Referee assignment in the Chilean football league using integer programming and patterns

This article uses integer linear programming to address the referee assignment problem in the First Division of the Chilean professional football league. The proposed approach considers balance in the number of matches each referee must officiate, the frequency of each referee being assigned to a given team, the distance each referee must travel over the course of a season, and the appropriate pairings of referee experience or skill category with the importance of the matches. Two methodologies are studied, one traditional and the other a pattern‐based formulation inspired by the home‐away patterns for scheduling season match calendars. Both methodologies are tested in real‐world and experimental instances, reporting results that improve significantly on the manual assignments. The pattern‐based formulation attains major reductions in execution times, solving real instances to optimality in just a few seconds, while the traditional one takes anywhere from several minutes to more than an hour.     

Sports scheduling: Problems and applications

Sports scheduling problems mainly consist in determining the date and the venue in which each game of a tournament will be played. Integer programming, constraint programming, metaheuristics, and hybrid methods have been successfully applied to the solution of different variants of this problem. This paper provides an introductory review of fundamental problems in sports scheduling and their formulations, followed by a survey of applications of optimization methods to scheduling problems in professional leagues of different sport disciplines such as football, baseball, basketball, cricket, and hockey. A case study illustrates a real‐life application of integer programming to the schedule of the yearly Brazilian football tournament.     

Modeling and analysis for multi-period, multi-product and multi-resource production scheduling

This study presents a framework for solving the multi-period, multi-product and multi-resource production-scheduling (M³PS) problem. Practically, the main concern for an M³PS problem is how to satisfy two management policies: (1) each product is manufactured in a continuous manner so that once the product is on a production line, it will complete its production procedure without interruption, and (2) the number of the product's types is limited during one period. By defining the decision variables and taking into account the machine's capacity and the customers' demand, a mixed integer programming (MIP) Model is formulated. To solve this MIP problem, a two-phase approach is proposed. In phase 1, the search space of the MIP Model is transformed into a preliminary pattern by a heuristic mining algorithm so that a hyper assignment problem can be formed as a reference model to be solved. In phase 2, a stochastic global optimization procedure that incorporates a genetic algorithm with neighborhood search techniques is designed to obtain the optimal solution. A numerical experiment is presented with an illustration, and it shows that the proposed model is adequate to cope with complicate scheduling problems.     

A genetic algorithm-based approach for solving the resource-sharing and scheduling problem

We introduce a heuristic that is based on a unique genetic algorithm (GA) to solve the resource-sharing and scheduling problem (RSSP). This problem was previously formulated as a continuous-time mixed integer linear programming model and was solved optimally using a branch-and-bound (B&B) algorithm. The RSSP considers the use of a set of resources for the production of several products. Producing each product requires a set of operations with precedence relationships among them. Each operation can be performed using alternative modes which define the subset of the resources needed, and an operation may share different resources simultaneously. The problem is to select a single mode for each operation and accordingly to schedule the resources, while minimizing the makespan time. The GA we propose is based on a new encoding schema that adopts the structure of a DNA in nature. In our experiments we compared the effectiveness and runtime of our GA versus a B&B algorithm and two truncated B&B algorithms that we developed on a set of 118 problem instances. The results demonstrate that the GA solved all the problems (10 runs each), and reaches optimality in 75% of the runs, had an average deviation of less than 1% from the optimal makespan, and a runtime that was much less sensitive to the size of the problem instance.     

A Hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization

Hybrid methods are promising tools in integer programming, as they combine the best features of different methods in a complementary fashion. This paper presents such a framework, integrating the notions of genetic algorithm, linear programming, and ordinal optimization in an effort to shorten computation times for large and/or difficult integer programming problems. Capitalizing on the central idea of ordinal optimization and on the learning capability of genetic algorithms to quickly generate good feasible solutions, and then using linear programming to solve the problem that results from fixing the integer part of the solution, one may be able to obtain solutions that are close to optimal. Indeed ordinal optimization guarantees the quality of the solutions found. Numerical testing on a real-life complex scheduling problem demonstrates the effectiveness and efficiency of this approach.     

