A hybrid optimization-simulation approach for robust weekly aircraft routing and retiming

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on-time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8–16.0%, cumulative delay was reduced by 25.4–33.1%, and the number of delayed passengers was reduced by 8.2–51.6%.     

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

This paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem

In this paper, we study two closely related airline planning problems: the robust weekly aircraft maintenance routing problem (RWAMRP) and the tail assignment problem (TAP). In real life operations, the RWAMRP solution is used in tactical planning whereas the TAP solution is implemented in operational planning. The main objective of these two problems is to minimize the total expected propagated delay (EPD) of the aircraft routes. To formulate the RWAMRP, we propose a novel weekly line-of-flights (LOF) network model that can handle complex and nonlinear cost functions of EPD. Because the number of LOFs grows exponentially with the number of flights to be scheduled, we propose a two-stage column generation approach to efficiently solve large-scale real-life RWAMRPs. Because the EPD of an LOF is highly nonlinear and can be very time-consuming to accurately compute, we propose three lower bounds on the EPD to solve the pricing subproblem of the column generation. Our approach is tested on eight real-life test instances. The computational results show that the proposed approach provides very tight LP relaxation (within 0.6% of optimal solutions) and solves the test case with more than 6000 flights per week in less than three hours. We also investigate the solutions obtained by our approach over 500 simulated realizations. The simulation results demonstrate that, in all eight test instances, our solutions result in less EPDs than those obtained from traditional methods. We then extend our model and solution approach to solve realistically simulated TAP instances.     

Optimal vehicle speed trajectory on a signalized arterial with consideration of queue

Vehicle speed trajectory significantly impacts fuel consumption and greenhouse gas emissions, especially for trips on signalized arterials. Although a large amount of research has been conducted aiming at providing optimal speed advisory to drivers, impacts from queues at intersections are not considered. Ignoring the constraints induced by queues could result in suboptimal or infeasible solutions. In this study, a multi-stage optimal control formulation is proposed to obtain the optimal vehicle trajectory on signalized arterials, where both vehicle queue and traffic light status are considered. To facilitate the real-time update of the optimal speed trajectory, a constrained optimization model is proposed as an approximation approach, which can be solved much quicker. Numerical examples demonstrate the effectiveness of the proposed optimal control model and the solution efficiency of the proposed approach.     

Computing 4D near-optimal trajectories for dynamic air traffic flow management with column generation and branch-and-price

Abstract

The current air traffic system faces recurrent saturation problems. Numerous studies are dedicated to this issue, including the present research on a new dynamic regulation filter holding frequent trajectory optimisations in a real-time sliding horizon loop process. We consider a trajectory optimisation problem arising in this context, where a feasible four-dimensional (4D) trajectory is to be built and assigned to each regulated flight to suppress sector overloads while minimising the cost of the chosen policy. We model this problem with a mixed integer linear programme and solve it with a branch-and-price approach. The pricing sub-problem looks for feasible trajectories in a dynamic three-dimensional (3D) network and is solved with a specific algorithm based on shortest path labelling algorithms and on dynamic programming. Each algorithm is tested on real-world data corresponding to a complete traffic day in the European air traffic system; experimental results, including computing times measurement, validate the solution process.     

Distributed optimization and coordination algorithms for dynamic speed optimization of connected and autonomous vehicles in urban street networks

Dynamic speed harmonization has shown great potential to smoothen the flow of traffic and reduce travel time in urban street networks. The existing methods, while providing great insights, are neither scalable nor real-time. This paper develops Distributed Optimization and Coordination Algorithms (DOCA) for dynamic speed optimization of connected and autonomous vehicles in urban street networks to address this gap. DOCA decomposes the nonlinear network-level speed optimization problem into several sub-network-level nonlinear problems thus, it significantly reduces the problem complexity and ensures scalability and real-time runtime constraints. DOCA creates effective coordination in decision making between each two sub-network-level nonlinear problems to push solutions towards optimality and guarantee attaining near-optimal solutions. DOCA is incorporated into a model predictive control approach to allow for additional consensus between sub-network-level problems and reduce the computational complexity further. We applied the proposed solution technique to a real-world network in downtown Springfield, Illinois and observed that it was scalable and real-time while finding solutions that were at most 2.7% different from the optimal solution of the problem. We found significant improvements in network operations and considerable reductions in speed variance as a result of dynamic speed harmonization.     

