Genetic Algorithm Based on Duality Principle for Bilevel Programming Problem in Steel-making Production

Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems (BLPPs) are the optimization problemswith hierarchical structure. In steel-making production, the plan is not only decided by the steel-making scheduling, but also by the transportation equipment. This paper proposes a genetic algorithmto solve continuous and ingot casting scheduling problems. Based on the characteristics of the problems involved, a genetic algorithm is proposed for solving the bilevel programming problem in steel-making production. Furthermore, based on the simplex method, a new crossover operator is designed to improve the efficiency of the genetic algorithm. Finally, the convergence is analyzed. Using actual data the validity of the proposed algorithm is proved and the application results in the steel plant are analyzed.     

石化企业蒸汽动力系统优化设计建模及应用

在石化企业蒸汽动力系统(SPS)热力学分析与数学规划集成优化策略的指导下,建立了多周期设计与运行协同优化的混合整数线性规划模型(MILP)。通过热力学效率、电热供应比2个指标筛选组合子系统,采用设计负荷离散化的方法确定SPS初始超结构,大大降低了优化设计问题模型的规模和复杂度。案例分析部分采用提出的优化设计方法和建模求解策略,得到了最优设计和运行方案,同传统设计方法相比,模型求解时间大大降低,方案可操作性大大提高,证实了文中提出的优化设计策略、筛选规则和优化设计模型的可行性和有效性。     

Bilevel optimization formulation for parameter estimation in liquid-liquid phase equilibrium problems

Excess Gibbs free energy models contain parameters which for a given mixture are estimated from measurements of phase-splits. Local composition models are very flexible and can accurately predict complex phase behavior. However, in many cases it has been reported that use of local composition models leads to prediction of more phase splits or more phases than measured, modeling homogeneous azeotropes as heterogeneous, etc. Here, a formulation is proposed that addresses these limitations of current parameter estimation methods. The formulation is based on a bilevel program, i.e., an optimization problem embedded in another one. Minimizing the error between model predictions and measurements gives the upper-level program. The lower-level programs are given by the minimization of the Gibbs free energy, or equivalently the satisfaction of the Gibbs tangent plane criterion. Each of the experiments is cast as a separate lower-level program. Additional requirements on the phase behavior of the system, such as enforcing the correct number of phase splits and the correct number of phases in each phase split, are similarly formulated as additional lower-level programs. Global optimization techniques are necessary even to obtain a feasible point since the lower-level programs are nonconvex. The proposed formulation is applied to problems from the literature, in which inappropriate fitting of the parameters of the non-random two-liquid (NRTL) model to experimental data has been reported to result in significant model errors, such as the prediction of an additional spurious phase split. The discussion is restricted to binary mixtures, however, the formulation can in principle be applied also to multicomponent mixtures.     

二层规划及在产量优化决策中的应用

给出求解二层规划模型极大型最优解的分枝定界算法的思想,并以徐州矿务局原煤最优产量的决策为背景,研究了二层规划的实际应用。     

Green biomanufacturing promoted by automatic retrobiosynthesis planning and computational enzyme design

Biomanufacturing,which uses renewable resources as raw materials and uses biological processes to pro-duce energy and chemicals,has long been regarded as a production model that replaces the unsustain-able fossil economy.The construction of non-natural and efficient biosynthesis routes of chemicals is an important goal of green biomanufacturing.Traditional methods that rely on experience are difficult to support the realization of this goal.However,with the rapid development of information technology,the intelligence of biomanufacturing has brought hope to achieve this goal.Retrobiosynthesis and com-putational enzyme design,as two of the main technologies in intelligent biomanufacturing,have devel-oped rapidly in recent years and have made great achievements and some representative works have demonstrated the great value that the integration of the two fields may bring.To achieve the final inte-gration of the two fields,it is necessary to examine the information,methods and tools from a bird's-eye view,and to find a feasible idea and solution for establishing a connection point.For this purpose,this article briefly reviewed the main ideas,methods and tools of the two fields,and put forward views on how to achieve the integration of the two fields.     