Modeling and solving the project selection and scheduling

This paper considers the integrated bi-objective problem of projects selection and scheduling to optimize both total expected benefit and resource usage variation. The benefit is time-dependent. Although this integrated problem has become a very active field of research, the available model and algorithms suffer from serious shortcomings. This paper analyzes the available methods and develops a novel mathematical model, in form of a mixed integer linear program, for the problem. Then, it proposes an ant colony optimization algorithm employing four features of ant generation, colonial, Pareto front updating, and pheromone updating mechanisms. To evaluate the proposed algorithm, it is compared with two available genetic algorithm and scatter search. Using comprehensive numerical experiments and statistical tools, it is shown that the proposed ant colony optimization outperforms the two available algorithms.     

基于预防维护的单机调度问题

在两种维护约束下,研究完工时间之和最小化的单机调度问题.第1种维护约束是,固定周期预防维护;第2种维护约束是,机器工作期间可连续加工的最大工件个数受限.对于这种带有约束的调度问题,根据问题的规模,采用4种方法进行求解.针对小规模问题,建立一个二值整数规划模型,并根据最优解的特性制定剪枝规则,进而给出分支定界算法.针对中...     

基于改进遗传算法的泊位岸桥协调调度优化

针对集装箱码头资源调度不合理造成资源浪费的问题,在考虑岸桥装卸成本的基础上,以在港集装箱船总的作业成本最小为优化目标,建立了基于非线性混合整数规划的泊位岸桥协调调度优化模型。为使模型更加接近码头操作的实际情况,模型假设船舶装卸时间依赖于为其分配的岸桥数。采用基于可拓关联函数的改进遗传算法对模型进行求解。改进算法强调了不可行解的重要性,用可拓关联度来衡量种群中不可行解的优劣程度,通过在种群迭代中始终保持一定数量的不可行解来维持种群多样性,从而克服传统算法局部搜索能力较差的缺陷。数值实验验证了模型和算法的可行性和有效性,与不考虑岸桥装卸成本的模型相比,能够有效减少港口资源的浪费。     

化工工业多品种成批轮番生产的集成分批与调度

针对化工工业流程式多品种成批轮番生产集成分批与调度问题,分析多阶段、共享设备、物料输入输出变动转化率、库存限制和品种切换调整时间的工艺特点,建立连续时间表示的混合整数线性规划模型,提出二维粒子群优化算法。设计粒子编码为生产设备的加工状态,通过有效的解码程序将粒子解释为分批和调度。算法采用收缩算子提高局部求精能力,并引入发散算子和速度扰动策略保持种群的多样性。实验结果表明了所提出的算法具有良好的性能。     

Inter‐sample avoidance in trajectory optimizers using mixed‐integer linear programming

This paper proposes an extension to trajectory optimization using mixed‐integer linear programming. The purpose of the extension is to ensure that avoidance constraints are respected at all times between discrete samples, not just at the sampling times themselves. The method is very simple and involves applying the same switched constraints at adjacent time steps. This requires fewer additional constraints than the existing approach and is shown to reduce computation time. A key benefit of efficient inter‐sample avoidance is the facility to reduce the number of time steps without having to compensate by enlarging the obstacles. A further extension to the principle is presented to account for curved paths between samples, proving useful in cases where narrow passageways are traversed. Copyright © 2013 John Wiley & Sons, Ltd.     

Inventory Minimization and Production Scheduling: the Case of a Large Hong Kong Company

The background of this study is a rather classical but complex inventory control/production planning/line scheduling problem of a major soft-drink company in Hong Kong. The issue that stands out for this many-product high-sales manufacturer is the storage space of its central warehouse, which often finds itself in the state of overflow or near capacity with finished goods and work-in-process inventory. This phenomenon can create immediate interruptions of production, capital tie-ups and subsequent potential of lost sales. Another obviously important concern is the meeting of forecast demands. A mathematical modelling approach that entails techniques of multi-period aggregate optimization is proposed to tackle the overall problem. The dual objectives are to achieve better production planning and line scheduling in order to minimize inventory build-up and maximize demand satisfaction. Numerical results for a sample problem are reported as an illustration to this proposed two-phase approach.     