Metaheuristics for efficient aircraft scheduling and re-routing at busy terminal control areas

Intelligent decision support systems for the real-time management of landing and take-off operations can be very effective in helping air traffic controllers to limit airport congestion at busy terminal control areas. The key optimization problem to be solved regards the assignment of airport resources to take-off and landing aircraft and the aircraft sequencing on them. The problem can be formulated as a mixed integer linear program. However, since this problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY solver (a state-of-the-art optimization solver to deal with complex routing and scheduling problems) in order to improve the possibility of finding good quality solutions quickly. The proposed framework starts from a good initial solution for the aircraft scheduling problem with fixed routes (given the resources to be traversed by each aircraft), computed via a truncated branch-and-bound algorithm. A metaheuristic is then applied to improve the solution by re-routing some aircraft in the terminal control area. New metaheuristics, based on variable neighbourhood search, tabu search and hybrid schemes, are introduced. Computational experiments are performed on an Italian terminal control area under various types of disturbances, including multiple aircraft delays and a temporarily disrupted runway. The metaheuristics achieve solutions of remarkable quality, within a small computation time, compared with a commercial solver and with the previous versions of AGLIBRARY.     

Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach.     

Optimisation of motorway operations via ramp metering and variable speed limits

This paper presents a modelling and optimisation framework for deriving ramp metering and variable speed control strategies. We formulate the optimal control problems aiming to minimise the travel delay on motorways based upon a macroscopic cell transmission model of traffic. The optimal ramp metering optimisation is formulated as a linear programming (LP) while the variable speed control problem is formulated as a mixed integer LP. The optimisation models are applied to a real scenario over a section of M25 motorway in the UK. This paper also includes various analyses on the sensitivity of the optimal control solutions with respect to different network configurations and model assumptions.     

Effective aircraft maintenance schedule adjustment following incidents

In the real world, planned aircraft maintenance schedules are often affected by incidents. Airlines may thus need to adjust their aircraft maintenance schedules following the incidents that occur during routine operations. In tradition, such aircraft maintenance schedule adjustment has been performed manually, a process which is neither effective nor efficient, especially when the problem scale is large. In this study, an aircraft maintenance schedule adjustment model is developed, with the objective of minimizing the total system cost, subject to the related operating constraints. The model is formulated as a zero-one integer program and is solved using a mathematical programing solver. The effectiveness of the model is evaluated by application to a case study using data from an aircraft maintenance center in Taiwan. The test results show the proposed model, as well as the scheduling rules abstracted from the results are useful for the decision maker to adjust good maintenance schedules.     

Preference-based evolutionary algorithm for airport surface operations

In addition to time efficiency, minimisation of fuel consumption and related emissions has started to be considered by research on optimisation of airport surface operations as more airports face severe congestion and tightening environmental regulations. Objectives are related to economic cost which can be used as preferences to search for a region of cost efficient and Pareto optimal solutions. A multi-objective evolutionary optimisation framework with preferences is proposed in this paper to solve a complex optimisation problem integrating runway scheduling and airport ground movement problem. The evolutionary search algorithm uses modified crowding distance in the replacement procedure to take into account cost of delay and fuel price. Furthermore, uncertainty inherent in prices is reflected by expressing preferences as an interval. Preference information is used to control the extent of region of interest, which has a beneficial effect on algorithm performance. As a result, the search algorithm can achieve faster convergence and potentially better solutions. A filtering procedure is further proposed to select an evenly distributed subset of Pareto optimal solutions in order to reduce its size and help the decision maker. The computational results with data from major international hub airports show the efficiency of the proposed approach.     

Controlled time of arrival windows for already initiated energy-neutral continuous descent operations

Continuous descent operations with controlled times of arrival at one or several metering fixes could enable environmentally friendly procedures without compromising terminal airspace capacity. This paper focuses on controlled time of arrival updates once the descent has been already initiated, assessing the feasible time window (and associated fuel consumption) of continuous descent operations requiring neither thrust nor speed-brake usage along the whole descent (i.e. only elevator control is used to achieve different metering times). Based on previous works, an optimal control problem is formulated and numerically solved. The earliest and latest times of arrival at the initial approach fix have been computed for the descent of an Airbus A320 under different scenarios, considering the potential altitudes and distances to go when receiving the controlled time of arrival update. The effects of the aircraft mass, initial speed, longitudinal wind and position of the initial approach fix on the time window have been also investigated. Results show that time windows about three minutes could be achieved for certain conditions, and that there is a trade-off between robustness facing controlled time of arrival updates during the descent and fuel consumption. Interestingly, minimum fuel trajectories almost correspond to those of minimum time.     

