Network Synthesis Problem Research Articles

A P-graph Approach for Planning Sustainable Rice Straw Management Networks

The Philippines produces up to 15.2 Mt of rice straw waste annually. Unmanaged rice straw waste disposal can lead to pollution from open field burning. On the other hand, rice straw agricultural waste can be used sustainably to produce valuable products such as mushrooms, fodder, pellets, or bioenergy, in a rice straw management system. Such systems can be optimized using Process Integration tools so that the raw materials are used efficiently at the maximum profit and with a minimal carbon footprint. The P-graph framework is an efficient Process Integration tool that solves Process Network Synthesis problems. A P-graph finds the optimal and suboptimal solutions for further analysis, which is useful in decision-making. This work developed a P-graph model for a rice straw management network considering the straw collection and storage steps and the production of both bioenergy and non-bioenergy products. The model can generate optimal and sub-optimal solutions (based on profit) and can simulate raw material disruption scenarios. The model is demonstrated through a case study on three rice straw fields with a maximum total rice straw yield of 96.84 t/yr. The case study considered the operating and raw material costs but did not consider the fixed and investment costs in the calculation of the profit. The results show that mushroom production using rice straw as substrate is the optimal solution with a potential profit of US$ 14 659.60/yr, followed by pellet production with a potential profit of US$ 12 627.90/yr. Disruption scenarios at reduced diesel, manual labor, and rice straw show that mushroom production is still the optimum solution, showing the robustness of the solution. This basic model shows that P-graphs can be applied to rice straw management networks to aid with decision-making for sustainability. Caution must be exercised as the results are context- and location- specific.

A novel optimization framework integrating multiple initialization, automatic topologization and MINLP reduction to accelerate large-scale heat exchanger network synthesis

Ensuring the solution feasibility and achieving an acceptable solution time for the non-deterministic polynomial-time hard (NP-hard) problem of heat exchanger network (HEN) synthesis is still challenging. In this study, we developed a novel optimization framework for efficiently solving large-scale HEN synthesis problems to obtain near global optimal solutions, simultaneously addressing the solution's infeasibility and time. The optimization framework consists of a multiple initial HEN design model (M-INI model), a new distance-based auto structure transformer (A-STR transformer), and a reduced non-linear programming model (R-NLP model). The M-INI model generates various HEN designs based on pinch analysis by varying the minimum approach temperature and the modes of stream splitting and mixing. The A-STR transformer is first proposed to automatically convert various HEN designs into associated superstructure-based topologies as multiple initial starting points for accelerating the solution of the R-NLP model. A strategy for approximating the temperature difference calculation is further applied to reduce the computational loads. Four case studies were conducted using the proposed method to minimize the total annual cost (TAC). The solutions of general cases 1 and 2 are almost equal to the best results in the literature, while the solution time is reduced by 98.7 % and 99.8 %, respectively, which demonstrates the performance of the proposed method. Especially, the method was applied to two practical industrial HEN cases: a large-scale low-grade heat recovery system and a crude distillation unit. The results of large-scale case 3 show that the optimal solution near the global optimal solution only requires 251.7 s. Case 4 includes pre-splitting in scenario A and free splitting in scenario B. Compared to scenario A, the TAC and solution time in scenario B were reduced by 33.9 % and 93.1 %, indicating that the pre-splitting strategy excludes the optimal from the search space. The proposed novel optimization framework demonstrates the efficiency and applicability of handling large-scale HEN synthesis problems. It can also guide engineers in the design of a large-scale HEN with lower costs and effort.

Synthesis of heat-integrated water networks: Integration of heat pumps

A typical heat-integrated water network (HIWN) synthesis problem aims to minimise freshwater and utility consumption while establishing trade-offs between operating and investment costs by exploring different water and heat integration opportunities. Heat integration between hot and cold water streams is performed to save external heating and cooling utilities required to achieve the target temperatures of these streams. This paper proposes a mathematical programming approach to integrate water-to-water heat pumps into the HIWNs. A simple cascade heat pump system with isobutane as a natural working fluid enables a larger temperature lift between the heat pump source and the sink. The objective function of the proposed mixed-integer nonlinear programming (MINLP) model is to minimise the total annualised cost (TAC). The TAC includes operating costs for freshwater, heating/cooling utilities, electricity, and investment in heat exchangers and heat pumps. A sensitivity analysis is performed to evaluate the economic feasibility of the system by varying the heating/electricity cost ratio and depreciation period for the capital investment. The results show that additional utility savings can be obtained by integrating heat pumps into the HIWNs. For threshold problems, a heat pump is feasible for heating/electricity price ratios from 1.175, and heating utility is replaced by electricity for a 1:1 ratio. However, for pinched problems, the feasibility of the heat pump is shifted to lower heating/electricity price ratios, from 0.3 to 0.5, depending on the annualisation factor for the investment.

