Optimal Design of Multistage Flash Desalination Process Based on the Modified Genetic Algorithm (MGA)

2011 ◽  
Vol 233-235 ◽  
pp. 1044-1049
Author(s):  
Lian Ying Wu ◽  
Yang Dong Hu ◽  
Cong Jie Gao
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Flow Rate ◽  
Water Flow Rate ◽  
System Optimization ◽  
Mixed Integer ◽  
Total Annual Cost ◽  
Continuous Variables ◽  
Integer Variables ◽  
Modified Genetic Algorithm

In this paper, a rigorous mathematical model of multistage flash system (MSF) is presented based on a detailed physicochemical representation of the process, including all the fundamental elementary phenomena. In particular, Comparison to the mathematical model of reference, two integer variables, which are the number of recovery stage (NR) and the number of rejection stage (NJ), are introduced to the model. Additionally, two special variables, which are the ratio of recirculation brine water flow rate and distillation flow rate and the ratio of make-up flow rate and the distillation flow rate, are introduced to the model as the continuous variables too. Then, the MSF system is described as a mixed-integer nonlinear programming (MINLP). The objective is to minimize the total annual cost (TAC), which is mainly composed of the operating costs and investment cost. Here the modified genetic algorithm (MGA), which is characterized as mixing coding way, is adopted for the system optimization. A case study and a discussion of the results are presented.

System Optimization of Stabilization Ponds

1992 ◽  
Vol 26 (7-8) ◽  
pp. 1679-1688 ◽  
Author(s):  
N. Meisheng ◽  
Z. Kezhao ◽  
L. Lianquan
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Removal Rate ◽  
System Optimization ◽  
Land Price ◽  
Stabilization Ponds ◽  
Set Up ◽  
Bod Removal

In order to study the system optimization of stabilization ponds, this paper has set up its mathematical model. A series of optimization systems of stabilization ponds are recommended through optimum method under different flow rate, land price and total BOD removal rate. The three parameters are discussed, and the optimum method is improved.

scholarly journals OPTIMIZATION OF TOPOLOGICAL STRUCTURES OF CENTRALIZED LOGISTICS NETWORKS IN THE PROCESS OF REENGINEERING

2021 ◽  
pp. 23-31
Author(s):  
Vladimir Beskorovainyi ◽  
Antonii Sudik
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Time Complexity ◽  
Large Scale ◽  
System Optimization ◽  
Distributed Objects ◽  
Computational Point ◽  
Topological Structures ◽  
Logistics Networks ◽  
Current State

The subject of research in the article is the topological structures of closed logistics networks. The purpose of the work is to create a mathematical model and methods for solving problems of optimization of topological structures of centralized logistics networks in the process of reengineering, taking into account many topological and functional constraints. The article solves the following tasks: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; formalization of the problem of system optimization of logistics networks as territorially distributed objects; development of a mathematical model of the problem of optimization of centralized three-level topological structures of logistics networks at the stage of reengineering; development of a method for solving the problem of optimization of centralized three-level topological structures of logistics networks at the reengineering stage; estimation of time complexity of the method of optimization of centralized three-level topological structures of logistics networks. The following methods are used: methods of systems theory, methods of utility theory, optimization and operations research. The following results were obtained: analysis of the current state of the problem of system optimization of logistics networks and methods of its solution; the problem of system optimization of logistics networks as territorially distributed objects has been formalized; developed a mathematical model of the problem of reengineering three-level topological structures of logistics networks in terms of cost and efficiency for the case of combined production and processing points; methods of directed search of variants of construction of a logistic network which use procedures of coordinate optimization and modeling of evolution on the basis of genetic algorithm are developed; estimates of the accuracy and time complexity of optimization methods of centralized three-level topological structures of logistics networks are obtained. Conclusions: Based on the results of the study of methods for solving the problem, an approximation of their accuracy and time complexity was performed. In practice, this will allow you to choose a more efficient method for solving large-scale practical problems, based on the required accuracy, available computing and time resources. The method based on the coordinate optimization procedure has a significantly higher accuracy, but it is more complex from a computational point of view. The accuracy of the evolutionary method based on a genetic algorithm can be increased by increasing the number of iterations. The practical use of the proposed mathematical model and methods of reengineering the topological structures of centralized closed logistics systems by jointly solving problems for direct and reverse flows will reduce the cost of transport activities of companies. Keywords: closed logistics; logistics network; optimization; reengineering; structure; topology.

Optimal Design of Gas Turbine Cogeneration Plants in Consideration of Discreteness of Equipment Capacities

2004 ◽  
Author(s):  
Ryohei Yokoyama ◽  
Koichi Ito
Keyword(s):  
Optimal Design ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Design Problem ◽  
Continuous Functions ◽  
Performance Characteristics ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Capital Costs ◽  
Integer Variables

To attain the highest economic and energy saving characteristics of gas turbine cogeneration plants, it is necessary to rationally determine capacities and numbers of gas turbines and auxiliary equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Some optimization approaches based on the mixed-integer linear programming have been proposed to this design problem. However, equipment capacities have been treated as continuous variables, and correspondingly performance characteristics and capital costs of equipment have been assumed to be continuous functions with respect to their capacities. This is because if equipment capacities are treated discretely, the number of integer variables increases drastically, and the problem becomes too difficult to solve. As a result, the treatment of equipment capacities as continuous variables causes discrepancies between existing and optimized values of capacities, and expresses the dependence of performance characteristics and capital costs on capacities with worse approximations. In this paper, an optimal design method is proposed in consideration of discreteness of equipment capacities. A formulation for keeping the number of integer variables as small as possible is presented to solve the optimal design problem easily. This method is applied to the design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.

