Linear-in-Parameter Models Based on Parsimonious Genetic Programming Algorithm and Its Application to Aero-Engine Start Modeling

A novel Parsimonious Genetic Programming （PGP） algorithm together with a novel aero-engine optimum data-driven dynamic start process model based on PGP is proposed. In application of this method, first, the traditional Genetic Programming（GP） is used to generate the nonlinear input-output models that are represented in a binary tree structure; then, the Orthogonal Least Squares algorithm （OLS） is used to estimate the contribution of the branches of the tree （refer to basic function term that cannot be decomposed anymore according to special rule） to the accuracy of the model, which contributes to eliminate complex redundant subtrees and enhance GP＇s convergence speed; and finally, a simple, reliable and exact linear-in-parameter nonlinear model via GP evolution is obtained. The real aero-engine start process test data simulation and the comparisons with Support Vector Machines （SVM） validate that the proposed method can generate more applicable, interpretable models and achieve comparable, even superior results to SVM.

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.

A Weighted Goal Programming Model for the DASH Diet Problem: Comparison with the Linear Programming DASH Diet Model

A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.

Application of Linear Programming Model to Refugee Migrating Problem

The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

Managing Tourism Development in the Dutch City of Utrecht using a Linear Programming Model of the Tourist Carrying Capacity

As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the adaption of the linear programming model,the paper intends to not only quantify the optimum number of visitors to Utrecht but also formulate a number of policy recommendations based on the reconstruction of this optimum.The paper draws the following conclusions:(1) tourist carrying capacity of Utrecht is not yet exceeded;(2) restrictive accommodation policy does not currently seem necessary;(3) the cultural-historical attractions are not yet optimally used;(4) investing in strategic provisions is currently not necessary.And from the conclusion,the paper further puts forward the following suggestions on the city’s tourism development strategy:(1) to identify "tourist flood plains";(2) to encourage the tourist disclosure of these alternatives;(3) to invest even more explicitly in residential tourism and,where possible,curb day tourism;(4) to introduce a new business model.

Linear Programs in Cost Accounting： A Linear Cost Model

This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. Dependent variable of linear model is unit cost. Independent variables are cost accounting variables. They are supply cost, labor cost, and administration cost. This study assumes a direct relationship between supply-labor-administration costs and unit cost. Therefore, it establishes a linear cost model. The major research question of this study is to apply linear goal programming to cost accounting. The goal of this linear program is to find unit cost of product. This study uses quantitative method and human capital method. The main research result is linear costing model itself.

Application of Linear Programming Algorithm in the Optimization of Financial Portfolio of Golden Guinea Breweries Plc, Nigeria

In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.

Integer Programming Formulations for Maximum Lifetime Broadcasting Problems in Wireless Sensor Networks

Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.

Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

基于改进云模型和线性规划优化算法的山区泥石流危险性评价

泥石流是一种由暴雨或地震诱发常发生在山区的破坏力强大的地质灾害,为了提前预防和减少其破坏能力,使用特定算法评价其危险性十分必要。采用云模型雾化特性对各评价指标权重进行一致性检验后耦合,得到合理的权重阈值区间。以线性规划优化算法通过设定目标函数后对各评价指标在权重区间内动态取值,从而得到各个泥石流沟渠最危险评分。改进了单指标的云数字特征公式,构建覆盖更全面的综合云模型,输入最大危险评分对研究区泥石流沟渠进行危险性分级。将该研究应用在汶川地震后北川县产生的72条泥石流沟渠实例中,其评价结果显示与研究区实际地形环境情况相吻合,为相似类型泥石流灾害的预防提供了新思路。

梅钢转炉合金模型开发

为降低转炉合金成本,采用线性规划为核心算法,开发了转炉合金模型。模型通过设计碳冗余质量分数和磷冗余质量分数、确定合金收得率和LF增碳质量分数等主要参数、基于优先加足低价合金的原则分配转炉合金用量,在满足钢水成分的前提下降低了合金成本,可产生经济效益3.27元/t。

低轨星座传感器资源调度的自主任务规划建模方法

低轨星座传感器资源的优化调度是复杂多约束下的任务规划问题,为了满足多个运动目标全程跟踪与监视的资源实时优化调度需求,提出一种星上自主快速求解的规划模型.在对自主任务规划问题进行详细建模的基础上,考虑各项约束条件与优化因素,将原问题转化成简易的0-1线性整数规划模型,并构建多目标跟踪试验场景对所提方法进行了仿真验证.仿真结果表明,基于简易规划模型的资源调度可实现多目标的全程跟踪与监视.

基于混合整数规划的数据中心冷却能耗优化

以广州某数据中心水蓄冷冷却系统为研究对象,提出了一种基于混合整数线性规划的模型预测控制方法.该方法以数据中心冷却系统的能耗最低为优化目标,通过对冷却系统和环境条件进行建模,并结合能源成本和冷却系统效率,确定最佳的冷水机组运行策略和水蓄冷冷却系统的时序控制.在优化过程中,考虑了冷水机组的最小连续运行时间对冷却系统能耗的影响,并确定了最佳取值,提高了机组的稳定性,减少了因冷机频繁启停带来的能耗浪费.通过全年能耗模拟,相较于传统控制方法,该方法将总能耗降低了6.52%,总运行费用降低了6.93%.

