Network Synthesis Problem Research Articles

Application of the parallel adaptive genetic simulated annealing algorithm for the synthesis of heat exchanger networks

A robust hybrid genetic algorithm that can be used to solve process synthesis problems with mixed integer nonlinear programming (MINLP) models is developed. The proposed hybrid approach constructs an efficient genetic simulated annealing algorithm for global search, whereas the iterative hill climbing method as a local search technique is incorporated into genetic simulated annealing loop to speed up the convergence of the algorithm. To efficiently locate quality solutions to complex nonconvex MINLP problems, a self-adaptive scheme is developed in the parallel adaptive genetic simulated annealing to maintain a better tradeoff between the global and local search, which can improve the convergence speed and computational efficiency compared with some other hybrid genetic algorithm methods. For the evaluations, we use some well-known standard benchmark functions. The computational results demonstrate the effectiveness and robustness of the present approach. Further, the proposed algorithm is tailored to find optimum solution to heat exchanger network synthesis problem. The results presented prove that the proposed method is a very efficient global optimization tool for large dimensional, nonconvex MINLP problems. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd.

Solving Large-Scale Heat Exchanger Network Synthesis Problems Using Particle Swarm Optimization

Heat exchanger network synthesis has been one of the most popular subjects in process design over the last 50 years. Various studies and optimization techniques have been proposed for designing optimal network with minimum total annual cost. Simultaneous synthesis approach via mathematical programming aims to find the optimal network without decomposition, which has been paid more attentions on the research recently. However, these methods might be not solvable or inefficient for large-scale problems. This paper makes an attempt to construct simultaneous synthesis model with split streams and to develop an efficient optimization framework based on particle swarm optimization for large-scale heat exchanger network synthesis problems. One example including 20 process streams is solved to give an illustration of the method.

A Novel Approach for Targeting and Optimal Design of Efficient Seawater Reverse Osmosis Desalination Networks

Seawater reverse osmosis (SWRO) desalination processes are widely used. The optimal design of such systems resembles a network synthesis problem and has been addressed using superstructure optimization approaches. However, to date these approaches suffer from a limited ability to identify structurally distinct design alternatives, despite requiring significant computational times to determine globally optimal solutions, even for simple cases involving superstructures of only two membrane units. Moreover, existing approaches do not adequately take into consideration water quality information to keep the optimization problems solvable within reasonable times. However, SWRO design strongly depends upon the quality of the feed water and the product water specifications. This casts doubt about the relevance of the results obtained from current superstructure optimization approaches. This paper introduces a novel approach to optimal SWRO design that addresses the major shortcomings of previous approaches. We introduce a novel SWRO synthesis approach, based on the coordinated use of process superstructure representations and global optimization. The approach determines globally optimal solutions to the SWRO network synthesis problems from optimization of full superstructures. It further supports design engineers with a better understanding of the design space and trade-offs between complexity and efficiency. This is achieved through reduced superstructures of distinct design classes. The approach takes into consideration all relevant process conditions and constraints typically associated with SWRO systems. Thermodynamic insights have led to lean superstructure representations throughout which can be solved within short computational times. In contrast to previous approaches that consider sea water to consist of two components only, i.e. “water” and “salt (TDS)”, our superstructure models account for detailed water quality information to ensure practicality. The models capture the performance of the most commonly used membrane elements, as predicted by commercially used simulators including ROSA (Dow) and IMSDesign (Hydranautics) and allow tracing of individual components throughout the system. A detailed economic assessment captures all the significant capital and operating costs associated in SWRO processes, including intake, pre and post treatment. The approach is illustrated using a case study involving four different seawater qualities for which design targets and optimal designs are obtained within short CPU times.

Preliminary synthesis of work exchange networks

In many chemical plants such as LNG, refineries, air enrichment, and ammonia compression is a major consumer of energy. In such plants, some process streams may need compression, while others may need expansion. Optimal integration of these streams may yield major savings in energy. In this work, we introduce a work exchanger network synthesis problem that is analogous to the well-known heat exchange network synthesis problem. We model the details of compressor and turbine operating curves to identify high-pressure and low-pressure streams that should be matched for work exchange via compression/turbine stages located on a single shaft. We propose a superstructure for the work exchange network configuration and develop a mixed-integer nonlinear program (MINLP) to minimize the total annualized cost for a constant speed of the single shaft. We use this preliminary model to optimize shaft speed, and demonstrate the benefits of an optimized network via an illustrative case study.

