Improvements to a large neighborhood search heuristic for an integrated aircraft and passenger recovery problem

Because most commercial passenger airlines operate on a hub-and-spoke network, small disturbances can cause major disruptions in their planned schedules and have a significant impact on their operational costs and performance. When a disturbance occurs, the airline often applies a recovery policy in order to quickly resume normal operations. We present in this paper a large neighborhood search heuristic to solve an integrated aircraft and passenger recovery problem. The problem consists of creating new aircraft routes and passenger itineraries to produce a feasible schedule during the recovery period. The method is based on an existing heuristic, developed in the context of the 2009 ROADEF Challenge, which alternates between three phases: construction, repair and improvement. We introduce a number of refinements in each phase so as to perform a more thorough search of the solution space. The resulting heuristic performs very well on the instances introduced for the challenge, obtaining the best known solution for 17 out of 22 instances within five minutes of computing time and 21 out of 22 instances within 10 minutes of computing time.     

Scatter search for trainees to software project requirements stable allocation

In this paper, we study a centralized, stable matching scheme, which allocates trainees to software project requirements, to minimize retraining and relocation costs when the preference lists of the project requirements may contain ties of arbitrary lengths. This particular trainees’ assignment problem is important because the allocation decisions not only influence the costs but also impact software project deliverables and intern attrition rates. It is also an NP-hard problem because of the inclusion of the ties, and the costs in the stable allocation model. We, therefore, have designed a GRASP-based scatter search method, to solve the large size instances of our assignment problem efficiently. The GRASP method uses randomized algorithms to generate initial trial solutions. A repair heuristic based on regret minimization idea is designed to convert an unstable solution to a stable solution during an improvement phase. Computational experiments suggest that the proposed algorithm significantly reduces run time compared to the CPLEX, and produces solutions that are at an average 4.5% away from the best CPLEX solutions for the large size problem instances. Moreover, our scatter search method consistently provides better quality solutions than the two state of the art methods from the prior literature.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

面向靠桥率及道口冲突率的航班-机位指派问题优化模型及其启发式算法研究

在给定航班时刻表条件下,对于进出港航班的机位分配,除了必须满足航班、飞机和机位之间的技术性要求之外,还要考虑尽量提高整个机场的机位利用率,且方便旅客出入港及时、安全和便捷.文章以飞机机型、所属航空公司、客运/货运航班、国内/国际航班等匹配条件为约束条件,以航班-机位分配完成率、靠桥率、道口非冲突率为目标,建立了一个航班-机位指派问题的全局优化模型.基于国内某机场的真实应用场景及其待决策变量维度的超大规模,导致模型求解成为一个NP-COMPLETE的混合整数规划问题.文章提出一种启发式快速求解算法,基于贪婪规则建立若干优先级队列的航班冲突调整方案,按照3个指标重要程度渐次探求近似最优解.而且,对于每一步贪婪规则的改进,文章都进行了算法有效性检验以及计算性能的对比实验.最终多重对比实验的结果表明,新算法的结果在与理论最优解差距不足3%的代价下,可节约超过90%求解时间.     

Network flow-based approaches for integrated aircraft fleeting and routing

Given a schedule of flights to be flown, the aircraft fleeting and routing problem (AFRP) consists of determining a minimum-cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance requirements and other activity constraints. We investigate network flow-based heuristic approaches for this problem. Computational experiments conducted on real-data given by TunisAir show that the proposed heuristic consistently yields very near-optimal solutions while requiring modest CPU effort.     

A Heuristic Algorithm for Assigning Crews Among Bases in an Airlift Operation

In this paper, the optimum assignment of crews among the bases in an airlift operation is considered. An airlift operation consists of transporting large quantities of equipment and personnel among various bases. The crews operating the aircraft rest for a constant period of time after arriving at the bases, before flying again. In order to minimize the waiting times of the aircraft at the bases for want of rested crews, the available crews are distributed initially among the bases.Using earlier results of the mean waiting time of an aircraft at a single base and the probability distribution of the inter-departure times of the aircraft from the base, the problem of optimum allocation of crews is formulated as a non-linear integer programming problem. A heuristic algorithm is developed using the Lagrange multiplier. Its solution is compared with the exact solution for a number of test cases, and the algorithm is found to perform well.     

Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective.     

Static target search path planning optimization with heterogeneous agents

Disruptions in airline operations can result in infeasibilities in aircraft and passenger schedules. Airlines typically recover aircraft schedules and disruptions in passenger itineraries sequentially. However, passengers are severely affected by disruptions and recovery decisions. In this paper, we present a mathematical formulation for the integrated aircraft and passenger recovery problem that considers aircraft and passenger related costs simultaneously. Using the superimposition of aircraft and passenger itinerary networks, passengers are explicitly modeled in order to use realistic passenger related costs. In addition to the common routing recovery actions, we integrate several passenger recovery actions and cruise speed control in our solution approach. Cruise speed control is a very beneficial action for mitigating delays. On the other hand, it adds complexity to the problem due to the nonlinearity in fuel cost function. The problem is formulated as a mixed integer nonlinear programming (MINLP) model. We show that the problem can be reformulated as conic quadratic mixed integer programming (CQMIP) problem which can be solved with commercial optimization software such as IBM ILOG CPLEX. Our computational experiments have shown that we could handle several simultaneous disruptions optimally on a four-hub network of a major U.S. airline within less than a minute on the average. We conclude that proposed approach is able to find optimal tradeoff between operating and passenger-related costs in real time.     