Using computational fluid dynamics in combating erosion-corrosion

Computational fluid dynamics was used to search for the links between the observed pattern of attack seen in a bauxite refinery's heat exchanger headers and the hydrodynamics inside the header. Validation of the computational fluid dynamics results was done by comparing then with flow parameters measured in a 1:5 scale model of the first pass header in the laboratory. Computational fluid dynamics simulations were used to establish hydrodynamic similarity between the 1:5 scale and full scale models of the first pass header. It was found that the erosion-corrosion damage seen at the tubesheet of the first pass header was a consequence of increased levels of turbulence at the tubesheet caused by a rapidly turning flow. A prismatic flow corrections device introduced in the past helped in rectifying the problem at the tubesheet but exaggerated the erosion-corrosion problem at the first pass header shell. A number of alternative flow correction devices were tested using computational fluid dynamics. Axial ribbing in the first pass header and an inlet flow diffuser have shown the best performance and were recommended for implementation. Computational fluid dynamics simulations have revealed a smooth orderly low turbulence flow pattern in the second, third and fourth pass as well as the exit headers where no erosion-corrosion was seen in practice. This study has confirmed that near-wall turbulence intensity, which can be successfully predicted by using computational fluid dynamics, is a good hydrodynamic predictor of erosion-corrosion damage in complex geometries.     

Targeting optimum resource allocation using reverse problem formulations and property clustering techniques

Decoupling the constitutive equations from the balance and constraint equations allows for reformulating a conventional forward problem into two reverse problems. The first reverse problem is the reverse of a simulation problem, where the process model is solved in terms of the constitutive (synthesis/design) variables instead of the process variables, thus providing the synthesis/design targets. The second reverse problem (reverse property prediction) solves the constitutive equations to identify unit operations, operating conditions and/or products by matching the synthesis/design targets. Visualization of the problem is achieved by employing recently developed property clustering techniques, which allows a high-dimensional problem to be visualized in two or three dimensions. The clusters by definition satisfy intra-stream and inter-stream conservation through linear “mixing” rules, which allows for the development of consistent additive rules along with their ternary representation.     

石化企业蒸汽动力系统优化设计策略研究

针对石化企业蒸汽动力系统(SPS)设计和综合方面存在的超结构复杂、模型求解困难的问题,提出了热力学分析与数学规划法相结合的系统设计策略。该策略通过将整个SPS看成是能够独立供应蒸汽或动力的子系统的组合,对各种可能组合子系统进行分析,综合电热供应比和供能效率2个指标剔除明显不合理的子系统,初步确定优化的候选子系统,然后对候选子系统设备设计负荷进行离散化,得到候选设备的数量和设计负荷。通过子系统筛选和候选设备数量和尺寸离散化,既避免了凭经验确定初始超结构遗漏最优解的不足,又大大降低了系统的超结构规模和优化设计的混合整数线性规划模型(MILP模型)的复杂度,保证了SPS多周期优化设计方案的最优性和可操作性。     

CFD-based optimization and design of multi-channel inorganic membrane tubes☆

As a major configuration of membrane elements,multi-channel porous inorganic membrane tubes were studied by means of theoretical analysis and simulation.Configuration optimization of a cylindrical 37-channel porous inorganic membrane tube was studied by increasing membrane filtration area and increasing permeation efficiency of inner channels.An optimal ratio of the channel diameter to the inter-channel distance was proposed so as to increase the total membrane filtration area of the membrane tube.The three-dimensional computational fluid dynamics(CFD) simulation was conducted to study the cross-flow permeation flow of pure water in the 37-channel ceramic membrane tube.A model combining Navier–Stokes equation with Darcy's law and the porous jump boundary conditions was applied.The relationship between permeation efficiency and channel locations,and the method for increasing the permeation efficiency of inner channels were proposed.Some novel multichannel membrane configurations with more permeate side channels were put forward and evaluated.     

Mixed-integer bilevel optimization for capacity planning with rational markets

We formulate the capacity expansion planning as a bilevel optimization to model the hierarchical decision structure involving industrial producers and consumers. The formulation is a mixed-integer bilevel linear program in which the upper level maximizes the profit of a producer and the lower level minimizes the cost paid by markets. The upper-level problem includes mixed-integer variables that establish the expansion plan; the lower level problem is an LP that decides demands assignments. We reformulate the bilevel optimization as a single-level problem using two different approaches: KKT reformulation and duality-based reformulation. We analyze the performance of these reformulations and compare their results with the expansion plans obtained from the traditional single-level formulation. For the solution of large-scale problems, we propose improvements on the duality-based reformulation that allows reducing the number of variables and constraints. The formulations and the solution methods are illustrated with examples from the air separation industry.     