Modeling, synthesis and optimization of heat exchanger networks. Application to fuel processing systems for PEM fuel cells

The development of biofuels has gained much attention in recent years. Thermodynamic analyses to obtain energy from biofuels using fuel cells were addressed in previous works for a variety of processes. In those processes, the determination of the best conditions to achieve high efficiency values in the conversion of chemical energy into electrical power is a critical issue from the net global energy efficiency point of view. In this regard, a main aspect is to address the energy integration of the whole process. In a previous paper, the authors dealt with energy integration studies for glycerin- and ethanol-based processors coupled to PEM fuel cells resorting on the “multi-stream heat exchanger” feature provided by the simulation tool HYSYS. In that work, the aim was to maximize the energy recovery from the process streams that renders the maximum achievable net global efficiency. In this paper, the aim is to synthesize and design the optimal heat exchangers network (i.e. determination of the process configuration and units sizes) while maintaining the net global efficiency of the whole system at its achievable value.Three modifications to the original SYNHEAT model developed in 1990 by Yee and Grossmann for synthesizing heat exchanger networks are proposed in this work aiming at a better problem description, and consequently searching for best problem solutions.First, a modification in computing the minimum approach temperature difference is proposed. Second, the called “operation line method” is coupled to the SYNHEAT model to built-up the network superstructure to be optimized. Finally, the SYNHEAT model’s hypothesis of constant cp value for modeling heat exchange between process streams is improved by considering enthalpy variable instead of temperature variable, which is convenient when latent heat is transferred.The model variables number involved in the heat exchanger network synthesis problems solved has been reduced to less than a half by applying the operation line method.The proposed methodology and modifications made are of general application and not just for the specific cases addressed in this work.

Comparison of Heat Exchanger Network Synthesis Using Floudas and Yee Superstructures

The simultaneous heat exchanger network (HEN) synthesis problem is generally formulated as a mixed integer non-linear programming (MINLP) problem by using superstructures, which embed several possible stream matches and various alternative HEN designs. The superstructures proposed by Yee et al. [1] and by Floudas et al. [2] are used for this purpose. In the present work, the graph theoretic principles used by Shivakumar and Narasimhan [3] to develop an efficient nonlinear program (NLP) formulation for Yee superstructure has been extended to the Floudas superstructure. A comparison of the NLP formulations based on the two superstructures, in terms of efficiency, scalability, convergence and quality of solution has been carried out using several test problems available in the literature. It has been shown that the Floudas superstructure is superior in terms of these performance metrics, and appears to be the best suited for optimisation based HEN synthesis.

Hybrid optimization approach for water allocation and mass exchange network

This study deals with the synthesis problem of mass exchange networks (MENs) with treatment option for waste minimization and minimal fresh solvent usage by adopting a hybrid combined graphical and mathematical programming approach based on state-space representation. A simple strategy has been proposed for the synthesis water allocation and mass exchange network (WAMEN), aiming at total recycle of effluent thus subsidizing the fresh water consumption to zero. The network synthesis problem has been decomposed into two main steps: (1) synthesizing a network candidate with simpler graphical tools and presenting in state-space representation (2) considering the state-space representation as an initial guess, the available results are formulated as a MINLP problem and the entire network is optimized. Optimized wastewater network along with mass exchange network for an oil refinery process is generated, illustrating the effectiveness of the proposed methodology. This simple procedure will be a useful tool for process engineers to design self-sustained solvent using networks with zero effluent discharge.

Circuit synthesis of passive descriptor systems—a modified nodal approach

AbstractIn this work we consider the problem of multiport passive reciprocal network synthesis by descriptor systems. A numerical method is presented that leads to circuit equations in modified nodal analysis. Copyright © 2008 John Wiley & Sons, Ltd.

Global Optimization of Reverse Osmosis Network for Wastewater Treatment and Minimization

Reverse osmosis (RO) has shown itself to be a viable technology for the treatment and minimization of industrial and domestic wastewater streams. The current research presents a deterministic branch-and-bound global optimization-based algorithm for the solution of the reverse osmosis network (RON) synthesis problem. The mathematical programming model describes the RON through nonconvex mixed-integer nonlinear programs (MINLPs). A piecewise mixed-integer linear program (MILP) is derived based on the convex relaxation of the nonconvex terms present in the MINLP formulation to approximate the original nonconvex program and to obtain a valid lower bound on the global optimum. The MILP model is solved at every node in the branch-and-bound tree to verify the global optimality of the treatment network within a pre-specified gap tolerance. Several constraints are developed to simultaneously screen the treatment network alternatives during the search, tighten the variable bounds, and consequently accelerate algorithm convergence. Water desalination is considered as a case study to illustrate the global optimization of the RO network.

