求解带有等式约束的混合整数非线性规划问题的粒子群算法

针对带有等式约束的混合整数非线性规划(MINLP)问题,建立了一种改进的粒子群优化(PSO)算法--简约空间法.利用等式约束将问题的维数降低,使带有等式约束的优化问题转化为无等式约束优化问题.通过测试函数和过程综合的实例对该算法进行了测试并与其他算法所得的结果进行了比较,结果表明,PSO算法在使用的普遍性、求解的准确性等方面都优于一般的算法,尤其对于非凸的MINLP问题,PSO算法是一种有效的求解方法.     

An adaptive discretization MINLP algorithm for optimal synthesis of decentralized energy supply systems

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and part-load performances are nonlinear. Thus, this optimization problem can be modeled as a nonconvex mixed-integer nonlinear programming (MINLP) problem. We present an adaptive discretization algorithm to solve such synthesis problems containing an iterative interaction between mixed-integer linear programs (MIPs) and nonlinear programs (NLPs). The proposed algorithm outperforms state-of-the-art MINLP solvers as well as linearization approaches with regard to solution quality and computation times on a test set obtained from real industrial data, which we made available online.     

Computational strategies for improved MINLP algorithms

In order to improve the efficiency for solving MINLP problems, we present in this paper three computational strategies. These include multiple-generation cuts, hybrid methods and partial surrogate cuts for the Outer Approximation and Generalized Benders Decomposition. The properties and convergence of the strategies are analyzed. Based on the proposed strategies, five new MINLP algorithms are developed, and their implementation is discussed. Results of numerical experiments for benchmark MINLP problems are reported to demonstrate the efficiency of the proposed methods.     

An integrated framework for scheduling and control using fast model predictive control

Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121–133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377–390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores‐Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698–6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece‐wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169–3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp‐MPC. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3304–3319, 2015     

An LSTM-based mixed-integer model predictive control for irrigation scheduling

The development of well-devised irrigation scheduling methods is desirable from the perspectives of plant quality and water conservation. Accordingly, in this article, a mixed-integer model predictive control system is proposed to address the daily irrigation scheduling problem. In this framework, a long short-term memory (LSTM) model of the soil–crop–atmosphere system is employed to evaluate the objective of ensuring optimal water uptake in crops while minimizing total water consumption and irrigation costs. To enhance the computational efficiency of the proposed method, a heuristic method involving the logistic sigmoid function is used to approximate the binary variable that arises in the mixed-integer formulation. Through computer simulations, the proposed scheduler is applied to homogeneous and spatially variable fields. The results of these simulation experiments reveal that the proposed method can prescribe optimal/near-optimal irrigation schedules that are typical of irrigation practice within practical computational budgets.     

New MINLP formulation for the multiperiod pooling problem

The modeling of blending tank operations in petroleum refineries for the most profitable production of liquid fuels in a context of time‐varying supply and demand is addressed. A new mixed‐integer nonlinear programming formulation is proposed that using individual flows and split fractions as key model variables leads to a different set of nonconvex bilinear terms compared with the original work of Kolodziej et al. These are better handled by decomposition algorithms that divide the problem into integer and nonlinear components as well as by commercial solvers. In fact, BARON and GloMIQO can solve to global optimality all problems resulting from the new formulation and test problems from the literature. A tailored global optimization algorithm working with a tight mixed‐integer linear relaxation from multiparametric disaggregation achieves a similar performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3728–3738, 2015     

多目标进化算法求解过程综合中的混合整数线性规划(MILP)与混合整数非线性规划问题(MINLP)

Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of crame is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.     

改进的自适应模拟退火算法及其在过程综合中的应用

为有效解决化工过程综合中的MINLP问题，针对连续变量的模拟退火算法搜索慢的缺点，提出了一种改进的自适应模拟退火算法（Adaptive Simulated Algorithms,ASA)，采取自适应调整温度和搜索步长两种策略，大大加快搜索速度，提高最优解的质量。实算结果充分体现了所提出算法的优点，并很好地应用于化工过程综合问题。     

An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms

In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29, 1914] is proposed, in order to speed up the convergence in nonconvex MINLP models that involve bilinear and concave terms. Bounding problems are constructed replacing these nonconvex terms by piecewise linear underestimators. These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value. When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion. The new algorithm is applied to five different synthesis problems in the areas of water networks, heat exchanger networks and distillation sequences. The results show a significant reduction in the computational cost compared with the previous version of the algorithm.     

