Novel bound contraction procedure for global optimization of bilinear MINLP problems with applications to water management problems

We propose a new method to obtain the global optimum of MINLP problems containing bilinearities. Our special method that contracts the bounds of one variable at a time allows reducing the gap between a linear lower bound and an upper bound obtained solving the original problem. Unlike some methods based on variable partitioning, our bound contraction procedure does not introduce new integers or intervals. We illustrate the method by applying it to water management problems.     

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.     

Cutting planes for improved global logic-based outer-approximation for the synthesis of process networks

In this work, we present an improved global logic-based outer-approximation method (GLBOA) for the solution of nonconvex generalized disjunctive programs (GDP). The GLBOA allows the solution of nonconvex GDP models, and is particularly useful for optimizing the synthesis of process networks, which yields MINLP models that can be highly nonconvex. However, in many cases the NLP that results from fixing the discrete decisions is much simpler to solve than the original problem. The proposed method exploits this property. Two enhancements to the basic GLBOA are presented. The first enhancement seeks to obtain feasible solutions faster by dividing the basic algorithm into two stages. The first stage seeks to find feasible solutions faster by restricting the solution time of the problems and diversifying the search. The second stage guarantees the convergence by solving the original algorithm. The second enhancement seeks to tighten the lower bound of the algorithm by the use of cutting planes. The proposed method for obtaining cutting planes, the main contribution of this work, is a separation problem based on the convex hull of the feasible region of a subset of the constraints. Results and comparison with other global solvers show that the enhancements improve the performance of the algorithm, and that it is more effective in the tested problems at finding near optimal solutions compared to general-purpose global solvers.     

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     

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems

In this paper we present a strategy to improve the relaxation for the global optimization of non-convex MINLPs. The main idea consists in recognizing that each constraint or set of constraints has a meaning that comes from the physical interpretation of the problem. When these constraints are relaxed part of this meaning is lost. Adding redundant constraints that recover that physical meaning strengthens the relaxation. We propose a methodology to find such redundant constraints based on engineering knowledge and physical insight.     

An improved decomposition algorithm for optimization under uncertainty

This paper proposes a modification to the decomposition algorithm of Ierapetritou and Pistikopoulos (1994) for process optimization under uncertainty. The key feature of our approach is to avoid imposing constraints on the uncertain parameters, thus allowing a more realistic modeling of uncertainty. A theoretical analysis of the earlier algorithm leads to the development of an improved algorithm which successfully avoids getting trapped in local minima while accounting more accurately for the trade-offs between cost and flexibility. In addition, the improved algorithm is 3–6 times faster, on the problems tested, than the original one. This is achieved by avoiding the solution of feasibility subproblems, the number of which is exponential in the number of uncertain parameters.     

A class of bilinear models for the optimization of energy conversion networks

Using principles from finite-time thermodynamics, this paper introduces a class of bilinear models suitable for financial optimization and risk management of commodity energy conversion processes. This class of high-level models is intended to predict the efficiency of energy conversion in campus scale utilities with complex energy requirements, multiple fuel sources, and significant operational flexibility. The models incorporate first and second law thermodynamic considerations. The bilinear character of these models derives from the multiplicative coupling between entropy flux and temperature driving forces that are intrinsic to the second law.Economic optimization of these models yields non-convex bilinear optimization problems. Special cases for optimal operation reduce to generalized eigenvalue problems, or more generally complex rank constraints that can be solved using numerical algebraic geometry. For general use, we propose a computational strategy based on a linear outer approximation coupled with a branch and bound methodology to reduce the search region.We demonstrate modeling and optimization using several example problems drawn from the existing literature on finite-time thermodynamics.     

用梯度法解算矿井通风网络

通过修正Scott—Hinsleym风嘲解算方法的缺陷．提出了一种新的全回路调节方法。该方法通过使所有独立回路分支风压代数和的平方和最小化的方法,建立了通风网络解算优化模型,并用梯度法对该模型进行解算,获得了一种新的风网解算算法。该方法理论上考虑到了通风网络中存在固定风量分支的情况,可实现所有回路的调节,并可实现按需分配归零误差。     

An improved framework for solving NLIPs with signomial terms in the objective or constraints to global optimality

Real application problems are often formulated as nonlinear integer programming problems or as discrete global optimization problems with signomial terms in the objective or constraints. Although various approaches have been proposed to solve the problems, they either utilize numerous extra binary variables and constraints to reconstruct the problems for finding a global solution or are unable to obtain globally optimized solutions. This study proposes a novel linearization method that employs a logarithmic number of extra binary variables and constraints to reformulate a signomial term with discrete variables. The original nonlinear integer program is therefore converted into a mixed-integer linear program solvable to obtain a global optimum. Several numerical experiments are presented to demonstrate the computational efficiency of the proposed methods in solving nonlinear integer problems, especially for treating signomial functions with large-interval variables or multiple variables.     