Integer version of the multipath flow network synthesis problem

We consider the following integer multipath flow network synthesis problem. We are given two positive integers q , n , ( 1 < q < n ), and a non-negative, integer, symmetric, n × n matrix R , each non-diagonal element r i j of which represents the minimum requirement of q -path flow value between nodes i and j in an undirected network on the node set N = { 1 , 2 , … , n } . We want to construct a simple, undirected network G = [ N , E ] with integer edge capacities { u e : e ∈ E } such that each of these flow requirements can be realized (one at a time) and the sum of all the edge capacities is minimum. We present an O ( n 3 ) combinatorial algorithm for the problem and we show that the problem has integer rounding property.

Heat exchanger network design using geometric mean temperature difference

The work presents a model which solves the heat exchanger network (HEN) synthesis problem using geometric mean temperature difference (GMTD) in place of the logarithmic mean temperature difference (LMTD). With the aid of logarithmic transformation and piecewise linearization, the problem is stated in a linear form and thus global optimality can be assured for the model. The accuracy of the approximation is discussed and the results obtained for three known case problems show that the usage of GMTD instead of LMTD can be justified. The GMTD-based model produces designs that are sufficiently accurate and comparable with the ones obtained using the LMTD.

Flowrate targeting for threshold problems and plant-wide integration for water network synthesis

Water reuse/recycle has gained much attention in recent years for environmental sustainability reasons, as well as the rising costs of fresh water and effluent treatment. Process integration techniques for the synthesis of water network have been widely accepted as a promising tool to reduce fresh water and wastewater flowrates via in-plant water reuse/recycle. To date, the focus in this area has been on water network synthesis problems, with little attention dedicated to the rare but realistic cases of so-called threshold problems. In this work, targeting for threshold problems in a water network is addressed using the recently developed numerical tool of water cascade analysis (WCA). Targeting for plant-wide integration is then addressed. By sending water sources across different geographical zones in plant-wide integration, the overall fresh water and wastewater flowrates are reduced simultaneously.

On dimensionality of attainable region construction for isothermal reactor networks

In this paper, a number of novel properties of reactor network synthesis (RNS) problems are presented and proved within the Infinite DimEnsionAl State-space (IDEAS) framework for isothermal reactor networks with and without the constant density assumption. These properties can then be used to reduce the dimension of the composition space (i.e., concentration space for constant density fluid (CDF) reactor networks, mass fraction space for variable density fluid (VDF) reactor networks) within which RNS is conducted and subsequently the attainable region (AR) construction. This procedure may be used to overcome the difficulty preventing the AR methodology and other RNS methods from being used for real industrial size problems.

Pollution prevention through reactor network synthesis: the IDEAS approach

A novel approach, called Infinite DimEnsional State-space (IDEAS), has been recently proposed for the synthesis of globally optimal reactor networks where homogeneous, isothermal, steady-state PFRs and CSTRs as well as mixing are allowed. Within the IDEAS framework, reactor network synthesis is formulated as an infinite dimensional linear optimisation problem. In this work, IDEAS will be applied to homogeneous and isothermal reactor network synthesis problems, with an eye on reducing byproduct formation, in the context of pollution prevention efforts. It will be shown that environmentally friendly reactor network design may be carried out, so that fundamental tradeoffs between desirable and undesirable product generation can be exactly quantified.

Synthesis of near-optimal topologically constrained property-based water network using swarm intelligence

The sustainability of water resources is one of the major concerns of the world. Industries are finding ways to minimize water costs and to reduce water pollution through efficient use of supplies. One of effective solutions is the use of water pinch technology or process integration techniques. Property integration emerged as the third trend of process integration technique (aside from energy and mass integration) to solve the problem of water network synthesis by considering physical stream properties such as pH or resistivity. Various techniques have been done to solve this property-based problem. In this paper, mixed integer non-linear programming (MINLP) problems with topological constraints is studied. Nowadays, various evolutionary algorithms are also used to solve such MINLP problems. In this study, particle swarm optimization is used to solve the property integration problem. A comparison is made between this algorithm and commercial genetic algorithm (GA) applications. Particle swarm optimization is observed to perform favorably compared to GA.

A New and Efficient NLP Formulation for Synthesizing Large Scale Multi-Stream Heat Exchanger Networks

The heat exchanger network (HEN) synthesis problem is generally formulated as a mixed integer nonlinear programming (MINLP) by using the concept of HEN superstructures. Although these MINLP formulations can be used to solve the HEN synthesis problem, the size of the problem of their application is restrained because of their complexity. In this study, a new nonlinear programming (NLP) formulation of the simultaneous model for multi-stream heat exchanger network (MSHEN) synthesis is proposed based on stream pseudo-temperature. This formulation can be used to solve MSHEN synthesis problem with temperature enthalpy (T-H) diagram method based on optimal stream heat transfer temperature difference contributions using genetic/simulated annealing algorithm (GA/SA). A significant reduction on the size and complexity of the problem is achieved by the NLP formulation. Large scale MSHEN synthesis problem with unequal heat transfer film coefficients and different construction materials can be solved using the NLP formulation. The performance and efficiency of the NLP formulation and algorithm are demonstrated through two examples.