Polymer brush coatings for combating marine biofouling

A variety of functional polymer brushes and coatings have been developed for combating marine biofouling and biocorrosion with much less environmental impact than traditional biocides. This review summarizes recent developments in marine antifouling polymer brushes and coatings that are tethered to material surfaces and do not actively release biocides. Polymer brush coatings have been designed to inhibit molecular fouling, microfouling and macrofouling through incorporation or inclusion of multiple functionalities. Hydrophilic polymers, such as poly(ethylene glycol), hydrogels, zwitterionic polymers and polysaccharides, resist attachment of marine organisms effectively due to extensive hydration. Fouling release polymer coatings, based on fluoropolymers and poly(dimethylsiloxane) elastomers, minimize adhesion between marine organisms and material surfaces, leading to easy removal of biofoulants. Polycationic coatings are effective in reducing marine biofouling partly because of their good bactericidal properties. Recent advances in controlled radical polymerization and click chemistry have also allowed better molecular design and engineering of multifunctional brush coatings for improved antifouling efficacies.     

Simultaneous model selection and parameter estimation for lithium‐ion batteries: A sequential MINLP solution approach

Equivalent circuit model (ECM) is a practical and commonly used tool not only in state of charge (SOC) estimation but also in state of health (SOH) monitoring for lithium‐ion batteries (LIBs). The functional forms of circuit parameters with respect to SOC in ECM are usually empirical determined, which cannot guarantee to obtain a compact and simple model. A systematical solution framework for simultaneous functional form selection and parameter estimation is proposed. A bi‐objective mixed‐integer nonlinear programming (MINLP) model is first constructed. Two solution approaches, namely the explicit and implicit methods, are then developed to balance model accuracy and model complexity. The former explicitly treats the model complexity as a constraint and the latter implicitly embeds the model complexity into the objective as a penalty. Both approaches require sequential solution of the transformed MINLP model and an ideal and nadir ideal solutions‐based criterion is utilized to terminate the solution procedure for determining the optimal functional forms, in which ideal solution and nadir ideal solution represent the best and worst of each objective, respectively. Both explicit and implicit approaches are thoroughly evaluated and compared through experimental pulse current discharge test and hybrid pulse power characterization test of a commercial LIB. The fitting and prediction results illustrate that the proposed methods can effectively construct an optimal ECM with minimum complexity and prescribed precision requirement. It is thus indicated that the proposed MINLP‐based solution framework, which could automatically guide the optimal ECM construction procedure, can be greatly helpful to both SOC estimation and SOH monitoring for LIBs. © 2015 American Institute of Chemical Engineers AIChE J, 62: 78–89, 2016     

离子膜法烧碱装置自动控制系统的优化

介绍了和利时公司MACSV控制系统在离子膜法烧碱生产过程中的应用,阐述了工艺流程及硬件配置。分析了各工序主要自动控制过程,对脱硝盐水系统pH值、电解槽出口气相总管压力、电解液浓度、氢气压缩机出口压力及合成炉氯氢流量比值等复杂控制系统进行优化,经过调试运行,各项技术指标达到设计要求,整个离子膜法烧碱系统实现自动控制。     

Automated reformulation of disjunctive constraints in MINLP optimization

In this paper, a general method for handling disjunctive constraints in a MINLP optimization problem is presented. This method automates the reformulation of an, in a abstract modeling language given, optimization problem into a mathematical problem that is solvable with existing optimization tools. This implementation can use common MILP solvers for linear problems and nonlinear methods for quasi-convex optimization problems. It also includes the possibility to use the logics in the system and solve the system logically using subproblems.     

