An Exact Penalty Approach for Mixed Integer Nonlinear Programming Problems

We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.

Nonlinear Model-Based Process Operation under UncertaintyUsing Exact Parametric Programming

In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onprocess synthesis problems. The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms, with the first one being developed for the deterministic case, and thesecond for the parametric case （p-MINLP）. The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker （KKT） conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution tech-niques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, twoprocess synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicitfunction of the uncertain parameters.

基于机会约束MINLP模型的多工况氢气网络操作优化技术

随着日益严格的环保标准以及新能源需求的不断增加,氢气已经成为炼油厂的重要资源。针对炼油厂存在多种工况的情况,在氢源产氢量、氢阱耗氢量、市场价格不确定的环境下,以氢气网络运行与CO_(2)排放成本(TOEC)之和为目标,考虑氢源标况流量、氢阱标况流量、氢气含量、压缩机、变压吸附(PSA)装置、燃料和管道约束,建立了多工况机会约束混合整数非线性规划(MCC-MINLP)氢气网络操作优化模型。对某炼油厂涉氢装置运行数据进行拟合,得到不同工况下产氢量与耗氢量的分布情况后,在不同置信水平下求解MCC-MINLP模型,得到了各工况的氢气网络最优操作方案。计算结果表明,通过增加一套PSA装置以及对应管道,可以减少15.17%~16.68%的新氢使用量并优化原氢气网络结构,优化后氢气网络的TOEC降低了2.19%~2.34%。

Hierarchical On-line Scheduling of Multiproduct Batch Plants with a Combined Approach of Mathematical Programming and Genetic Algorithm

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.

Synthesis of refrigeration system based on generalized disjunctive programming model

Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is developed for the optimal design of refrigeration cycle and heat exchanger network(HEN) simultaneously. Taking the heat integration between the external heat sources/sinks and the refrigeration cycle into consideration, a superstructure with sub-coolers is developed. Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming(GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system. The GDP model is then reformulated as a Mixed Integer Nonlinear Programming(MINLP) problem with the aid of binary variables and Big-M Constraint Method. The efficacy of the process synthesis model is demonstrated by a case study of ethylene refrigeration system. The result shows that the optimization can significantly reduce the exergy loss as well as the total compression shaft work.

基于时间约束的单源/p个中转点配送系统的MINLP模型

配送系统设计时,除了使系统的总费用最小外,还要满足各需求点对时间的要求。在说明了建模的假设条件后,建立了考虑时间约束的单源、p个中转点配送系统的混合整数非线性规划(MINLP)模型。根据模型的特殊结构开发了一种求解全局最优解的启发式算法,用Matlab编写了算法的计算程序,使用LINGO和Matlab软件将该算法与分枝定界法和舍入松弛法进行了比较,结果表明该启发式算法在寻求全局最优解和计算时间上都较其他两种方法更优。最后用实际调研的数据作为一个算例对模型进行了数值演算。

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。

基于MINLP模型的飞机冲突解脱研究

在飞机冲突避免和解脱问题中,为避免发生各种可能的冲突,所有飞机在飞行时彼此之间的距离必须要大于给定的最小安全间隔标准。针对同一空域中自由飞行的有限架飞机之间的冲突问题,提出一种基于速度和航向角变化两种策略相结合的混合整数非线性规划(MINLP)模型,以实现彼此的分离。算例仿真方面通过与集中于一种策略的冲突解脱模型进行比较,验证所提模型的有效性,并且其结果显示MINLP模型不仅可以利用全局优化软件在较短时间内为每架飞机提供一个最优解决方案,而且还能有效提高飞机在飞行过程中的安全性。

Optimal synthesis of compression refrigeration system using a novel MINLP approach

The optimal design of a compression refrigeration system(CRS) with multiple temperature levels is very important to chemical process industries and also represents considerable challenges in process systems engineering. In this paper, a general methodology for the optimal synthesis of the CRS, which simultaneously integrates CRS and Heat Exchanger Networks(HEN) to minimize the total compressor shaft work consumption based on an MINLP model, has been proposed. The major contribution of this method is in addressing the optimal design of refrigeration cycle with variable refrigeration temperature levels. The method can be used to make major decisions in the CRS design, such as the number of levels, temperature levels, and heat transfer duties. The performance of the developed methodology has been illustrated with a case study of an ethylene CRS in an industrial ethylene plant, and the optimal solution has been examined by rigorous simulations in Aspen Plus to verify its feasibility and consistency.