A penalty-shift-insertion-based algorithm to minimize total flow time in no-wait flow shops

This paper proposes a penalty-shift-insertion (PSI)-based algorithm for the no-wait flow shop scheduling problem to minimize total flow time. In the first phase, a penalty-based heuristic, derived from Vogel’s approximation method used for the classic transportation problem is used to generate an initial schedule. In the second phase, a known solution is improved using a forward shift heuristic. Then the third phase improves this solution using a job-pair and a single-job insertion heuristic. Results of the computational experiments with a large number of randomly generated problem instances show that the proposed PSI algorithm is relatively more effective and efficient in minimizing total flow time in a no-wait flow shop than the state-of-the-art procedures. Statistical significance of better results obtained by the proposed algorithm is also reported.     

The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints

The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines.     

A two-phase multiple objective approach to university timetabling utilising optimisation and evolutionary solution methodologies

The timetabling problem is generally large, highly constrained and discrete in nature. This makes solution by exact optimisation methods difficult. Therefore, often a heuristic search is deemed acceptable providing a simple (non-optimal) solution. This paper discusses the timetabling problem for a university department, where a large-scale integer goal programming (IGP) formulation is implemented for its efficient optimal solution in two phases. The first phase allocates lectures to rooms and the second allocates start-times to lectures. Owing to the size and complicated nature of the model, an initial analysis procedure is employed to manipulate the data to produce a more manageable model, resulting in considerable reductions in problem size and increase of performance. Both phases are modelled as IGPs. Phase 1 is solved using a state-of-the-art IGP optimisation package. However, due to the scale of the model, phase 2 is solved to optimality using a genetic algorithm approach.     

An efficient composite heuristic for the symmetric generalized traveling salesman problem

The main purpose of this paper is to introduce a new composite heuristic for solving the generalized traveling salesman problem. The proposed heuristic is composed of three phases: the construction of an initial partial solution, the insertion of a node from each non-visited node-subset, and a solution improvement phase. We show that the heuristic performs very well on 36 TSPLIB problems which have been solved to optimality by other researchers. We also propose some simple heuristics that can be used as basic blocks to construct more efficient composite heuristics.     

A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the construction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solution. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut problem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP).     

The dynamic frequency assignment problem

In this paper, we consider a frequency assignment problem occurring in a military context. The main originality of the problem pertains to its dynamic dimension: new communications requiring frequency assignments need to be established throughout a battlefield deployment. The problem resolution framework decomposes into three phases: assignment of an initial kernel of communications, dynamic assignment of new communication links and a repair process when no assignment is possible. Different solution methods are proposed and extensive computational experiments are carried out on realistic instances.     

Flight gate scheduling with respect to a reference schedule

This paper considers the problem of assigning flights to airport gates. We examine the general case in which an aircraft serving a flight may be assigned to different gates for arrival and departure processing and for optional intermediate parking. Restrictions to this assignment include gate closures and shadow restrictions, i.e., the situation where certain gate assignments may cause blocking of neighboring gates. The objectives include maximization of the total assignment preference score, a minimal number of unassigned flights during overload periods, minimization of the number of tows, maximization of a robustness measure as well as a minimal deviation from a given reference schedule. We show that in case of a one period time horizon this objective can easily be integrated into our existing model based on the Clique Partitioning Problem. Furthermore we present a heuristic algorithm to solve the problem for multiple periods.     

Routing and wavelength assignment by partition colouring

The problem of routing and wavelength assignment in all-optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths, followed by the solution of a partition colouring problem in a conflict graph. A new tabu search heuristic is also proposed for the partition colouring problem, which may be viewed as an extension of the graph colouring problem. Computational experiments are reported, showing that the tabu search heuristic outperforms the best heuristic for partition colouring by approximately 20% in the average and illustrating that the new approach for the problem of routing and wavelength assignment is more robust than a well established heuristic for this problem.     

A facility neighborhood search heuristic for capacitated facility location with single-source constraints and flexible demand

We consider a generalization of the well-known capacitated facility location problem with single source constraints in which customer demand contains a flexible dimension. This work focuses on providing fast and practically implementable optimization-based heuristic solution methods for very large scale problem instances. We offer a unique approach that utilizes a high-quality efficient heuristic within a neighborhood search to address the combined assignment and fixed-charge structure of the underlying optimization problem. We also study the potential benefits of combining our approach with a so-called very large-scale neighborhood search (VLSN) method. As our computational test results indicate, our work offers an attractive solution approach that can be tailored to successfully solve a broad class of problem instances for facility location and similar fixed-charge problems.     

A Neural-Tabu Search Heuristic for the Real Time Vehicle Routing Problem

The Real Time Vehicle Routing Problem RTVRP is a dynamic routing problem where requests are generated dynamically during the operation horizon without any previous knowledge. Received requests need to be answered as fast as possible and then assigned to a vehicle to be served. Due to timing constraints of the RTVRP, a solving approach should give the best compromise between the cost of the provided solution and the computation time needed to find it. In this paper, we present a neural-tabu search solving scheme for the RTVRP. The developed approach is composed by two phases; The first part consists of learning and reproducing previous routing decisions using a feed forward neural network with a particular structure. The second phase is based on a tabu search heuristic that takes its initial solution from the assignment provided by the neural module. If the reaction time is still available, the tabu search module will continue ameliorating the final solution. To evaluate the proposed approach a set of problems are simulated and solved. The obtained results are compared to those given by the First Come First Served FCFS and Nearest Neighbor NN policies and also to the optimal solutions provided by the GNU Linear Programming Kit GLPK.      

An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.