06/00311 Solving large-scale retrofit heat exchanger network synthesis problems with mathematical optimization methods: Björk, K.-M. and Nordman, R. Chemical Engineering and Processing,2005, 44, (8), 869–876

06/00311 Solving large-scale retrofit heat exchanger network synthesis problems with mathematical optimization methods: Björk, K.-M. and Nordman, R. Chemical Engineering and Processing,2005, 44, (8), 869–876

The application of polynomial matrix factorization in active network synthesis

PurposeTo investigate the general necessary condition for synthesis of square, real rational matrices of complex frequency as admittance matrices of active multiports with resistors, inductors, capacitors and possibly multiport transformers and to prove that this condition is also sufficient for synthesis of stable, square, real rational matrices of complex frequency as admittance matrices of balanced active multiports having only resistors, capacitors and voltage‐amplifiers with sufficiently large amplifications. The main aim of the paper is to provide a new and general method for stable admittance matrices synthesis and to develop strict realization algorithm by active balanced transformerless multiport networks.Design/methodology/approachThe objectives of the paper are achieved by using factorization of regular polynomial matrices in complex frequency with certain degree as products of other regular polynomial matrices with specified degrees. A set of sufficient conditions for such a factorization is presented and derived a pertinent algorithm as the starting point for investigation and solving network synthesis problem and generation of class of equivalent realizations.FindingsTheorem 1 states that sufficient condition for factorization of Pth order, generally regular polynomial matrix P(s) in complex frequency s with degree L, whose determinant has K distinct zeros, in form P(s)=P1(s)·P2(s), where 1≤p2=P20≤L−1 is degree of polynomial matrix P2(s), reads: K&gt;(P−1)·L+p2−1. The coefficient‐matrices of s, s2,… in P1(s) and P2(s) are real or complex depending on whether distinct zeros of det P(s) are real or complex, respectively. Theorem 2 states that: (a) for realization of Pth order matrix of real rational functions in complex frequency s (i.e. RRF matrix) as admittance matrix of active balanced RLC P‐port network with multiport transformers, or without them, P generalized controlled‐sources and P controlling‐ports are necessary, in general; and (b) P balanced voltage‐controlled voltage‐sources (VCVSs) with real and by module greater than unity controlling coefficients (“voltage amplifications”) are sufficient for realization of stable admittance RRF matrix by active, balanced, transformerless, RC P‐port network.Originality/valueThis is a research paper with the following two main contributions (original results). First, a theorem on sufficient conditions for factorization of regular polynomial matrices in complex frequency; and second, a theorem relating to sufficient conditions for synthesis of matrices of real rational functions in complex frequency by active, balanced, transformerless networks. The results may be interesting for network theorists and researchers in the field of electric circuits and systems.

Fairly Linear Mixed Integer Nonlinear Programming Model for the Synthesis of Mass Exchange Networks

A fairly linear optimization model for the synthesis of mass exchange networks has been developed. Superstructure, detailed modeling equations, and solutions of example problems are presented. The predominantly linear character of the model can be kept as long as single-component mass exchange network synthesis problems and packed columns as mass exchangers are considered. At the cost of introducing nonlinear constraints, the optimization model can be extended to handle multicomponent problems and staged columns as well. The new model applies the key ideas of the simultaneous heat exchanger network synthesis model of Yee and Grossmann [Comput. Chem. Eng.1990, 14 (10), 1165-1184].

Optimization in telecommunication networks

Network design and network synthesis have been the classical optimization problems in telecommunication for a long time. In the recent past, there have been many technological developments such as digitization of information, optical networks, internet, and wireless networks. These developments have led to a series of new optimization problems. This manuscript gives an overview of the developments in solving both classical and modern telecom optimization problems. The classical (still actual) network design and synthesis problems are described with an emphasis on the latest developments on modelling and solving them. Mathematical theorems will be related to the models described. This includes menger's disjoint paths theorem, the ford–fulkerson max-flow-min-cut theorem, and also gomory–hu trees and the okamura-seymour cut-condition finally, we describe recent optimization problems such as routing, wavelength assignment, and grooming in optical networks.