解决高维INLP和MINLP问题的混沌差分进化算法

为改进差分进化(Differential Evolution,DE)算法的搜索能力,提出一种新的混沌差分进化算法(CGLSDE).首先,该算法利用混沌序列替换DE参数并采用混沌全局搜索算法来改进DE的全局搜索能力;其次,CGLSDE算法还采用了单维和多维的混沌局部搜索来改进DE的局部搜索能力.仿真结果表明:CGLSDE算法在解决高维整数非线性规划(INLP)问题和高维混合整数非线性(MINLP)问题上,其性能要好于其它3种混沌差分进化算法.

Modeling and optimization methods of integrated production planning for steel plate mill with flexible customization

With diversified requirements and varying manufacturing environments, the optimal production planning for a steel mill becomes more flexible and complicated. The flexibility provides operators with auxiliary requirements through an implementable integrated production planning. In this paper, a mixed-integer nonlinear programming(MINLP) model is proposed for the optimal planning that incorporates various manufacturing constraints and flexibility in a steel plate mill. Furthermore, two solution strategies are developed to overcome the weakness in solving the MINLP problem directly. The first one is to transform the original MINLP formulation to an approximate mixed integer linear programming using a classic linearization method. The second one is to decompose the original model using a branch-and-bound based iterative method. Computational experiments on various instances are presented in terms of the effectiveness and applicability. The result shows that the second method performs better in computational efforts and solution accuracy.

重大突发公共卫生事件中的方舱医院建设情景重建研究

方舱医院建设是应对各类重大突发公共卫生事件的一项重要举措。现有研究大多从医学或政府管理视角定性地探讨方舱医院发挥的重要作用,还鲜有从情景重建视角研究方舱医院床位扩容的最优时空分布。本文首先构建针对重大突发公共卫生事件演化的SEIHRD模型,继而将方舱医院床位扩容问题构建为有限应急资源分配组合优化模型并设计免疫优化算法进行求解。测试结果显示,本文所给出的方舱医院床位扩容时空分布优化方案,能够对重大突发公共卫生事件中的方舱医院建设情景进行有效重建。方舱医院床位数量及其时间节点设置对累计感染者人数具有显著影响,这表明在疫情暴发初期尽早设立方舱医院,能够有效提升收治率、减少总感染人数。同时也要注意,应急救援资金投入存在阈值效应,需要设计合理的方舱医院床位扩容方案以避免应急预算资源的过度浪费。

铁路枢纽双编组站静态配流协同优化研究

枢纽内跨编组站进行协同配流有助于优化枢纽内的车流接续,提高全局配流质量。引入跨编组站协同配流思想,构建铁路枢纽双编组站静态配流协同优化模型,以最小化双编组站的配流总代价、最大化双编组站的总满轴列车数为优化目标,考虑车流量约束、列车到解编发作业与枢纽小运转列车走行的接续时间约束、出发列车满轴与不违编约束、调机资源使用约束。以列车等级、编组去向数及出发时刻排序作为配流代价。设计理想点算法将多目标转化为单目标进行求解,最后运用算例对模型及算法的有效性进行验证。结果表明,双编组站联合配流相较于两编组站单独配流,可使满轴列车总数增加1列、站存车总数减少13辆、配流总代价降低5.4%,从而达到更佳的配流效果。

耦合有机朗肯循环的换热网络全局优化

针对换热网络与有机朗肯循环耦合集成优化问题,建立了严谨的混合整数非线性规划(MINLP)模型。同时,通过添加与物流匹配的关键约束,剔除掉重复性的网络结构,开发了一种新型的枚举算法,将复杂的MINLP模型分解为混合整数线性规划(MILP)和非线性规划(NLP)两个子模型。迭代运行MILP模型,枚举出所有可行的网络结构;再利用全局求解器BARON优化每一个网络结构所对应的NLP模型,求得固定结构的年度总费用;最后对比所有网络结构的年度总费用,筛选出全局最优的设计方案。案例分析结果表明,该算法仅需16 s就能收敛至全局最优解,与文献相比,年度总费用降低33.4%,且所提出的网络结构约束能使重复性的网络结构数量减少81.25%,从而提高算法的优化求解效率。

