysis was based on the queue in the system to identify the longest queue in workstations. After analysis of the assembly line, the result showed that the longest waiting time observed is cab preparation and drop, bumper, engine subassembly fitment of soundproof with respective numbers 14.4, 13.97, 13.00, 13.70 minutes, with respective average number waiting of 24.87%, 17.57%, 25.91% and 23.39%. Using different scenarios for the improvement of the production line showed that the waiting time observed in-cab preparation and drop, bumper, engine subassembly, fitment of soundproof has greatly reduced for the two workstations added and three operators respectively from 14.4 to 3.97 and 3.1, from 13.97 to 3.77 and 2.48, from 13.00 to 4.21 and 3.83, from 13.70 to 0.00 and 2.37 minutes, with respective average number waiting from 24.87% to 5% and 2%, from 17.57% to 5% and 0.9%, from 25.91% to 5% and 4%, and from 23.39% to 0.00% and 3%. To conclude the research study was able to demonstrate the modelling approach using simulation for analysis of a production line assembly. The contribution of this research was so enormous, this study has improved the output production up to 144%.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41348045","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 : 2021-06-17DOI: 10.4236/ojop.2021.102004
D. Golembiovsky, A. Pavlov, S. Daniil
The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.
{"title":"Experimental Study of Methods of Scenario Lattice Construction for Stochastic Dual Dynamic Programming","authors":"D. Golembiovsky, A. Pavlov, S. Daniil","doi":"10.4236/ojop.2021.102004","DOIUrl":"https://doi.org/10.4236/ojop.2021.102004","url":null,"abstract":"The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49175040","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 : 2021-01-01DOI: 10.4236/OJOP.2021.102003
H. Amuji, Cecilia N. Aronu, Obioma G. Onukwube, C. Igboanusi
Every couple would want to have balanced sex of babies and a given number of children. But in reality, most couples do not achieve it. Some end up bearing particular sex of baby, this has caused a lot of pressure and untold hardship for couples. In Nigeria, the preference for a son is so strong that any family that does not have a son does not belong. The reason for the preference is mainly for economic and continuation of family lineage. Inability to bear the desired sex of a baby makes couples bear more children than they could cater for. This has caused poverty, overpopulation and reduces life expectancy for many families in Nigeria. In this paper, we have developed a model that will help couples select the desired sex of their babies and avoid unwanted pregnancies. The method is easy to apply whether educated or not. The application of the method will help to reduce family-based violence due to imbalanced sex of babies.
{"title":"Modelling of Pre-Sex Selection: An Effective Method for Family Planning and Control of Overpopulation","authors":"H. Amuji, Cecilia N. Aronu, Obioma G. Onukwube, C. Igboanusi","doi":"10.4236/OJOP.2021.102003","DOIUrl":"https://doi.org/10.4236/OJOP.2021.102003","url":null,"abstract":"Every couple would want to have balanced sex of babies and a given number of children. But in reality, most couples do not achieve it. Some end up bearing particular sex of baby, this has caused a lot of pressure and untold hardship for couples. In Nigeria, the preference for a son is so strong that any family that does not have a son does not belong. The reason for the preference is mainly for economic and continuation of family lineage. Inability to bear the desired sex of a baby makes couples bear more children than they could cater for. This has caused poverty, overpopulation and reduces life expectancy for many families in Nigeria. In this paper, we have developed a model that will help couples select the desired sex of their babies and avoid unwanted pregnancies. The method is easy to apply whether educated or not. The application of the method will help to reduce family-based violence due to imbalanced sex of babies.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70475041","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 : 2021-01-01DOI: 10.4236/ojop.2021.104008
F. Nahayo, A. Bagorizamba, Marc Bigirimana, I. Irakoze
{"title":"Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System","authors":"F. Nahayo, A. Bagorizamba, Marc Bigirimana, I. Irakoze","doi":"10.4236/ojop.2021.104008","DOIUrl":"https://doi.org/10.4236/ojop.2021.104008","url":null,"abstract":"","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70475057","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}
Optimal control is one of the most popular decision-making tools recently in many researches and in many areas. The Lorenz-Rossler model is one of the interesting models because of the idea of consolidation of the two models: Lorenz and ossler. This paper discusses the Lorenz-Rossler model from the bifurcation phenomena and the optimal control problem (OCP). The bifurcation property at the system equilibrium is studied and it is found that saddle-node and Hopf bifurcations can be holed under some conditions on the parameters. Also, the problem of the optimal control of Lorenz-Rossler model is discussed and it uses the Pontryagin’s Maximum Principle (PMP) to derive the optimal control inputs that achieve the optimal trajectory. Numerical examples and solutions for bifurcation cases and the optimal controlled system are carried out and shown graphically to show the effectiveness of the used procedure.