基于CSA-AFSA算法的集装箱港口连续型泊位分配优化

为提升集装箱港口运营效率,笔者研究了考虑潮汐因素与泊位偏好的连续型泊位分配问题。引入了船舶时空矩形不可重叠约束和潮汐时间窗约束,构建以最小化船舶等待、延迟离港、泊位偏离以及在港期间油耗费用和最小为目标的混合整数线性规划模型;根据模型特征,采用CPLEX求解软件、鱼群算法、布谷鸟搜索算法和布谷鸟鱼群混合算法进行求解,以计划周期为36 h的20个不同规模的船舶到港数据为研究算例,通过算例求解得到符和潮汐时间窗、泊位偏好等要求的泊位分配方案。算例求解表明:算例规模较小时,CPLEX可以在较短时间内求出最优泊位分配方案;算例规模较大时,CPLEX求解时间较长,布谷鸟鱼群混合算法可以在平均3 min内求出与CPLEX差距为0.39%~4.20%的次优解;不同算法间的对比表明,布谷鸟鱼群混合算法求解能力更优,混合算法所得泊位分配方案中,乘潮船舶的进出港时刻均在潮汐高水位时段,且85%以上的船舶在偏好泊靠点200 m内接受装卸服务。

含分布式新能源和需求响应负荷的虚拟电厂定价机制及优化调度

面对电网中分布式风电、光伏发电以及柔性负荷的广泛接入,将这些资源通过虚拟电厂(VPP)进行聚合,采用合理的电价机制来引导用户参与需求响应,可以有效提升新能源的消纳能力并降低整体运营成本。传统的分时电价机制往往难以实现需求响应负荷与新能源出力的良好匹配,可能会导致需求响应的不合理或过度反应。为此,针对包括分布式风电、分布式光伏发电和柔性负荷的VPP,提出了一种基于新能源出力的VPP内部定价机制,并设置电力交易优先级来引导VPP内部各资源优化运行,以VPP的整体运营成本最小化为目标,构建了一个VPP优化调度的混合整数线性规划模型。基于内蒙古某地区的实际数据进行仿真计算,结果表明,与基于传统分时电价的优化结果相比,该方法能显著提高新能源的利用率并降低VPP的运行费用。

线性规划的历史与发展

本文介绍了线性规划的起源与发展过程,对比了丹齐格与坎托罗维奇各自在线性规划方面的贡献.

基于CPM的多模式资源约束项目调度建模与复杂度分析

为有效降低多模式资源约束项目调度模型的复杂度和解空间,构建3类混合整数线性规划模型。运用紧上界TTUB缩减时间序列T的上界和关键路径法缩减各项活动结束时间的上下界,以降低模型复杂度和解空间。为验证改进模型的有效性,从MRCPSP标杆案例库中选取1106组规模不等的算例进行求解。结果表明,基于CPM的多模式资源约束项目调度模型解空间更小;决策变量同比缩小3~65倍,约束数同比缩小1~4倍;平均求解时间同比减少53%~112%,求解性能显著优于其他模型。为验证紧上界T_(TUB)的参数α性能,1106组算例结果表明,α越接近1,模型的复杂度越低,解空间越小。但随着算例规模增加,算例可行解探寻难度增加。因此,对大规模算例,α值应适当放宽。

考虑路径关系的干线多路径绿波优化模型

针对协调路径数目增加后绿波带宽变窄问题,本文提出一种考虑路径关系的多路径协调控制优化模型。分析路径的相关关系,构建上下行分区和路径分解模型;引入子区划分参数,改进经典多路径模型,构建子区内部协调约束;分析路径在相邻子区之间的衔接特征,构建子区间连接性约束条件;综合考虑子路径长度和流量构建权重系数,以各子路径绿波带宽加权和最大为优化目标,建立多路径协调控制优化模型。为验证模型的有效性,选取南京市典型干道为研究对象开展案例分析。实验结果表明,本文提出的模型可以有效增大绿波带宽,相较于对比模型,加权绿波带宽和提高49.44%。利用VISSIM验证了方案的应用效果,仿真结果表明,本文模型方案可以获得更高的通行效益。相较于对比方案,关键路径车均延误和车均停车次数明显降低,干道车均延误和车均停车次数分别降低了20%和27%,车辆平均速度提高了17%。本文模型可为城市道路干线协调控制提供理论基础。

基于换电的共享电动汽车调度与服务定价

为解决共享电动汽车出行模式车辆失衡与电能补给问题,基于集充统配换电模式,考虑共享电动汽车电能补给、换电站选址与电池配送路径间的耦合关系,基于时空网络构建以最大化利润为目标的共享电动汽车调度与服务定价优化模型,并通过共享电动汽车需求-价格函数逆变换,将非线性非凸模型转换成更易求解的非线性凸模型。数值试验结果表明:协同决策换电站位置、电池配送路径、共享电动汽车调度方案与服务价格,可提高共享电动汽车出行服务商利润;基于割线的外逼近算法比基于切线的外逼近算法和拉格朗日松弛算法更适于求解所提出的模型。参数敏感度分析结果显示,潜在共享电动汽车出行需求与电能可得性都是影响共享电动汽车出行服务商利润的重要因素。