A mixed-integer linear program for optimizing sensor locations along freeway corridors

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation.     

Disruption Management of an Inequality-Based Multi-Fleet Airline Schedule by a Multi-Objective Genetic Algorithm

Abstract

This paper presents a novel application of a Method of Inequality-based Multi-objective Genetic Algorithm (MMGA) to generate an efficient time-effective multi-fleet aircraft routing algorithm in response to the schedule disruption of short-haul flights. It attempts to optimize objective functions involving ground turn-around times, flight connections, flight swaps, total flight delay time and a 30-minute maximum delay time of original schedules. The MMGA approach, which combines a traditional Genetic Algorithm (GA) with a multi-objective optimization method, can address multiple objectives at the same time, then explore the optimal solution. The airline schedule disruption management problem is traditionally solved by Operations Research (OR) techniques that always require a precise mathematical model. However, airline operations involve too many factors that must be considered dynamically, making a precise mathematical model difficult to define. Experimental results based on a real airline flight schedule demonstrate that the proposed method, Multi-objective Optimization Airline Disruption Management by GA, can recover the perturbation efficiently within a very short time. Our results further demonstrate that the application can yield high quality solutions quickly and, consequently, has potential to be employed as a real-time decision support tool for practical complex airline operations.     

A multiple transfer function model for air traffic control systems

This paper considers the problem of modeling dynamic fluctuations in aircraft concentration within a group of air traffic control sectors. Using simultaneous time series recorded for each of the sectors, a multiple transfer function noise model is constructed. The modeling procedure demonstrates a data-dependent approach to ATC systems analysis which does not rely on describing the movement of individual aircraft.     

User perspectives in public transport timetable optimisation

The present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line.In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers’ route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence.The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD).     

Nonlinear programming methods based on closed-form expressions for optimal train control

This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train’s running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction – speedholding – coasting – maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewise-quadratic, based on which the terminal speed, travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed- and moving-block signalling systems.     

Optimisation of dynamic motorway traffic via a parsimonious and decentralised approach

This paper presents an optimisation framework for motorway management via ramp metering and variable speed limit. We start with presenting a centralised global optimal control problem aiming to minimise the total travel delay in a motorway system. Given the centralised global optimal control solutions, we propose a set of decentralised ramp metering and speed control strategies which operate on a novel parsimonious dynamic platform without needing an underlying traffic model. The control strategies are applied to a case on UK M25 motorway. The results show that the proposed set of decentralised control is able to deliver a performance that is close to the global optimal ones with significantly less computational and implementation effort. This study provides new insights to motorway management.     

Solving train formation problem using simulated annealing algorithm in a simplex framework

The train formation plan (TFP) determines the train services and their frequencies and assigns the demands. The TFP models are often formulated as a capacitated service network design problem, and the optimal solution is normally difficult to find. In this paper, a hybrid algorithm of the Simplex method and simulated annealing is proposed for the TFP problem. The basic idea of the proposed algorithm is to use a simulated annealing algorithm to explore the solution space, where the revised Simplex method evaluates, selects, and implements the moves. In the proposed algorithm, the neighborhood structure is based on the pivoting rules of the Simplex method that provides an efficient method to reach the neighbors of the current solution. A state‐of‐the‐art method is applied for parameters tuning by using the design of experiments approach. To evaluate the proposed model and the solution method, 25 test problems have been simulated and solved. The results show the efficiency and the effectiveness of the proposed approach. The proposed approach is implemented to develop the TFP in the Iranian railway as a case study. It is possible to save significant time and cost through solving the TFP problem by using the proposed algorithm and developing the efficient TFP plan in the railway networks. Copyright © 2012 John Wiley & Sons, Ltd.     

Global optimization method for network design problem with stochastic user equilibrium

In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.