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.     

A new approach for global optimization of a class of MINLP problems with applications to water management and pooling problems

One of the biggest challenges in solving optimization engineering problems is rooted in the nonlinearities and nonconvexities, which arise from bilinear terms corresponding to component material balances and/or concave functions used to estimate capital cost of equipments. The procedure proposed uses an MILP lower bound constructed using partitioning of certain variables, similar to the one used by other approaches. The core of the method is to bound contract a set of variables that are not necessarily the ones being partitioned. The procedure for bound contraction consists of a novel interval elimination procedure that has several variants. Once bound contraction is exhausted the method increases the number of intervals or resorts to a branch and bound strategy where bound contraction takes place at each node. The procedure is illustrated with examples of water management and pooling problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2320–2335, 2012     

改进的教学优化算法及其应用

针对教学优化算法（TLBO）收敛速度慢,容易陷入局部最优的问题,本文提出了一种改进的方法。算法的改进主要在两方面：一是对教学因子（TF）进行自适应调整,使TF随算法迭代减小,这样算法在搜索前期采用全局搜索,搜索空间快速收敛于最优解附近,提高搜索速度,搜索后期采用局部精细搜索以获得高精度的解。二是引入信任权重,对学生已获得的知识采取部分信任的策略,避免对已获取知识的过分信任,增加学生个体与教师及学生之间的信息共享,利于算法跳出局部最优。算法在8个标准测试函数上应用,仿真结果表明改进的算法有更快的收敛速度并且能够跳出局部最优。最后将改进的算法应用到乙烯裂解炉裂解运行效益优化中,显著提高了裂解炉的效益。     

一种改进的知识进化算法及其在化工动态优化中的应用

智能优化算法在动态优化问题的求解中,一方面可以一定的概率收敛到全局最优,避免局部极值而得到了广泛应用;但另一方面,基于随机机制的仿生智能算法也面临收敛速度慢、寻优效率较低的瓶颈,限制了其工业实时应用的场合。为此,从提高智能优化算法在动态优化问题的求解效率出发,提出了一种改进的基于知识引导的进化算法结构,主要包括候选控制策略-时域与控制域的离散策略、知识库空间的进化、知识引导的种群进化。该算法分别在批式反应器等4个典型化工动态优化问题上进行了仿真验证,计算结果表明,该方法能够以较小的种群规模通过知识的引导,以较少的计算代价找到较好的全局解,有效提高了算法的收敛效率。     

一种改进的差分进化算法及其在补料分批式生化反应器动态优化中的应用

动态优化是生物化工过程中的重要课题,求解动态优化问题通常有两种方法:解析法和数值法。基于智能进化算法的数值方法在动态优化中的应用越来越广泛,但是这些方法局部寻优能力不强,容易陷入局部最优,并且求解速度相对较慢。针对这些方法的不足,提出了一种改进的差分进化算法,设计了新的局部寻优算子来增强算法的局部寻优能力,并且采用一种新的控制策略表示方法来求解动态优化问题。通过求解补料分批式生化反应器的动态优化实例,证明了算法的有效性和鲁棒性。通过与其他几种方法进行对比,实验结果表明,所提出的方法在优化结果和计算代价方面都有优势。     

Planning and scheduling of flexible process networks under uncertainty with stochastic inventory: MINLP models and algorithm