A comparison of silver‐ and copper‐charged polypropylene feed spacers for biofouling control

Implementation of nanofiltration (NF) and reverse osmosis (RO) processes in treating traditional water sources can provide a steady‐state level of removal that eliminates the need for regeneration of ion exchange resins or granular activated carbon. Moreover, RO can help meet future potable water demands through desalination of seawater and brackish waters. The productivity of membrane filtration is severely lowered by fouling, which is caused by the accumulation of foreign substances on the surface and/or within pores of membranes. Microbial fouling, or biofouling, is the growth of microorganisms on the membrane surface and on the feed spacer as present between the envelopes. The fouling of membranes has demanded and continues to demand considerable attention from industry and research communities. Many of these applications use membranes in a spiral wound configuration that contains a feed spacer. The goal of this project was to develop low‐biofouling polypropylene (PP) spacers through the functionalization of PP by a spacer arm with metal chelating ligands charged with biocidal metal ions, investigate the use of this metal‐charged polypropylene (PP) feed spacers that target biofouling control, and to use some traditional and one novel techniques to autopsy the membranes after filtration to gain a better understanding of the biofouling mechanism and how the modified spacers are affecting it. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

MINLP formulations for solving strip packing problems in LCD mother glass production

Mother glass production for liquid crystal displays involves the cutting of small rectangles from a large rectangle (strip) to minimize the length of the strip used. This is called the strip packing problem. The main concept for formulating this problem is to generate cutting patterns that can be used to produce items from the strip. This problem is a non-convex mixed integer nonlinear programming (MINLP) problem due to the bilinear terms in the demand and objective function. To obtain global optimal solutions, this problem should be transformed into several linear forms. Numerical examples based on the strip packing problem in LCD mother glass production are provided. Different objective functions for two problems are presented and compared.     

Polymer membranes for biofouling mitigation: a review

ABSTRACT

Nanofiltration (NF) membranes were introduced during the ’80s with characteristics in between those of reverse osmosis and ultrafiltration membranes. This article aims at critically reviewing advances in NF research including relevance of fabrication techniques, modifications, and current problems. We also have a comprehensive look at fouling mitigation as well as its prevention by treating NF membranes with functionalized carbon nanotubes. It was found that some parameters such as porosity, crystallinity of polymer and hydrophobicity/hydrophilicity can affect the performance of membranes. NF membranes can be widely utilized in broad spectrum of applications particularly in desalination and wastewater treatment.

Abbreviations: VA: Vertically align; MMM: Mixed matrix membrane; PAN: Polyacrylonitril; PAA: Poly(amic acid); HA: Humic Acid; BPA: Bisphenol A; MPD: m-phenylene diamine; PES: Polyether sulfone; LBL: Layer by layer; PEO: Poly(ethylene-oxide); PVA: Poly(vinyl alcohol); TR: Thermally rearranged; TR-PBO: Thermally rearranged polybenzoxazole; CVD: Chemical vapor deposition; PMMA: Poly(methy methacrylate; PET: polyetherimid; Psf: polysulfone; FSCMs: Fixed site carrier membranes; SILMs: Supported ionic liquid membranes; TFC: Thin film composite; IP: Interfacial polymerization; PE: Polyethylene; PP: Polypropylene; PC: Polycarbonate; PET: Polyethylene naphthalate; AMPS: 2-acrylamido-2-methylpropanesulfonic acid; NPs: Nanoparticles; TFC: Thin film composite; MPD: m-phenylenediamine; TMC: Trimesoyl chloride; CPES: Carboxylic polyethersulfon; ECPN: Electrically conducting polymer nanocomposites; mPDA:1,3-phenylenediamine; SWCNTs: Single wall carbon nanotubes; MWCNT: Multi wall carbon nanotubes; PVC: Polyvinyl chloride; NOMs: Natural organic matter; AAO: Anodic aluminium oxide; PVDF: Polyvinylidene fluoride; MD: Membrane distillation; PHGH: Polyhexamethylene guanidine hydrochloride; TMBPA: Tetramethyl Bisphenol A; APDEMS: Aminopropyldiethoxymethylsilane; PLGA: Poly(lactide-co-glycolide); PEVA: Poly(ethylene-co-vinyl alcohol); PCL: Poly(ε-caprolactone); PS: Polystyrene; PU: Polyurethane; PGA: Poly(glycolide); TE: Tissue engineering; SEM: Scanning electron microscopy; TEM: Transmission electron microscopy; EDX: Energy dispersive X-ray spectroscopy; BOD: Biological oxygen demand; COD: Chemical oxygen demand; TSS: Total suspended solids; SMBR: Submerged membrane bioreactor; NVP: N-vinyl-2-pyrrolidinone; NVF: N-vinylformamide; NVC: N-vinylcaprolactam; HEMA: 2-hydroxylethyl methacrylate; AA: Acrylic acid; AAm: Acrylamide; AAG: 2-Acrylamidoglycolic acid; AMPS: 2-acrylamido-methyl-propane sulfonic acid; SPMA: 3-sulfopropyl methacrylate; GAMA: d-gluconamidoethyl methacrylate; MPDSAH inner salt: [(methacryloylamino)propyl]-dimethyl (3-sulfopropyl) ammonium hydroxide inner salt; BSA: Bovine serum albumin; PDA: 2,4-phenylenediamine; EDA: Ethylene diamine; PDMSO: Poly(dimethylsiloxane); GPUs: Gas Permeation Units; ZIF: Zeolitic imidazolate framework; UF: ultrafiltration; MF: microfiltration; RO: Reverse osmosis; MD: Membrane distillation     