Experimental design for optimization of peroxide formulation stability and cost

Cleaning formulations typically contain, in addition to surfactant, a bleaching agent that is usually hydrogen peroxide. This active agent has the disadvantage that it becomes unstable with time, which necessitates the use of various additives in the formulation to ensure its stability. In this work, a study of the different types of surfactants, chelating agents, radical scavengers, stabilizers, and solvents commonly used in the bleaching industry, was made to identify the mixture that better stabilizes an aqueous solution of hydrogen peroxide. The strategy used starts with a screening step based on a hyper-Greco-Latin square design. In subsequent steps, a Box-Wilson design is used to construct a response surface model to identify the composition ensuring the highest possible stability in the formulation. A desirability function is then obtained that allows the stability of the formulation to be maximized and its cost simultaneously minimized. Such a function is optimized using the Nelder-Mead algorithm. The stability study was made by heating the mixtures at 60°C for variable periods of time. A mixture containing four of these additives was found to provide the best stability, and the solvent did not have any effect on the stabilization. However, this mixture exceeded the expectations in terms of cost, so the composition was adjusted to obtain the best compromise between stability and cost. As the stabilizer is the more expensive additive, in this optimization step its composition was reduced. In the final formulation, the stabilizer concentration can be reduced by up to 23% with respect to that obtained in the previous step without detracting from stability, thereby saving 18.8%.     

A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants

Short-term scheduling of multipurpose batch plants is a challenging problem for which several formulations exist in the literature. In this paper, we present a new, simpler, more efficient, and potentially tighter, mixed integer linear programming (MILP) formulation using a continuous-time representation with synchronous slots and a novel idea of several balances (time, mass, resource, etc.). The model uses no big-M constraints, and is equally effective for both maximizing profit and minimizing makespan. Using extensive, rigorous numerical evaluations on a variety of test problems, we show that in contrast to the best model in the literature, our model does not decouple tasks and units, but still has fewer binary variables, constraints, and nonzeros, and is faster.     

MILP-based optimization of oxygen distribution system in integrated steel mills

Simultaneous multiperiod optimization is conducted for minimizing the oxygen emission of an oxygen-distribution system, based on the generalized MILP-based model, which covers various configurations of the captive oxygen factory in integrated steel mills. By simultaneously optimizing all of the variables, such as the load of air separation units (ASU), the on-off states of compressors, the load of liquefiers, etc., the model can promptly provide mill managers with responsive solutions for adjusting the variables involved on the supply-side to minimize oxygen emission. The case study in this paper shows that the proposed model performs well in minimizing oxygen emission, and provides a global optimization result covering the entire planning horizon. Moreover, based on the proposed model, the emission amounts can be rapidly and readily calculated for various scheduling scenarios of ASU maintenance, which is helpful to the manager seeking to optimally schedule ASU maintenance in time.     

Parametric optimization of packed bed for activated coal fly ash waste heat recovery using CFD techniques

Coal fly ash is an industrial solid waste generated from coal preparation during the processing and cleaning of coal for electric power generation. Comprehensive investigation on the reutilization of waste heat of activated coal fly ash is of great economic significance. The method of recovering the waste heat, proposed in this study,is the transfer of heat from activated coal fly ash to gas with the movement of air using the packed bed, providing valuable energy sources for preheating the raw coal fly ash to reduce the overall energy consumption. The investigation is carried on the heat transfer characteristics of gas–solid(activated coal fly ash) phases and air temperature fields of the packed bed under some key conditions via computational fluid dynamics. A two dimensional geometry is utilized to represent key parts of packed bed. The distribution mechanism of the temperature field for gas phase is analyzed based on the transient temperature contours at different times. The results show that the obtained rule of gas–solid heat transfer can effectively evaluate the influences of operating parameters on the air temperature in the packed bed. Simultaneously, it is found that no temperature differences exist in the hot air at the outlet of the packed bed. The investigation provides guidance for the design and optimization of other similar energy recovery apparatuses in industries.     

