Best Practice Simulated Annealing for the Airline Crew Scheduling Problem

We report about a study of a simulated annealing algorithm for the airline crew pairing problem based on a run-cutting formulation. Computational results are reported for some real-world short- to medium-haul test problems with up to 4600 flights per month. Furthermore we find that run time can be saved and solution quality can be improved by using a problem specific initial solution, by relaxing constraints as far as possible, by combining simulated annealing with a problem specific local improvement heuristic and by multiple independent runs.     

航空公司机组排班计划研究

以中国国际航空公司北京-成都航班为例,提出一种航空公司制定机组排班计划的新方法。首先以机组异地停留时间最短为目标,应用匈牙利算法生成“机组航班串”;然后,应用人员排班方法求得保证机组每周连休两日的条件下完成“机组航班串”飞行任务的最少机组数;最后,对这些机组制定具体的排班计划。应用该方法制定的机组排班计划使得航空公司在保证机组每周连休两日的条件下能够以最少的机组完成航班飞行任务,且机组在异地的停留时间最短。     

Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. We develop a new approach for solving the problem that is based on enumerating hundreds of millions random pairings. The linear programming relaxation is solved first and then millions of columns with best reduced cost are selected for the integer program. The number of columns is further reduced by a linear programming based heuristic. Finally an integer solution is obtained with a commercial integer programming solver. The branching rule of the solver is enhanced with a combination of strong branching and a specialized branching rule. The algorithm produces solutions that are significantly better than ones found by current practice.     

Parallel Integer Optimization for Crew Scheduling

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Göteborg, Sweden, based on distributing the variables. A lazy variant of this approach which decouples communication and computation is even useful on networks of workstations. Furthermore, we develop a new sequential active set strategy which requires less work and is better adapted to the memory hierarchy properties of modern RISC processors. This algorithm is also suited for parallelization on a moderate number of networked workstations.     

An Integrated Optimization Model for Train Crew Management

Train crew management involves the development of a duty timetable for each of the drivers (crew) to cover a given train timetable in a rail transport organization. This duty timetable is spread over a certain period, known as the roster planning horizon. Train crew management may arise either from the planning stage, when the total number of crew and crew distributions are to be determined, or from the operating stage when the number of crew at each depot is known as input data. In this paper, we are interested in train crew management in the planning stage. In the literature, train crew management is decomposed into two stages: crew scheduling and crew rostering which are solved sequentially. We propose an integrated optimization model to solve both crew scheduling and crew rostering. The model enables us to generate either cyclic rosters or non-cyclic rosters. Numerical experiments are carried out over data sets arising from a practical application.     

机组排班的混合集合规划方法研究

机组成本是仅次于燃料成本的第二大直接运营成本,合理的进行机组人员排班对降低航空公司运营成本有着重要意义。然而,机组排班问题是复杂性非常高的组合优化问题,属于NP难题。本文在分析机组排班问题研究进展的基础上,采用混合集合规划方法,综合考虑多种约束,建立了更具有实用性的机组排班优化模型。本文将运筹学理论与业务逻辑相结合,设计了高效的求解策略。利用多组航空公司真实数据对模型进行测试,测试结果表明,模型可以在较短时间内有效求解达到实际应用规模的机组排班问题。     

Constraint Programming Based Column Generation for Crew Assignment

Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.     

Crew Assignment via Constraint Programming: Integrating Column Generation and Heuristic Tree Search

The Airline Crew Assignment Problem (ACA) consists of assigning lines of work to a set of crew members such that a set of activities is partitioned and the costs for that assignment are minimized. Especially for European airline companies, complex constraints defining the feasibility of a line of work have to be respected. We developed two different algorithms to tackle the large scale optimization problem of Airline Crew Assignment. The first is an application of the Constraint Programming (CP) based Column Generation Framework. The second approach performs a CP based heuristic tree search. We present how both algorithms can be coupled to overcome their inherent weaknesses by integrating methods from Constraint Programming and Operations Research. Numerical results show the superiority of the hybrid algorithm in comparison to CP based tree search and column generation alone.     

An Optimization Based Approach to the Train Operator Scheduling Problem at Singapore MRT

Singapore Mass Rapid Transit (SMRT) operates two train lines with 83 kilometers of track and 48 stations. A total of 77 trains are in operation during peak hours and 41 during off-peak hours. In this article we report on an optimization based approach to develop a computerized train-operator scheduling system that has been implemented at SMRT. The approach involves a bipartite matching algorithm for the generation of night duties and a tabu search algorithm for the generation of day duties. The system automates the train-operator scheduling process at SMRT and produces favorable schedules in comparison with the manual process. It is also able to handle the multiple objectives inherent in the crew scheduling system. While trying to minimize the system wide crew-related costs, the system is also able to address concern with respect to the number of split duties.     

Airline crew scheduling from planning to operations

Crew scheduling problems at the planning level are typically solved in two steps: first, creating working patterns, and then assigning these to individual crew. The first step is solved with a set covering model, and the second with a set-partitioning model. At the operational level, the (re) planning period is considerably smaller than during the strategic planning phase. We integrate both models to solve time critical crew recovery problems arising on the day of operations. We describe how pairing construction and pairing assignment are done in a single step, and provide solution techniques based on simple tree search and more sophisticated column generation and shortest-path algorithms.     

Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods

The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. Given its high complexity, the ICS problem has been traditionally tackled using a sequential two-stage approach, where a crew pairing problem is solved in the first stage and a crew assignment problem in the second stage. Recently, Saddoune et al. (2010b) developed a model and a column generation/dynamic constraint aggregation method for solving the ICS problem in one stage. Their computational results showed that the integrated approach can yield significant savings in total cost and number of schedules, but requires much higher computational times than the sequential approach. In this paper, we enhance this method to obtain lower computational times. In fact, we develop a bi-dynamic constraint aggregation method that exploits a neighborhood structure when generating columns (schedules) in the column generation method. On a set of seven instances derived from real-world flight schedules, this method allows to reduce the computational times by an average factor of 2.3, while improving the quality of the computed solutions.     

基于禁忌算法的中枢辐射航线网络鲁棒优化方法

文章针对航空公司构建中枢辐射航线网络问题展开研究,采用鲁棒优化的方法建立数学模型,针对鲁棒解的特点以及问题的复杂性,将禁忌算法和最短路算法相结合并加以改进,提出了一种适应于求解大型问题的启发式算法,并通过实例进行了仿真实现.     

The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies

In the Home Care Crew Scheduling Problem a staff of home carers has to be assigned a number of visits to patients’ homes, such that the overall service level is maximised. The problem is a generalisation of the vehicle routing problem with time windows. Required travel time between visits and time windows of the visits must be respected. The challenge when assigning visits to home carers lies in the existence of soft preference constraints and in temporal dependencies between the start times of visits.     

考虑地区因素的航空收益管理

对于中国这样一个因地区经济水平不同而造成地区消费差异极度巨大的国家,航空公司应该怎样设置卖票策略使自己的各个航班的效用最大,传统的方法是票价系统因地而异,但这种方法有很大的随意性,并且对订票系统改变较大,操作成本高。本文将采用一个新的方法讨论该问题。首先,引进一个反映地区消费水平的参数,简称地区因子。然后结合一个单阶段航班,建立考虑地区因子的随机动态模型,同时证明了与效用函数相关的一些性质:比例边际效用函数是分别关于时间,待订票数和地区因子的单调增加函数。基于这些性质,对连接不同地域的航班,我们只要调整地区因子,再采用阀值控制策略就能使航班的效用最大且空置率得到有效抑制。最后,给出了一个实例。     

Convexity in Scheduling Problems

凸性在连续性最优化理论中起着重要的作用．它在离散性最优化中的相应概念尚待研究．本文运用差分和次梯度的概念给出排序问题中离散凸性的描述，并指出凸性在构造最优排序中的重要性．     

Multifunction Radar: Task Scheduling

Multifunction radar has to perform several types of tasks. Some of them are systematic: the case of probing and guidance tasks. Others are random: the case when a new object is detected in the sky and should be confirmed and tracked. The tasks that consist of tracking targets are also random, since these targets may follow unexpected trajectories, possibly asking for a search in the neighborhood of the forecasted position of the target. The goal of this paper is to propose a strategy that maximizes the number of useful tasks performed, taking into account their priorities. The more efficient the radar, i.e. the higher the quality of the information provided, the greater the energy consumption, which leads to a reduction of the number of feasible tasks. Thus, the goal is to find a trade-off between energy consumption and the number of tasks to perform by unit of time that maximizes the quantity of useful information.     

A Self-Adjusting Algorithm for Driver Scheduling

Public transport driver scheduling is a world wide problem, which is NP-hard. Although some mathematically based methods are being used in the transport industry, there is still much scope for improvements. This paper presents a novel evolutionary approach that simulates the self-adjusting process on a single schedule. Five factors characterized by fuzzy membership functions are first aggregated to evaluate the shift structure. This evaluating function is incorporated into a constructing heuristic to make shift selection. A self-adjusting algorithm is then designed to guide the constructing heuristic to improve a given initial schedule iteratively. In each generation an unfit portion of the working schedule is removed. Broken schedules are repaired by the constructing heuristic until stopping condition is met. Experimental results on real-world driver scheduling problems has demonstrated the success of the proposed approach.     

活动执行时间可提前的多模式反应性项目调度优化

研究不确定活动工期下活动执行时间可提前的多模式反应性项目调度问题。首先对反应性研究现状进行综述;其次建立以最小化反应性总成本为目标的优化模型;随后基于问题特点设计禁忌搜索算法;最后通过具体案例分析关键参数对反应性成本的影响,并得出结论:执行时间提前得到的反应性成本及完工时间明显低于执行时间不可提前的结果;随着项目推进,总成本及影响的活动数量总体上呈减小趋势,但项目完工时间在某些时刻维持不变;对于工期增加较大的活动,将其本身或紧前活动提前启动,或将其转换至活动工期较短的模式可降低反应性成本。研究可为不确定环境下反应性计划制定提供决策支持。     

炼油生产调度优化模型研究

本文针对炼油厂一次加工采用原油混烧方式的特点,研究了以满足二次加工质量卡边要求为目标的生产调度优化模型,为保证产品质量的稳定和降低原油成本,研究了原油需求预测模型,并介绍了两个模型求解算法的特点。