scholarly journals Optimization of Distillation Sequences with Nonsharp Separation Columns

Processes ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 323 ◽  
Author(s):  
Xi Wang ◽  
Zengzhi Du ◽  
Yunlu Zhang ◽  
Jingde Wang ◽  
Jianhong Wang ◽  
...  
Keyword(s):  
Nonlinear Programming ◽  
Solution Space ◽  
Operating Conditions ◽  
Mixed Integer ◽  
Separation Processes ◽  
Integer Nonlinear Programming ◽  
Minlp Problem ◽  
Separation Sequence ◽  
Computationally Intensive ◽  
Separation Columns

Nonsharp distillation sequences are widely used in industrial separation processes; however, most current research has not discussed this topic, except in sequences with heat integration under special operating conditions, including complex columns. The sequence with nonsharp separation has the features of general distillation sequences, which are usually optimized by adjusting the separation sequence and the design/operation parameters of each column in the sequence, making the optimization a mixed integer nonlinear programming (MINLP) problem, which is usually hard to solve. With inclusion of nonsharp separation columns, the sequence optimization becomes even more complicated and computationally intensive. This work aimed to optimize the distillation sequence, including nonsharp distillation alongside simple columns and dividing wall columns. Inspired by the dynamic programing method for sharp distillation sequence, a framework for automatic optimization is proposed to decompose the MINLP problem into integer programming (IP) and nonlinear programming (NLP) problems. The optimization processes of sharp and nonsharp distillation sequences are compared and the solution space in terms of the possible number of distillation sequences with nonsharp separation is discussed. Two optimization cases, including an industrial one, are included to validate the proposed framework.

Optimal Retrofitting of Structures Using Braces

2014 ◽  
Vol 553 ◽  
pp. 807-812
Author(s):  
Sawekchai Tangaramvong ◽  
Francis Tin-Loi
Keyword(s):  
Nonlinear Programming ◽  
Mixed Integer ◽  
Design Domain ◽  
Ground Structure ◽  
Binary Variables ◽  
Integer Nonlinear Programming ◽  
Initial Basis ◽  
Minlp Problem ◽  
Multiple Load ◽  
Bounded System

The paper presents a mathematical programming based approach for the efficient retrofitting, with braces, of structures subjected to multiple load cases and serviceability limitations, simultaneously. The method is based on a simple ground structure concept that generates within a design domain all possible cross braces, and then automates the decision as to which brace members are retained or eliminated using unknown 0-1 variables. The optimization minimizes simultaneously the total number and volume of design braces. The governing problem takes the form of a disjunctive and combinatorial optimization program, cast as a mixed integer nonlinear programming (MINLP) problem. We propose a two-step optimization algorithm to solve the MINLP, in which the first step processes a standard nonlinear programming (NLP) problem by relaxing the binary variables to a continuous bounded system, the results of which form an initial basis for the second and final solve of the MINLP problem with binary variables.

scholarly journals Distributed Energy-Efficient and Secure Offloading in Air-to-Ground MEC Networks

2021 ◽  
Author(s):  
Wanning Liu ◽  
Yitao Xu ◽  
Ducheng Wu ◽  
Haichao Wang ◽  
Xueqiang Zheng ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Nonlinear Programming ◽  
Energy Efficient ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Distributed Energy ◽  
Integer Nonlinear Programming ◽  
Minlp Problem ◽  
System Energy ◽  
Simulation Results

Abstract This paper mainly investigates the energy-efficient and secure offloading problem in air-to-ground MEC networks. The proposed efficient offloading mechanism is as per the requirements of the heterogeneous tasks of ground users. Further, the optimizing offloading rate, offloading object, and channel access jointly formulate system energy consumption and eavesdropping rate minimization. A distributed two-stage offloading scheme is proposed for achieving the sub-optimal solution for the Mixed-integer Nonlinear Programming (MINLP) problem. Finally, simulation results demonstrate that the proposed scheme is superior to several benchmark schemes.

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