Optimal Launch Vehicle Configuration from Existing Solid Rocket Motors Using Genetic Algorithm

2013 ◽  
Vol 422 ◽  
pp. 127-131
Author(s):  
Fredy M. Villanueva ◽  
Lin Shu He ◽  
Da Jun Xu
Keyword(s):  
Genetic Algorithm ◽  
Launch Vehicle ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Continuous Variables ◽  
Solid Rocket Motors ◽  
Rocket Motors ◽  
Maximum Angle ◽  
Vehicle Configuration ◽  
Solid Rocket

This paper describes the optimization approach of a three stage solid propellant launch vehicle configuration from existing solid rocket motors (SRM). The optimal launch vehicle (LV) is capable of delivering a small satellite of 100 kg to a circular low earth orbit of 400, 500 and 600 km altitude. The overall LV configuration and the trajectory profile were optimized simultaneously, thus the existing SRM parameters for first, second and three stages, vertical flight time, launch maneuver variable, maximum angle of attack, coasting time between first and second stage and the second coasting time between second and third stages were optimized. A genetic algorithm global optimization method has been implemented to perform the analysis, the algorithm consider mixed integer continuous variables. The results show that the proposed optimization approach was able to find the optimal solution for all three variants with very acceptable values, and the approach proved to be reliable for conceptual design level.

Optimal Design of Gas Turbine Cogeneration Plants in Consideration of Discreteness of Equipment Capabilities

2004 ◽  
Vol 128 (2) ◽  
pp. 336-343 ◽  
Author(s):  
Ryohei Yokoyama ◽  
Koichi Ito
Keyword(s):  
Optimal Design ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Design Problem ◽  
Continuous Functions ◽  
Performance Characteristics ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Capital Costs ◽  
Integer Variables

To attain the highest economic and energy-saving characteristics of gas turbine cogeneration plants, it is necessary to rationally determine capacities and numbers of gas turbines and auxiliary equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Some optimization approaches based on the mixed-integer linear programing have been proposed to this design problem. However, equipment capacities have been treated as continuous variables, and correspondingly, performance characteristics and capital costs of equipment have been assumed to be continuous functions with respect to their capacities. This is because if equipment capacities are treated discretely, the number of integer variables increases drastically and the problem becomes too difficult to solve. As a result, the treatment of equipment capacities as continuous variables causes discrepancies between existing and optimized values of capacities and expresses the dependence of performance characteristics and capital costs on capacities with worse approximations. In this paper, an optimal design method is proposed in consideration of discreteness of equipment capacities. A formulation for keeping the number of integer variables as small as possible is presented to solve the optimal design problem easily. This method is applied to the design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.

scholarly journals An Innovative Formulation Tightening Approach for Job-Shop Scheduling

2021 ◽  
Author(s):  
Bing Yan ◽  
Mikhail Bragin ◽  
Peter Luh
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Integer Linear Programming ◽  
Data Preprocessing ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Job Shops ◽  
Production Environment ◽  
Binary Variables ◽  
Integer Variables

<p></p><p>Job shops are an important production environment for low-volume high-variety manufacturing.<i> </i>Its scheduling has recently been formulated as an Integer Linear Programming (ILP) problem to take advantages of popular Mixed-Integer Linear Programming (MILP) methods, e.g., branch-and-cut. When considering a large number of parts, MILP methods may experience difficulties. To address this, a critical but much overlooked issue is formulation tightening. The idea is that if problem constraints can be transformed to directly delineate the problem convex hull in the data preprocessing stage, then a solution can be obtained by using linear programming methods without much difficulty. The tightening process, however, is fundamentally challenging because of the existence of integer variables. In this paper, an innovative and systematic approach is established for the first time to tighten the formulations of individual parts, each with multiple operations, in the data preprocessing stage. It is a major advancement of our previous work on problems with binary and continuous variables to integer variables. The idea is to first link integer variables to binary variables by innovatively combining constraints so that the integer variables are uniquely determined by the binary variables. With binary and continuous variables only, it is proved that the vertices of the convex hull can be obtained based on vertices of the linear problem after relaxing binary requirements. These vertices are then converted to tight constraints for general use. This approach significantly improves our previous results on tightening individual operations. Numerical results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other ILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved. </p><p></p>

scholarly journals A Crew Model using GAIIPDM in Repetitive Projects

2019 ◽  
Vol 8 (3) ◽  
pp. 7621-7626
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Exact Solutions ◽  
Total Expenditure ◽  
Modified Genetic Algorithm ◽  
Task Time

Several indistinguishable or comparative tasks/works in a project are generally alluded to as repetitive projects. A project have group of tasks which is repetitive in nature in all over the project or a similar plan in different positions are commonly known as repetitive project. In repetitive project businesses, distinctive crew choices are accessible for each task, and selecting the best choice to a task is a noteworthy test for administrators of a project. Since acquiring optimum results is found computationally escalated for this type of problems, a modified Genetic Algorithm based technique is developed to schedule projects to satisfy different goals like minimizing total task time and the total expenditure of the project, with the constraints of precedence connections between different tasks, precedence connections between different sites and the due time within which different tasks to be finished. The performance of the proposed method is compared with solutions created using existing algorithms like simple GA and ABC. Exact solutions generated by solving the developed mathematical model is utilized for validating the solutions acquired by modified GA. The computational outcomes demonstrate that the proposed GAIIPDM methodology performs significantly well in terms of quality of solutions.

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