Comparing Structural Constraints for Accelerated Branch and Bound Solver of Process Network Synthesis Problems

The P-Graph methodology can be used to find the optimal solution for large processing system. This methodology solves the combinatorial part of the problem more efficiently than the traditional branch and bound method due to the utilized relationships inherent in the structure. However, reducing the number of possibilities developed in the constraint functions also plays a major role in this algorithm. In this publication, we present a new constraint function that also takes into account the minimum cost structure and compares it with earlier versions.

Synthesis of multiperiod heat exchanger networks: n-best networks with variable approach temperature

In industrial processes, the stream parameters of the heat exchanger network (HEN) synthesis problem can vary during different periods. As a result of the change in inlet and outlet temperatures and the flow rates of the streams, the optimal HEN and the optimal heat transfer areas of the heat exchangers can be different in each period. In our previous work, the standard HEN synthesis for minimum utility consumption was extended to consider varying stream parameters, where bypasses at the heat exchangers are used to ensure the exit streams meet the expected outlet temperatures. This requires optimization of the total annualized cost based on the maximal heat transfer areas of the heat exchangers for each period. Minimum approach temperature is applied to ensure that the areas of the heat exchangers stay within reasonable limits in the solution network. Since minimum approach temperature affects both the structure of the HEN and the total annualized cost, its value needs to be determined during the optimization procedure. The current work proposes a procedure for HEN synthesis which determines the best, n-best, or all feasible HENs for all periods considering variable approach temperature. The proposed method extends the P-graph-based HEN synthesis method for determining all feasible networks in all periods. Three case studies are used to demonstrate the application of the proposed method. The case studies show that while the commonly applied minimum approach temperature of 10 °C does indeed gives near-optimal results, some problems need different values, such as 25 °C or 30 °C.

Компьютерное проектирование больших трубопроводных сетей высокого ранга оптимальности

The paper presents a computer-aided optimal design of hydraulic systems. The method is based on dividing the network synthesis problem into two stages resulting in a dimensional reduction. This allows the optimal networks design of the higher rank. The proposed technique is intended for automated design of large pipeline networks for rural and interregional water supply.

Optimal synthesis of Philippine agricultural residue-based integrated biorefinery via the P-graph method under supply and demand constraints

Agricultural residues can be utilized by developing countries as a feedstock for producing various bioenergy products to be able to meet local demand. Such initiatives may help reduce the dependence of a country on fossil fuel imports and, at the same time, maximize a vast amount of untapped biomass resources. The production of biofuels and biochemicals can be made possible by developing and implementing integrated biorefineries (IBR). An IBR consists of integrated process units that convert biomass into multiple bioenergy products. The design and synthesis of IBRs is a challenging task due to the number of possible pathways in producing a particular product while considering the type of feedstock and equipment. The P-graph (process graph) method is an excellent tool in process network synthesis (PNS) problems, and is an approach based on graph theory and efficient combinatorial algorithms. Its effectiveness in determining an optimal structure for solution recommendations is evident in a number of systems. In this work, a P-graph based approach was used to optimally synthesize an IBR using locally available agricultural waste as input. Optimal and sub-optimal solutions were generated by maximizing hourly profit. A sensitivity analysis on the effect of the price of key products on the optimal solution was conducted. The model was able to solve the problem given a feedstock supply and product demand constraint. Two case studies, a rice- and a corn-based IBR, were used to demonstrate the applicability of the proposed method. From the results, the rice- and corn-based IBRs generated a profit of 376.88 USD/h and 7746.93 USD/h. The difference in profit is mainly driven by the supply of biomass and prices of key products. This work will provide a reference in creating IBR using local feedstock, thereby valorizing agricultural residues. This may enable increased revenues for farmers from the sale of biomass.