An ILS heuristic for the ship scheduling problem: application in the oil industry

This paper addresses a real‐life rescheduling problem of a pipe‐laying support vessel (PLSV) fleet in charge of subsea oil well connections. The short‐term schedule of these vessels is subject to uncertainties inherent to its operations, resulting in ships idleness or delays in oil production. The objective of this study is to develop methods to support a Brazilian oil and gas company in overcoming impacts caused by operational disruptions, while reaching its planned production level. The PLSV rescheduling problem was treated as an identical parallel machine scheduling problem, where the machines represent the vessels and the jobs are the activities for the subsea well connections. We propose a mathematical programming model and a method based on the iterated local search (ILS) metaheuristic to solve the problem. This paper contributes to this by considering simultaneously setup times, machine eligibility, release dates, due dates, and machine availability. Both methods were applied on 10 instances based on real PLSV data. Taking into account an objective function that measures the operational impact on schedules, the ILS provided an average improvement above 91% in schedules when compared to the initial solution provided by the studied company. The ILS outperformed a mathematical programming model for the problem, in eight instances, within a 30‐minute execution time limit, fitting to the company process.     

考虑学习效应的单人作业车间调度算法

单人负责多台机器的单一工序作业车间场景中,工人由于重复操作机器而产生学习效应.针对考虑依赖工件位置学习效应的单人单工序作业车间最小化最大完工时间的调度问题,建立一种混合整数规划模型.为解决该问题,设计一个考虑学习效应的贪婪算子,利用该算子构造两种贪婪算法,并提出一种基于贪婪的模拟退火算法.为衡量混合整数规划模型、贪婪算法和基于贪婪的模拟退火算法的性能,设计两种规模问题的数据实验.通过实验得出:现代混合整数规划模型求解器可以解决机器数量和工件总数量乘积小于75的小规模问题;基于贪婪的模拟退火算法求解此问题具有有效性,适用于各种规模的问题;间隔插入贪婪算法解决此问题速度较快,效果良好,可以应用于需要快速求解的场景.     

A hybrid evolutionary algorithm for task scheduling and data assignment of data-intensive scientific workflows on clouds

A growing number of data- and compute-intensive experiments have been modeled as scientific workflows in the last decade. Meanwhile, clouds have emerged as a prominent environment to execute this type of workflows. In this scenario, the investigation of workflow scheduling strategies, aiming at reducing its execution times, became a top priority and a very popular research field. However, few work consider the problem of data file assignment when solving the task scheduling problem. Usually, a workflow is represented by a graph where nodes represent tasks and the scheduling problem consists in allocating tasks to machines to be executed at a predefined time aiming at reducing the makespan of the whole workflow. In this article, we show that the scheduling of scientific workflows can be improved when both task scheduling and the data file assignment problems are treated together. Thus, we propose a new workflow representation, where nodes of the workflow graph represent either tasks or data files, and define the Task Scheduling and Data Assignment Problem (TaSDAP), considering this new model. We formulated this problem as an integer programming problem. Moreover, a hybrid evolutionary algorithm for solving it, named HEA-TaSDAP, is also introduced. To evaluate our approach we conducted two types of experiments: theoretical and practical ones. At first, we compared HEA-TaSDAP with the solutions produced by the mathematical formulation and by other works from related literature. Then, we considered real executions in Amazon EC2 cloud using a real scientific workflow use case (SciPhy for phylogenetic analyses). In all experiments, HEA-TaSDAP outperformed the other classical approaches from the related literature, such as Min–Min and HEFT.     