考虑新能源随机波动和T接线的城市电网连锁故障风险评估

新能源的大量接入给城市电网的安全运行和重要用户可靠供电带来很大挑战,其功率的随机波动易引发电网出现连锁故障风险。提出了一种考虑新能源出力随机波动和城市电网110k V网架T接线开关投切的连锁故障风险评估方法。该方法在连锁故障发生概率和后果严重度的计算中都计及了系统状态的概率分布特性的影响,并采用基于半不变量法的概率潮流计算反映系统状态与新能源功率二者的概率分布特性之间的关系。另外,建立包含110 kV网架T接线开关投切的最小切负荷的混合整数非线性规划模型,并以最小切负荷量来表征系统在连锁故障的严重度。此优化模型通过决策故障下的各组T接线开关的投切状态,减少连锁故障下的切负荷量,进而有效降低连锁故障的风险。同时,通过机会约束描述重要用户负荷节点电压的安全运行范围,以确保重要用户负荷不停电的概率满足给定的置信水平,从而保证重要用户的安全可靠供电。最后,通过某个实际城市片区电网算例验证了所提出的连锁故障风险评估方法的正确有效性。

考虑空间需求不均的模块化公交线路运行方案优化研究

传统固定容量公交车辆难以应对公交线路上空间分布不均的需求。为解决这一问题,引入模块化公交车辆,通过编组与解编的方式实现车队在运行中的容量动态变化,以更贴合需求在空间上的变化。基于运行时空图重构的方法,建立描述模块化公交线路运行方案的优化模型,所构建模型为混合整数非线性规划(Mixed Integer-Nonlinear Program,MINLP)模型,模型决策变量包括车队的运行方案以及模块化公交单元的运行方案。为方便求解,采用时间离散化手段,通过一系列方法将所构建的MINLP模型转化为易于求解的混合整数线性规划(Mixed Integer-Linear Program,MILP)模型,并基于成都市真实公交线路与乘客需求数据进行案例分析。实验结果表明,与传统容量固定式公交相比,模块化公交的应用能够使乘客成本降低11.44%,运营成本降低31.35%,综合降低20.32%的系统总成本。敏感性分析实验结果分析了系统供给与需求变化对系统成本产生的影响。

基于子系统规模调配的烯烃生产过程模拟与优化

针对单个烯烃生产系统节能潜力有限的问题,提出基于烯烃生产子系统规模调配的方法,构建混合整数非线性规划(MINLP)优化模型。以单位产量1 t×h^(-1)为基准规模,当丙烷脱氢和乙烷裂解的规模系数分别为50.0和89.4时(即产量分别为50.0 t×h^(-1)和89.4 t×h^(-1)),系统的能量回收率达到最大,为82.6%。与两者独立子系统相比,公用工程负荷减少502.7 MW,对应的中低压蒸气消耗量减少544.9 t×h^(-1),电能减少0.5 MW,碳排放量减少0.5 t×h^(-1),节能减排的效果非常显著。结果表明,多个系统间能量交互可以有效提高能量回收率,且最优的规模系数使系统整体能量回收率达到最大。

天然气管网稳态运行优化模型的非线性界增强方法

天然气管网稳态运行优化问题在提升能源使用效率、降低运行成本等多方面发挥着重要的作用。该问题由于网络结构复杂、规模大、非线性程度高,所以建模成的混合整数非线性规划模型求解难度非常大。本文基于混合整数线性规划的界增强方法,提出了适用于该问题结构的非线性界增强方法,能够缩紧变量的上下界,使得在线性化方法中更好地逼近原混合整数非线性规划模型。数值结果显示新的方法能够得到更优的可行解,并且加快了天然气管网稳态运行优化问题的求解。

潮汐客流需求驱动的地铁列车不成对运行图节能优化方法

针对城市轨道交通客流潮汐现象引起的大客流方向乘客滞留和小客流方向运力虚靡且牵引能耗高的问题,本文提出一种结合快慢车和变编组的不成对运输组织策略,并结合变编组技术提升运力供给灵活度的同时减少运能浪费,此外,开行部分跨站快车加速车底周转。基于此,构建开行方案、时刻表与车底运用计划协同优化模型,决策列车的双向开行频率、编组类型、停站方案、首站发车时刻及车底周转计划,从而最小化乘客的总旅行时间和全线总牵引能耗成本;并设计定制的变邻域搜索算法求解混合整数非线性规划模型。广州地铁14号线案例结果表明:与实际的成对运输方案相比,本文不成对运行方案可以将乘客总旅行时间减少6.52%,全线总牵引能耗降低34.20%,总目标函数减少11.40%;快车的开行加速了车底周转,减少了6列上线列车单元数量,可以更好地实现不成对运输组织;变编组技术可以进一步提升不成对运输计划的灵活性,大幅缩减上线列车单元数量,使线路的平均满载率提升约20%,线路总牵引能耗优化率提升约33%。结合快慢车和变编组技术的不成对运输策略实现运力精准灵活配置的同时节约列车运行能耗成本,达到运营降本增效的目的。