Integrating process and controller models for the design of self-optimizing control

The steady-state behavior of an existing plant depends on the independent input variables, process equipment and process controllers. This paper presents a method for formulating models that represent the effects of controllers when they are included within a steady-state process flowsheet. The method replaces the controller equations with the equivalent stationarity conditions representing the relationship between the controlled variables and the implemented manipulated variables at steady state. The method is demonstrated for the centralized multivariable Dynamic Matrix Control algorithm applied to two processes, binary distillation and gasoline blending. The integrated process and control system simulation is used to design controllers that improve the profitability of processes without extensive real-time calculations; this is sometimes termed self-optimizing control. For both processes, controllers were designed that yielded higher profit than standard control methods and that approached the highest possible profit achieved by frequent real-time optimization.     

Scheduling multistage, multiproduct batch plants with nonidentical parallel units and unlimited intermediate storage

Scheduling production optimally in multistage multiproduct plants with nonidentical parallel units is a very difficult but routine problem that has received limited attention. In this paper, we construct, analyze, and rigorously compare a variety of novel mixed-integer linear programming formulations using unit-slots, stage-slots, process-slots, a variety of slot arrangements and sequence-modeling techniques, 4-index and 3-index binary variables, etc. While two of our 4-index models are an order of magnitude faster than existing models on 22 test problems of varying sizes, we find that no single model performs consistently the best for all problems. Our work suggests that the best strategy for solving difficult scheduling problems may be to use a set of competitive models in parallel and terminate them all, when one of them achieves the desired solution. We also develop several heuristic models based on our formulations and find that even a heuristic based on an inferior model can surpass others based on superior models. Thus, it may not always be wise to just aim for a single best model for a given scheduling problem, but a host of novel and competitive models, as we have done in this paper.     

Simulation of velocity profiles in a laboratory electrolyser using computational fluid dynamics

A commercial CFD code, Fluent, has been used to analyse the design of a filter-press reactor operating with characteristic linear flow velocities between 0.024 and 0.192 m s⁻¹. Electrolyte flow through the reactor channel was numerically calculated using a finite volume approach to solve the Navier-Stokes equations. The length of the channel was divided into 7 sections corresponding to distances of 0, 0.01, 0.04, 0.08, 0.12, 0.14 and 0.15 m from the electrode edge nearest to the inlet. The depth of the channel was divided into three planes parallel to the channel bottom. For each channel section, a velocity profile was obtained at each depth together with the average velocity in each plane. The flow predictions show that the flow development, as the electrolyte passes through the cell, is strongly affected by the manifold causing strong vortex structures at the entrance and exit of the channel. Although the flow disturbances are a function of the flow rate, they gradually disappear downstream along the channel length. Simulated velocity profiles are considered for the typical current density range used in the FM01-LC reactor.     

Clinically relevant cancer chemotherapy dose scheduling via mixed-integer optimization

Cancer is a class of diseases characterized by an imbalance between cell proliferation and programmed cell death. Chemotherapy is commonly employed as a treatment by clinicians, who must deliver the agent on a schedule that balances treatment efficacy with the toxic side effects. Engineers have considered the development of drug administration schedules for simulated cancer patients constrained by pharmacokinetic (PK) and pharmacodynamic (PD) models. The results typically involve mathematically elegant solutions, although the clinical utility of such results is limited by the formulation of the problem as well as the level of abstraction. At issue is the common disconnect between solutions that are mathematically vs. clinically optimal. The focus of this work is to develop a methodology which can explicitly account for the constraints clinicians consider implicitly. To demonstrate the clinical relevance of this methodology two case studies were considered: a theoretical system from the literature and a preclinical mouse model. The problem formulation is accomplished in a mixed-integer programming framework that is capable of solving problems with complex objectives and constraints yielding results that are clinically relevant.     

A computerized and integrated approach for heat exchanger network design in multipurpose batch plants

Significant savings in the utility cost of batch plants can be obtained by heat integration. In this study, an integrated mathematical programming approach is developed for the determination of the cost optimal heat exchanger network for multipurpose batch chemical plants. A single step, interactive computer program (BatcHEN) which is developed for the determination of the campaigns (i.e. the set of products which can be produced simultaneously), the heat exchange areas of all possible heat exchangers in the campaigns and finally the heat exchanger network are all discussed. A matrix search algorithm is used for the determination of the campaigns. Heat exchange areas for the possible heat exchangers are found by solving a nonlinear optimization model with a grid search algorithm. Finally the heat exchanger network optimization is modeled as a mixed integer linear programming problem and then solved by the modeling and optimization software GAMS/XA.