Node dynamic adaptive non-structural model for efficient synthesis of heat exchanger networks

Balancing the trade-off between structural diversity (solution space) and optimization efficiency is an urgent challenge in the modeling and global optimization of heat exchanger network synthesis problems. This paper presents a node dynamic adaptive non-structural model without stream splitting to enhance optimization efficiency under the premise of ensuring an adequate solution space. The node-based non-structural stream matching mechanism can be used to make the solution space scalable and achieve the efficacy of multi-stage stage-wise superstructure with a finite number of nodes. Two node dynamic adaptive strategies (uniformly distributed and random) are established to periodically adjust the number of nodes in process streams and the node distribution of existing heat exchanger units, thereby preventing a decrease in computational efficiency due to an excess number of preset nodes while still satisfying the solution space requirements. The node dynamic adaptive non-structural model is optimized using the random walk algorithm with compulsive evolution. The proposed method was applied to four well-known heat exchanger network case studies. High-quality solutions were obtained, and they are more economical than most of the optimal results previously reported in the literature. These results demonstrate the enhanced computational efficiency and applicability of the proposed synthesis method based on a node dynamic adaptive non-structural model for efficiently solving large-scale heat exchanger network synthesis problems.

Efficient Strategy for the Synthesis of Work and Heat Exchange Networks

The work and heat exchange network synthesis problem refers to the problem of determining a network of heat exchangers and pressure equipment that minimize the total annual cost or exergy consumption, where the thermodynamic paths (i.e., pressure-change and temperature-change paths) are variable. In this work, an efficient optimization strategy is presented, consisting of two synthesis phases. In the targeting phase, a novel targeting model is introduced to identify the optimal thermodynamic paths of process streams. The genetic algorithm in the outer level is applied to adjust the streams’ temperatures, and the golden section search method in the inner level is used to adjust the hot utility consumption. With the obtained thermodynamic paths, the detailed heat exchanger network is determined using a global search algorithm in the design phase. The integrated methodology is applied to four cases. Except for the illustrating example, results show a decrease of 4.26% in the total annual cost (TAC) for the liquefied natural gas (LNG) example, 48.7% in the TAC for the postcombustion CO2 capture example, and 1.05% in the TAC for the two-stage membrane separation process example.

Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

AbstractA new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD‐based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD‐based design model for one‐shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.

Synthesis of performance-optimal heat exchanger networks using attainable regions

The attainable region (AR) is a region in a performance space in which all physically realizable reactor network designs must exist. ARs have been used since the 1960s for solving reactor network synthesis problems. The benefits of these methods are that the feasibility of a performance target can be assessed prior to running a synthesis routine, the solutions they give are guaranteed to be physically realizable, and they are amenable to convex optimization. In this article, the theory of attainable regions is extended to bring these benefits to the heat exchanger network (HEN) synthesis problem, with constant thermophysical properties and no stream splits. The HENS problems of the optimal outlet stream temperature and the minimum utility usage problems are linear optimization problems, solvable by simplex search with n−1 state variables for an n-stream problem. The quality of solutions regarding number and size of heat exchangers is discussed, with examples.

Incremental design of water symbiosis networks with prior knowledge: The case of an industrial park in Kenya

Industrial parks have a high potential for recycling and reusing resources such as water across companies by creating symbiosis networks. In this study, we introduce a mathematical optimization framework for the design of water network integration in industrial parks formulated as a large-scale standard mixed-integer non-linear programming (MINLP) problem. The novelty of our approach relies on i) developing a multi-level incremental optimization framework for water network synthesis, ii) including prior knowledge of water demand growth and projected water scarcity to evaluate the significance of water-saving solutions, iii) incorporating a comprehensive formulation of the water network synthesis problem including multiple pollutants and different treatment units and iv) performing a multi-objective optimization of the network including freshwater savings and relative cost of the network. The significance of the proposed optimization framework is illustrated by applying it to an existing industrial park in a water-scarce region in Kenya. Firstly, we illustrated the benefits of including prior knowledge to prevent an over-design of the network at the early stages. In the case study, we achieved a more flexible and expandable water network with 36% lower unit cost at the early stage and 15% lower unit cost at later stages for overall maximum freshwater savings of 25%. Secondly, multi-objective analysis suggests an optimum freshwater savings of 14% to reduce the unit cost of the network by half. Moreover, the significance of symbiosis networks is highlighted by showing that intra-company connections can only achieve a maximum freshwater savings of 17% with significantly higher unit cost (+45%). Finally, we showed that the values of symbiosis connectivity index in the Pareto front correspond to higher freshwater savings, indicating the significant role of the symbiosis network in the industrial park under study. This is the first study, where all the above elements have been taken into account simultaneously for the design of a water reuse network.