The tactical planning and scheduling of chemical process networks consisting of both dedicated and flexible processes under demand and supply uncertainty is addressed. To integrate the stochastic inventory control decisions with the production planning and scheduling, a mixed‐integer nonlinear programming (MINLP) model is proposed that captures the stochastic nature of the demand variations and supply delays using the guaranteed‐service approach. The model takes into account multiple tradeoffs and simultaneously determines the optimal selection of production schemes, purchase amounts of raw materials, sales of final products, production levels of processes, detailed cyclic production schedules for flexible processes, and working inventory and safety stock levels of all chemicals involved in the process network. To globally optimize the resulting nonconvex MINLP problems with modest computational times, the model properties are exploited and a tailored branch‐and‐refine algorithm based on the successive piecewise linear approximation is proposed. To handle the degeneracy of alternative optima in assignment configurations of production scheduling, three symmetry breaking cuts are further developed to accelerate the solution process. The application of the model and the performance of the proposed algorithm are illustrated through three examples with up to 25 chemicals and 16 processes including at most 8 production schemes for each flexible process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1511–1532, 2013     

An algorithm for the optimization of kubelka-munk absorption and scattering coefficients

A new approach to the calculation of Kubelka-Munk absorption and scattering coefficients based on linear-leastsquares techniques is proposed. This algorithm characterizes colorants by determining the coefficients from typical mixtures. Several advantages are gained over traditional methods: Absorption and scattering can be determined without use of primary binary mixtures by using production-mixture history; colorants are characterized in the same manner in which they are used; and the approach is quite flexible in terms of manipulating the calculation.     

一种改进的差分进化算法及其在化工过程优化中的应用

Differential evolution （DE） is an evolutionary optimization method, which has been successfully used in many practical cases. However, DE involves large computation time, especially, when used to optimize the compurationally expensive objective function. To overcome this .difficulty, the concept of immunity based on vaccination is used to help proliferate excellent schemata and to restrain the degenerate phenomenon. To improve the effective- ness of vaccines, a new vaccine autonomous obtaining method, and a method of deciding the probability of vacci- nation are proposed. In addition, a method for modifying the search space dynamically is proposed to enhance the possibility of converging to the true global optimum. Experiments showed that the improved DE performs better than the classical DE significantly.     

基于GPU加速求解MINLP问题的SQP并行算法

针对确定性算法求解大型复杂混合整数非线性规划的时间不可接受问题,通过对序贯二次规划算法(SQP)和图形处理器(GPU)的架构特点分析,提出了基于GPU加速策略的并行化SQP算法。算法的主要思想是通过枚举法确定二元变量的取值,在保证取值完整的基础上,使用CPU+GPU的并行策略,同时运用大量线程进行非线性规划子问题的求解。算例的数值实验结果表明:本文所提出的算法较之传统串行计算具有较好的加速效果,特别适合求解二元变量较多,约束条件相对少的MINLP问题。     

Global optimization of multicomponent distillation configurations: 1. Need for a reliable global optimization algorithm

Nonazeotropic multicomponent mixtures are often separated into products by distillation configurations containing multiple distillation columns. One method of calculating the minimum vapor duty of a configuration is to sequentially calculate the minimum vapor duty of each mixture as it is split into two streams within a given column starting from the feed column. The other method simultaneously manipulates all the splits to yield the overall minimum vapor duty of the entire configuration. Of these two methods, the sequential minimization is attractive as it can be analytically solved. However, through extensive computations, we find that the sequential minimization method is not a valid substitute for the simultaneous minimization method. As the number of components in the feed increases, the fraction of the basic configurations for which sequential method yields a reasonable estimate decreases rapidly, thereby emphasizing the need for a more robust and reliable global optimization algorithm. © 2012 American Institute of Chemical Engineers AIChE J, 59: 971–981, 2013     

遗传算法在催化体系的全局结构优化中的应用

对催化体系进行全局结构优化,搜寻基态结构对预测催化剂结构、分析反应物的吸附特性、研究多相催化反应机理、构建实际反应路径等方面至关重要。遗传算法通过交叉、变异和选择等操作,模拟了自然淘汰进化过程,来搜索势能面上的基态结构。作为一种无偏优化算法,遗传算法的优化过程不依赖于输入结构,具有很强的全局搜索能力。对遗传算法在催化体系的全局结构优化问题中的应用进行了综述,介绍了遗传算法在实空间上进行全局结构优化的基本程序框架以及近年来结合并行计算、机器学习等技术发展的改进框架,并讨论了它们在团簇优化、负载型催化剂的结构优化问题上的相关应用,为遗传算法的进一步改进以及更广泛的应用提供理论指导。