{"title":"Optimal Control and Bifurcation Issues for Lorenz-Rössler Model","authors":"Saba Alwan, A. M. Al-Mahdi, O. Odhah","doi":"10.4236/ojop.2020.93006","DOIUrl":"https://doi.org/10.4236/ojop.2020.93006","url":null,"abstract":"Optimal control is one of the most popular decision-making tools recently in many researches and in many areas. The Lorenz-Rossler model is one of the interesting models because of the idea of consolidation of the two models: Lorenz and ossler. This paper discusses the Lorenz-Rossler model from the bifurcation phenomena and the optimal control problem (OCP). The bifurcation property at the system equilibrium is studied and it is found that saddle-node and Hopf bifurcations can be holed under some conditions on the parameters. Also, the problem of the optimal control of Lorenz-Rossler model is discussed and it uses the Pontryagin’s Maximum Principle (PMP) to derive the optimal control inputs that achieve the optimal trajectory. Numerical examples and solutions for bifurcation cases and the optimal controlled system are carried out and shown graphically to show the effectiveness of the used procedure.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48629871","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}
A two-dimensional horn antenna is used as a model for topology optimization. In order to employ the topology optimization, each point in the domain is controlled by a function which is allowed to take values between 0 and 1. Each point’s distinct value then gives it an effective permittivity, either close to that of polyimide or that of air, two materials considered in this study. With these settings, the optimization problem becomes finding the optimal distribution of materials in a given domain, and is solved under constraints of reflection and material usage by the Method of Moving Asymptotes. The final configuration consists of two concentric arcs of air while polyimide takes up the rest of the domain, a result relatively unsensitive to the choice of constraints and initial values. Compared to the unoptimized antenna, a slimmer main lobe is observed and the gain boosts.
{"title":"Two-Dimensional Topology Optimization of a Horn Antenna","authors":"Huaxu Dan","doi":"10.4236/ojop.2020.93004","DOIUrl":"https://doi.org/10.4236/ojop.2020.93004","url":null,"abstract":"A two-dimensional horn antenna is used as a model for topology optimization. In order to employ the topology optimization, each point in the domain is controlled by a function which is allowed to take values between 0 and 1. Each point’s distinct value then gives it an effective permittivity, either close to that of polyimide or that of air, two materials considered in this study. With these settings, the optimization problem becomes finding the optimal distribution of materials in a given domain, and is solved under constraints of reflection and material usage by the Method of Moving Asymptotes. The final configuration consists of two concentric arcs of air while polyimide takes up the rest of the domain, a result relatively unsensitive to the choice of constraints and initial values. Compared to the unoptimized antenna, a slimmer main lobe is observed and the gain boosts.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49515594","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}
The aim of this paper is to set up an efficient nonlinear application algorithm predictive model for a multi aircraft landing dynamic system called “Aircraft Landing Dynamic System, Release 2019A+ version “AIRLADYS R2019A+”. This programming software combines dynamic programming technic for mathematical computing and optimisation run under AMPL and KNITRO Solver. It uses also a descriptive programming technic for software design. The user interfaces designed in Glade are saved as XML, and by using the GtkBuilder GTK+ object these can be loaded by applications dynamically as needed. By using GtkBuilder, Glade XML files can be used in numerous programming languages including C, C++, C#, Java, Perl, Python, AMPL, etc. Glade is Free Software released under the GNU GPL License. By these tools, the solved problem is a mathematical modelization problem as a non-convex optimal control governed by ordinary non-linear differential equations. The dynamic programming technic is applied because it is a sufficiently high order and it does not require computation of the partial derivatives of the aircraft dynamic. This application will be coded with Linux system on 64 bit operating system, but it can also be run on the windows system. High running performances are obtained with results giving feasible trajectories with a robust optimizing of the objective function.