A novel two-step synthesis method with weakening strategy for solving large-scale heat exchanger networks

Efficiently solving large-scale heat exchanger network (HEN) synthesis problems remains a challenging task mainly due to the presence of discontinuity caused by integer variables as well as nonlinearity of the objective cost function. This paper focuses on efficiently solving large-scale HEN synthesis problems based on a chessboard presentation with no splits, and aims to achieve globally near-optimal solutions by using a two-step synthesis method along with a weakening strategy for fixed investment costs that is conducive to bypass the discontinuity. The first step is to generate the most promising network structure by using an improved cuckoo search algorithm to optimize integer and continuous variables simultaneously. In the second step, a cuckoo search algorithm is utilized to directly optimize the heat exchanger area of the optimal structure obtained in the first step. Meanwhile, fixed-cost weakening strategies are applied in the above two steps for improving the optimization efficiency. The proposed method has been tested on several HEN cases, and two of which, namely the 20- and 39-stream problems, are presented in this paper. For these two cases, although the solutions obtained do not contain stream splits, their total annual costs are close to best solutions with stream splits and lower than those best solutions with no-splits reported in the literature, and their chessboard network configurations are clear and simple. Based on these results, the developed method demonstrates the applicability to handle large-scale HEN problems, and is also useful for guiding the grassroots or retrofit design of large-scale HENs or other engineering process syntheses with less cost and less pollution.

Managing Alternative Patient Appointments Using P-Graph Methodology.

Patient appointment scheduling is one of the main challenging tasks in the healthcare administration and is constantly in the focus of theoretical researches. The aim of this study was to investigate the applicability of the P-graph (Process graph) methodology to find the n-best alternative for patient's scheduling. The patient appointment scheduling task was formalised as an integer linear programming problem and was considered as a process network synthesis problem. The optimal and n-best alternative solutions were determined by an efficient branch and bound algorithm implemented in a decision support system. Experimental results show, that the P-graph methodology can be effectively applied to produce the optimal scheduling for the examinations and to find the alternatives of the best scheduling.

A Nodes-Based Non-Structural Model Considering a Series Structure for Heat Exchanger Network Synthesis

The aim of heat exchanger network synthesis is to design a cost-effective network configuration with the maximum energy recovery. Therefore, a nodes-based non-structural model considering a series structure (NNM) is proposed. The proposed model utilizes a simple principle based on setting the nodes on streams such that to achieve optimization of a heat exchanger network synthesis (HENS) problem. The proposed model uses several nodes to quantify the possible positions of heat exchangers so that the matching between hot and cold streams is random and free. Besides the stream splits, heat exchangers with series structures are introduced in the proposed model. The heuristic algorithm used to solve NNM model is a random walk algorithm with compulsive evolution. The proposed model is used to solve four scale cases of a HENS problem, the results show that the costs obtained by NNM model can be respectively lower 3226 $/a(Case 1), 11,056 $/a(Case 2), 2463 $/a(Case 3), 527 $/a(Case 4) than the best costs listed in literature.

Modeling technique in the P-Graph framework for operating units with flexible input ratios

The P-Graph framework is an efficient tool that deals with the solution of Process Network Synthesis (PNS) problems. The model uses a bipartite graph of material and operating unit nodes, with arcs representing material flow. The framework includes combinatorial algorithms to identify solution structures, and an underlying linear model to be solved by the Accelerated Branch and Bound algorithmic method. An operating unit node in a P-Graph consumes its input materials and produces its products in a fixed ratio of operation volume. This makes it inadequate in modeling such real-world operations where input composition may vary, and may also be subject to specific constraints. Recent works address such cases by directly manipulating the generated mathematical model with linear programming constraints. In this work, a new general method is introduced which allows the modeling of operations with flexible input ratios and linear constraints in general, solely by tools provided by the P-Graph framework itself. This includes representing the operation with ordinary nodes and setting up their properties correctly. We also investigate how our method affects the solution structures for the PNS problem which is crucial for the performance of algorithms in the framework. The method is demonstrated in a case study where sustainable energy generation for a plant is present, and the different types of available biomass introduce a high level of flexibility, while consumption limitations may still apply.

