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.

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.

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.

Modified Filled Function to Solve NonlinearProgramming Problem

Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.

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.

A Hybrid Dynamic Programming Method for Concave Resource Allocation Problems

Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.

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。

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。

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。

基于弹性需求和动态定价的共享泊位分配

为解决共享车位管理中的车位分配与定价问题,考虑了价格变化对于用户不同停车时长选择的影响,分析在不同停车收费标准下用户停车时长选择的概率,并采用多项式拟合得到精细化的共享停车需求价格弹性函数。进而,为实现停车场价格的动态调整与车位分配,以平台收益最大与用户步行距离最小为目标,构建基于弹性需求和动态定价的泊位分配非线性混合整数规划模型,并设计了遗传算法。最后,设计了包含3个停车场共1000个泊位、共享平台运营时长为3 h的算例,对模型及算法加以验证,通过对比分析,基于弹性需求和动态定价的共享泊位分配方案相比于静态定价,实现平台收益增加19%且满足了大部分停车需求,说明动态定价下共享泊位分配模型及算法的有效性,为共享平台的车位管理提供了新思路。

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。

无人机通信中的资源分配及部署位置联合优化

为提升基于正交频分多址接入模式无人机辅助无线通信系统的网络性能,首先,以提升用户的公平性为系统方案设计指标,将包括子信道分配、调制模式选择、功率分配等通信资源和无人机位置联合建模为一个混合整数非线性优化问题;进一步,利用迭代优化的方式解决变量耦合性及非凸性等问题,将最大-最小问题转换为两个子问题:子信道分配和调制方式选择联合优化、无人机位置和子信道功率联合优化;然后,通过适当变换将子信道分配和调制方式选择联合优化建模为0-1线性优化问题进行求解,而无人机位置和子信道功率联合优化建模为凸优化问题求解;最后,进行实验仿真验证.研究结果表明,所提联合优化算法相比基本方案可有效提升网络用户的公平性.

多设备多任务场景下基于改进粒子群优化的计算卸载策略

在移动边缘计算网络中,针对多用户场景下本地设备上多个计算密集型任务的计算卸载问题,为获得最优的任务卸载决策和资源分配方案,提出了一种基于改进粒子群优化的计算卸载策略。首先,综合考虑时延和能耗相关的计算卸载总代价以及服务器任务均衡,通过本地设备的剩余能量和充电状态信息自适应调整时延与能耗权重,以最小化系统总代价为目标,建立多用户、多任务、多服务器的计算卸载模型。然后,使用改进粒子群优化算法来求解该问题,最终获得最优的任务卸载决策和资源分配方案。仿真结果表明,该方案相对于基于遗传算法的卸载方案,能够减小20%系统代价。

基于混合遗传算法的可变尺寸货物装箱问题研究

目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合整数规划模型进行求解,采用一种分段线性化方法,将该非线性模型进行线性化处理。由于所研究问题具有NP-hard属性,无论是CPLEX还是LINGO都无法有效求解大规模算例,因此设计一种有效结合遗传算法与深度、底部、左部方向优先装载(Deepest bottom left with fill,DBLF)的算法。结果大小规模算例实验验证结果表明,混合遗传算法能够在合理时间内获得最优解或近似最优解。结论所提出的可变尺寸包装方案有效提高了装载率,有益于客户和物流公司。

考虑负外部性成本的铁矿石航线配船多目标优化

针对实际铁矿石航运过程中所存在的船舶运营导致负外部性内部化问题,综合考虑船舶海上运输所造成的环境影响、港口拥堵以及交通事故等负外部性要素,并对其进行量化评估。通过分析铁矿石海上运输活动,将负外部性问题与航线配船相结合考虑,以负外部性成本最低与营运利润最大为目标,建立了铁矿石航线配船双目标优化模型,采用改进遗传算法进行求解与验证。以从巴西经过好望角到中国的3条铁矿石航线为例,对模型进行求解验证,并对船型和燃油价格进行灵敏度分析。结果表明:负外部性成本在航运企业运营收益中是不容忽略的,合理的船型运力配比在运输过程中会显著地减少负外部性成本。随着燃油价格上涨,会导致负外部成本大幅增加。可为航运相关企业提出优化建议,并为政府宏观调控运力和航运企业制定运输计划提供参考。