学习驱动的分布式异构混合流水车间批量流能效调度优化

本文研究了分布式异构混合流水车间批量流能效调度问题, 其中每个工厂的加工效率不同, 工件可以分割成若干子批进入加工系统. 以最大完成时间和总能耗为优化目标, 建立了混合整数规划模型. 本文提出了一种学习驱动的多目标进化算法, 包括学习驱动的全局搜索和局部搜索. 引入Q学习作为学习引擎, 以种群和非支配解集的评价作为环境反馈信号, 通过不断的学习来动态指导搜索操作的选择; 基于问题特征, 设计了算法的状态集、动作集和奖励机制. Q学习的引入能够及时感知当前搜索的状态, 减少搜索操作的盲目性, 提高搜索的效率. 通过对仿真数据集的测试, 表明所提出算法能够有效地求解分布式异构混合流水车间批量流能效调度问题.     

A linearized polynomial mixed integer programming model for the integration of process planning and scheduling

This paper presents a linearized polynomial mixed-integer programming model (PMIPM) for the integration of process planning and scheduling problem. First, the integration problem is modeled as a PMIPM in which some of the terms are of products of up to three variables, of both binary and continuous in nature. Then, an equivalent linearized model is derived from the polynomial model by applying certain linearization techniques. Although the linearized models have more variables and constraints than their polynomial counterparts, they are potentially solvable to the optimum in comparison to their equivalent polynomial models. Experiments show that the linearized model possesses certain characteristics that are absent from other models in the literature, and provides a fundamental framework for further research in this area.     

基于群智能算法的自动化码头协同调度研究

为了提高码头作业效率和服务水平,保障港口在激烈竞争中的生存和发展,研究自动化码头自动引导车、岸桥和自动化轨道吊的协同调度问题,根据边装边卸作业模式,建立混合整数规划模型,以完成船舶装卸时间最小化为目标,利用群智能算法中多种算法进行求解,通过数值实验证明了该模型的有效性,获得优化的调度方案,并对不同算法的性能进行比较,结果表明启发式的混合遗传粒子群算法能够在最短的时间内获得最优解,其在求解的质量和速度方面都表现得更为优秀,可以应用于码头的实际作业中。     

带作业范围约束的岸桥调度模型及其算法设计

受电缆线坑位置与缆线长度的限制,岸桥作业只能在一定的横向移动范围之内。考虑到这一现实要求,结合岸桥作业禁止跨越与安全距离等特有约束,以最小化装卸作业的makespan为目标,构建了新的岸桥作业调度混合整数规划模型。针对问题的NP-hard特性,设计了一种混合模拟退火算法,运用启发式算法生成质量较高的初始解,结合遗传算法的变异运算生成邻域新解,增强了解的多样性,引入禁忌搜索算法的禁忌表操作,避免了循环搜索,提高了求解效率。大规模实验结果表明所建立的模型是有效的,算法的求解质量与效率明显优于标准模拟退火算法与禁忌搜索算法。当实验规模逐渐增大时,与LINGO软件相比,算法在求解效率方面的优势越来越明显。     

性能随时间衰减的锅炉蒸汽系统循环调度

针对性能随时间衰减的锅炉蒸汽系统的循环调度问题进行了研究.首先建立了描述该问题的混合整数非线性模型;然后提出了确定各锅炉循环运行状态的时间分段策略以简化问题的求解;最后应用列队竞争算法对该混合整数非线性规划问题进行优化计算.采用某锅炉蒸汽系统循环调度的实例对所提出的方法进行了验证,计算结果表明循环调度优化能够获得比人工随机安排更优的调度方案,节能效果十分明显.     

Variable assignment and instruction scheduling for processor with multi-module memory

Multi-module memory has been employed in high-end digital signal processing system (DSP). It provides high memory bandwidth and low power operating mode for energy savings. However, making full use of these architectural features is a challenging problem for code optimization. In this paper, we propose an integer linear programming (ILP) model to optimize the performance and energy consumption of multi-module memories by solving variable assignment, instruction scheduling and operating mode setting problems simultaneously. The combined effect of performance and energy saving requirements has been considered as well. Specially, we develop two optimization techniques to improve the computation efficiency of our ILP model. The experimental results show that the optimal performance and energy solution can be achieved within a reasonable amount of time.