{"title":"An Efficient Non-Linear Application Algorithm Predictive Model for a Multi Aircraft Landing Dynamic System AIRLADYS R2019A+","authors":"F. Nahayo, S. Khardi","doi":"10.4236/ojop.2020.92002","DOIUrl":"https://doi.org/10.4236/ojop.2020.92002","url":null,"abstract":"The aim of this paper is to set up an efficient nonlinear application algorithm predictive model for a multi aircraft landing dynamic system called “Aircraft Landing Dynamic System, Release 2019A+ version “AIRLADYS R2019A+”. This programming software combines dynamic programming technic for mathematical computing and optimisation run under AMPL and KNITRO Solver. It uses also a descriptive programming technic for software design. The user interfaces designed in Glade are saved as XML, and by using the GtkBuilder GTK+ object these can be loaded by applications dynamically as needed. By using GtkBuilder, Glade XML files can be used in numerous programming languages including C, C++, C#, Java, Perl, Python, AMPL, etc. Glade is Free Software released under the GNU GPL License. By these tools, the solved problem is a mathematical modelization problem as a non-convex optimal control governed by ordinary non-linear differential equations. The dynamic programming technic is applied because it is a sufficiently high order and it does not require computation of the partial derivatives of the aircraft dynamic. This application will be coded with Linux system on 64 bit operating system, but it can also be run on the windows system. High running performances are obtained with results giving feasible trajectories with a robust optimizing of the objective function.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48575520","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 aims at investigating the optimization of supply chain networks (SCN) for industrial plants under vendor managed inventory (VMI) policy. The vendor uses Long Range Wide Area Network (LoRaWAN) to minimize the total cost of networks. The problem was developed as a mixed-integer non-linear program (MINLP) model, which helped in reducing the total cost of a VMI, to formulate the coordinated decision issue that incorporates the location inventory issue with the allocation task of LoRaWAN technology and its level of investment. We performed different strategies of investment of LoRaWAN technology of having objective function with three different scenarios: 1) Investment of LoRaWAN technology only in ordering operations; 2) Investment of LoRaWAN technology only in holding operations; 3) Investment of LoRaWAN technology in both holding and ordering operations. The simulation results indicated that the cost-saving obtained by the third scenario is significant due to the least total cost of the objective function as compared with the total cost of the objective function obtained by the first and second scenarios.
{"title":"Optimization of Supply Chain Networks Using MINLP Model with Deterministic Demand","authors":"Abdulhadi Altherwi, M. Zohdy","doi":"10.4236/ojop.2020.91001","DOIUrl":"https://doi.org/10.4236/ojop.2020.91001","url":null,"abstract":"This paper aims at investigating the optimization of supply chain networks (SCN) for industrial plants under vendor managed inventory (VMI) policy. The vendor uses Long Range Wide Area Network (LoRaWAN) to minimize the total cost of networks. The problem was developed as a mixed-integer non-linear program (MINLP) model, which helped in reducing the total cost of a VMI, to formulate the coordinated decision issue that incorporates the location inventory issue with the allocation task of LoRaWAN technology and its level of investment. We performed different strategies of investment of LoRaWAN technology of having objective function with three different scenarios: 1) Investment of LoRaWAN technology only in ordering operations; 2) Investment of LoRaWAN technology only in holding operations; 3) Investment of LoRaWAN technology in both holding and ordering operations. The simulation results indicated that the cost-saving obtained by the third scenario is significant due to the least total cost of the objective function as compared with the total cost of the objective function obtained by the first and second scenarios.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46160775","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 paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.
{"title":"A Smoothing Penalty Function Method for the Constrained Optimization Problem","authors":"Bingzhuang Liu","doi":"10.4236/ojop.2019.84010","DOIUrl":"https://doi.org/10.4236/ojop.2019.84010","url":null,"abstract":"In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.","PeriodicalId":66387,"journal":{"name":"最优化(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47036254","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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