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non‐convex mixed‐integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on–off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non‐convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4277–4296, 2016     

化工过程综合问题MINLP算法中整型变量的连续化

化工过程系统综合问题需要同时考虑设备结构参数和工艺操作参数,一般用整型变量表示设备的取舍,用连续变量表示操作参数,这就构成一个流程的超结构,在数学形式表现为一个混合整型非线性规划（MINLP）问题。混合整型非线性规划问题的求解成为化工过程综合优化的关键。今根据超结构中整型变量的特征,提出整型变量连续化处理的思路,将MINLP问题简化为NLP问题,然后采用罚函数法求解。最后将该算法运用于加氢脱烷基化（HDA）过程综合的实例研究,结果表明该算法克服了传统方法在处理整型变量时出现的麻烦,为有效快速地进行化工过程综合优化问题提供了一种新的途径。     

Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem

The maximum likelihood method is frequently used in parameter estimation. If the structure of the model is unknown, the maximization of the likelihood function can be replaced by minimizing an information criterion. One criterion that allows this to be done is Akaike’s information criterion (AIC). Minimizing the AIC is a mixed integer non-linear programming (MINLP) problem. In this paper, three different MINLP algorithms are compared in the solution of a simultaneous model structure determination and parameter estimation problem by minimizing the AIC criterion. The problem considered appears in quantitative Fourier transformed infra red (FTIR) spectroscopy where concentration estimates of certain gas components are to be obtained from measured absorbances at different wave numbers. The resulting problem is a large MINLP problem containing several hundreds, or even thousands, of variables including a huge number of possible model structures. It is, however, found that the studied algorithms solve the considered problem in quite a small number of iterations and a reasonable CPU-time.     

Fair profit allocation in supply chain optimization with transfer price and revenue sharing: MINLP model and algorithm for cellulosic biofuel supply chains

A mixed‐integer nonlinear programming (MINLP) formulation to simultaneously optimize operational decisions as well as profit allocation mechanisms in supply chain optimization, namely material transfer prices and revenue share policies among the supply chain participants is proposed. The case of cellulosic bioethanol supply chains is specifically considered and the game‐theory Nash bargaining solution approach is employed to achieve fair allocation of profit among the collection facilities, biorefineries, and distribution centers. The structural advantages of certain supply chain participants can be taken into account by specifying different values of the negotiation‐power indicators in the generalized Nash‐type objective function. A solution strategy based on a logarithm transformation and a branch‐and‐refine algorithm for efficient global optimization of the resulting nonconvex MINLP problem is proposed. To demonstrate the application of the proposed framework, an illustrative example and a state‐wide county‐level case study on the optimization of a potential cellulosic bioethanol supply chain in Illinois are presented. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3211–3229, 2014