Radial-Basis Function Neural Network Synthesis on the Basis of Decision Tree

The problem of neural network synthesis on the precedents is addressed. The aim of the study is to create methods for radial-basis neural network model constructing having high levels of generalization and accuracy, which do not require user participation in the process of model building. The method of decision tree transforming into a neural network model is proposed. For a given sample, a decision tree is built, on the basis of which leaf nodes the cluster centers' are allocated, after which the structure of the radial-basis network is synthesized by associating of selected clusters with neurons of the first layer, the cluster centers coordinates are placed into the weights of neurons of the first layer, and then the weights are adjusted. The method for transforming a regression tree into a radial-basis network is proposed. It allocates clusters for solved problem as a regression tree, but to improve accuracy for each cluster, it builds a particular linear regression model of the output feature dependence from the neuron???s output determining belonging to the corresponding cluster. The method of converting a random forest into a neural network model is proposed. Trees of the forest, built on a given sample, are transformed into separate neural network models, which are combined into joint network. The experiments on practical problems solving were carried out. Their results were confirmed the efficiency of the proposed methods.

Non-linear Programming via P-graph Framework

P-graph is a graph-theoretic method which is designed to solve process network synthesis (PNS) problem using combinatorial and optimisation algorithms. Due to its visual interface for data encoding and results display; and its capability of generating multiple solutions (optimal and sub-optimal) simultaneously, the utility of P-graph has expanded into a broad range of studies recently. However, this powerful graph-theoretic method still falls short of dealing with non-linear problems. The problem can be found from the cost estimation provided by P-graph software. Despite it allows users to input the sizing cost (noted as “proportional cost” in P-graph software), the capacity and the cost are assumed to be linearly correlated. This inaccurate and unreliable cost estimation has increased the difficulty of making optimal decisions and therefore lead to undesirable profit loss. This paper proposes to solve the fundamental linearity problem by implementing trained artificial neural networks (ANN) into P-graph. To achieve this, an ANN model which utilised thresholded rectified linear unit (ReLU) activation function is developed in a segregated computational tool. The identified neurons are then modelled in P-graph in order to convert the input into the nonlinear output. To demonstrate the effectiveness of the proposed method, an illustrative case study of biomass transportation is used. With the use of the trained neurons, the non-linear estimation of transportation cost which considered fuel consumption cost, vehicle maintenance cost and labour cost are successfully modelled in P-graph. This work is expected to pave ways for P-graph users to expand the utility of P-graph in solving other more complex non-linear problems.

Review of Mass Exchanger Network Synthesis Methodologies

In this paper, a review of the methodologies that have been applied to the synthesis of mass exchange networks is presented, including their chronology. The paper also discusses the differences between a heat exchanger network and a mass exchanger network, highlighting aspects where it is difficult to establish a direct analogy between the two networks. The paper reviews the different mass exchanger network synthesis problem types that have been synthesized using the existing methods, as well as discussions on the benefits of combining the synthesis of heat and mass exchange networks, and a critical analysis of the aspects of mass exchanger network problems that still need to be investigated to fully establish the utility of this process synthesis problem.

Passive controller realization of a bicubic admittance containing a pole at [formula omitted] with no more than five elements for inerter-based mechanical control

This paper is concerned with a passive network synthesis problem about the damper-spring-inerter realization of a bicubic admittance containing a pole at s=0 with at most five elements, where the least number of elements for the possible realizations is four. The admittances of many passive mechanisms (controllers) in inerter-based control systems are in this form. A specific four-element realizability that is a parallel connection of a spring and a three-element subnetwork is first solved. By utilizing the realizability constraints based on graph theory, it is proved that only one configuration can cover all the other four-element cases through the discussions of other possible network graphs. By deriving its realizability condition, a necessary and sufficient condition for the four-element realizations can be combined. More generally, the five-element realizability can be investigated. The specific five-element realizability that is the parallel connection of a spring and a four-element subnetwork is solved. By making use of realizability constraints described by network graphs and eliminating impossible configurations, a set of four configurations is found out to cover all the other five-element cases. By investigating their realizability conditions, a necessary and sufficient condition for the five-element realizations can be combined. The results of this paper can reduce the realizability redundancy compared with classical synthesis approaches like Bott–Duffin procedure, which provide a first critical step towards solving the minimal realization problem of such admittances. The results can be applied to the design and optimization of mechanical control systems based on inerters, and in the long term can also contribute to the development of other areas of circuits and systems.