scholarly journals A Hybrid Framework for Simultaneous Process and Solvent Optimization of Continuous Anti-Solvent Crystallization with Distillation for Solvent Recycling

Processes ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 63
Author(s):  
Jiayuan Wang ◽  
Lingyu Zhu ◽  
Richard Lakerveld
Keyword(s):  
Nonlinear Programming ◽  
Continuous Process ◽  
Continuous Mapping ◽  
Mapping Method ◽  
Mixed Integer ◽  
Separation And Purification ◽  
Solvent Selection ◽  
Integer Variables ◽  
Solvent Crystallization ◽  
Minlp Problem

Anti-solvent crystallization is frequently applied in pharmaceutical processes for the separation and purification of intermediate compounds and active ingredients. The selection of optimal solvent types is important to improve the economic performance and sustainability of the process, but is challenged by the discrete nature and large number of possible solvent combinations and the inherent relations between solvent selection and optimal process design. A computational framework is presented for the simultaneous solvent selection and optimization for a continuous process involving crystallization and distillation for recycling of the anti-solvent. The method is based on the perturbed-chain statistical associated fluid theory (PC-SAFT) equation of state to predict relevant thermodynamic properties of mixtures within the process. Alternative process configurations were represented by a superstructure. Due to the high nonlinearity of the thermodynamic models and rigorous models for distillation, the resulting mixed-integer nonlinear programming (MINLP) problem is difficult to solve by state-of-the-art solvers. Therefore, a continuous mapping method was adopted to relax the integer variables related to solvent selection, which makes the scale of the problem formulation independent of the number of solvents under consideration. Furthermore, a genetic algorithm was used to optimize the integer variables related to the superstructure. The hybrid stochastic and deterministic optimization framework converts the original MINLP problem into a nonlinear programming (NLP) problem, which is computationally more tractable. The successful application of the proposed method was demonstrated by a case study on the continuous anti-solvent crystallization of paracetamol.

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 Optimization model for the design of distributed wastewater treatment networks

2012 ◽  
Vol 66 (2) ◽  
pp. 263-273 ◽  
Author(s):  
Nidret Ibric ◽  
Elvis Ahmetovic ◽  
Midhat Suljkanovic
Keyword(s):  
Wastewater Treatment ◽  
Nonlinear Programming ◽  
Optimization Model ◽  
Mixed Integer ◽  
Programming Approach ◽  
Global Optimality ◽  
Total Treatment ◽  
Minlp Problem ◽  
Mathematical Programming Approach ◽  
Water Recirculation

In this paper we address the synthesis problem of distributed wastewater networks using mathematical programming approach based on the superstructure optimization. We present a generalized superstructure and optimization model for the design of the distributed wastewater treatment networks. The superstructure includes splitters, treatment units, mixers, with all feasible interconnections including water recirculation. Based on the superstructure the optimization model is presented. The optimization model is given as a nonlinear programming (NLP) problem where the objective function can be defined to minimize the total amount of wastewater treated in treatment operations or to minimize the total treatment costs. The NLP model is extended to a mixed integer nonlinear programming (MINLP) problem where binary variables are used for the selection of the wastewater treatment technologies. The bounds for all flowrates and concentrations in the wastewater network are specified as general equations. The proposed models are solved using the global optimization solvers (BARON and LINDOGlobal). The application of the proposed models is illustrated on the two wastewater network problems of different complexity. First one is formulated as the NLP and the second one as the MINLP. For the second one the parametric and structural optimization is performed at the same time where optimal flowrates, concentrations as well as optimal technologies for the wastewater treatment are selected. Using the proposed model both problems are solved to global optimality.

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.

Sign in / Sign up

Export Citation Format

Share Document