Geert De Maere

A multi-objective approach for robust airline scheduling

We present a memetic approach for multi-objective improvement of robustness influencing features (called robustness objectives) in airline schedules. Improvement of the objectives is obtained by simultaneous flight retiming and aircraft rerouting, subject to a fixed fleet assignment. Approximations of the Pareto optimal front are obtained by applying a multi-meme memetic algorithm. We investigate biased meme selection to encourage exploration of the boundaries of the search space and compare it with random meme selection. An external population of high quality solutions is maintained using the adaptive grid archiving algorithm. The presented approach is applied to investigate simultaneous improvement of reliability and flexibility in real world schedules from KLM Royal Dutch Airlines. Experimental results show that the approach enables us to obtain schedules with significant improvements for the considered objectives. A large scale simulation study was undertaken to quantify the influence of the robustness objectives on the operational performance of the schedules. Rigorous sensitivity analysis of the results shows that the influence of the schedule reliability is dominant and that increased schedule flexibility could improve the operational performance.

Addressing the Pushback Time Allocation Problem at Heathrow Airport

This paper considers the problem of allocating pushback times to departing aircraft, specifying the time at which they will be given permission to push back from their allocated stand, start their engines, and commence their taxi to the runway. The aim of this research is to first predict the delay (defined as the waiting time at the stand or runway) for each departure, then to use this to calculate a pushback time such that an appropriate amount of the delay is absorbed at the stand, prior to starting the engines. A two-stage approach is used, where the feasibility of the second stage (pushback time allocation) has to be considered within the first stage (takeoff sequencing). The characteristics of this real-world problem and the differences between it and similar problems are thoroughly discussed, along with a consideration of the important effects of these differences. Differences include a nonlinear objective function with a nonconvex component; the integration of two sequence dependent separation problems; separations that can vary over time; and time-slot extensions. Each of these factors has contributed to the design of the solution algorithm. Results predict significant fuel-burn benefits from absorbing some of the delay as stand hold, as well as delay benefits from indirectly aiding the runway controllers by reducing runway queue sizes. A system for pushback time allocation at London Heathrow has been developed by NATS (formerly National Air Traffic Services) based upon the algorithm described in this paper.

Interval type-2 intuitionistic fuzzy logic system for non-linear system prediction

This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parameters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems.

Pruning Rules for Optimal Runway Sequencing

This paper investigates runway sequencing for real-world scenarios at one of the world’s busiest airports, London Heathrow. Several pruning principles are introduced that enable significant reductions of the problem’s average complexity, without compromising the optimality of the resulting sequences, nor compromising the modeling of important real-world constraints and objectives. The pruning principles are generic and can be applied in a variety of heuristic, metaheuristic, or exact algorithms. They could also be applied to different runway configurations, as well as to other variants of the machine scheduling problem with sequence dependent setup times, the generic variant of the runway sequencing problem in this paper. They have been integrated into a dynamic program for runway sequencing, which has been shown to be able to generate optimal sequences for large-scale problems at a low computational cost, while considering complex nonlinear and nonconvex objective functions that offer significant flexibi...

Probabilistic Airline Reserve Crew Scheduling Model.

This paper introduces a probabilistic model for airline reserve crew scheduling. The model can be applied to any schedules which consist of a stream of departures from a single airport. We assume that reserve crew demand can be captured by an independent probability of crew absence for each departure. The aim of our model is to assign some fixed number of available reserve crew in such a way that the overall probability of crew unavailability in an uncertain operating environment is minimised. A comparison of different probabilistic objective functions, in terms of the most desirable simulation results, is carried out, complete with an interpretation of the results. A sample of heuristic solution methods are then tested and compared to the optimal solutions on a set of problem instances, based on the best objective function found. The current model can be applied in the early planning phase of reserve crew scheduling, when very little information is known about crew absence related disruptions. The main conclusions include the finding that the probabilistic objective function approach gives solutions whose objective values correlate strongly with the results that these solutions will get on average in repeated simulations. Minimisation of the sum of the probabilities of crew unavailability was observed to be the best surrogate objective function for reserve crew schedules that perform well in simulation. A list of extensions that could be made to the model is then provided, followed by conclusions that summarise the findings and important results obtained.

Interval Type-2 A-Intuitionistic Fuzzy Logic for Regression Problems

This paper presents an approach to prediction based on a new interval type-2 Atanassov-intuitionistic fuzzy logic system (IT2AIFLS) of the Takagi–Sugeno–Kang fuzzy inference with neural network learning capability. The gradient descent algorithm is used to adapt the parameters of the IT2AIFLS. The empirical comparison is made on the designed system using some benchmark regression problems—both artificial and real-world datasets. Analyses of our results reveal that IT2AIFLS outperforms its type-1 variant, other type-1 fuzzy logic approaches, and some type-2 fuzzy systems in the regression tasks. The reason for the improved performance of the proposed framework of IT2AIFLS is the introduction of nonmembership functions and intuitionistic fuzzy indices into the classical IT2FLS model. This increases the level of fuzziness in the proposed IT2AIFLS framework, thus providing more accurate approximations than AIFLS, classical type-1, and interval type-2 fuzzy logic systems.

Extended Kalman filter-based learning of interval type-2 intuitionistic fuzzy logic system

Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extended Kalman filter (DEKF) to optimize the parameters of an interval type-2 intuitionistic fuzzy logic system of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australias electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and interval type-2 fuzzy logic system (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform.

Time series forecasting with interval type-2 intuitionistic fuzzy logic systems

Conventional fuzzy time series approaches make use of type-1 or type-2 fuzzy models. Type-1 models with one index (membership grade) cannot fully handle the level of uncertainty inherent in many real world applications. The type-2 models with upper and lower membership functions do handle uncertainties in many applications better than its type-1 counterparts. This study proposes the use of interval type-2 intuitionistic fuzzy logic system of Takagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference that utilises more parameters than type-2 fuzzy models in time series forecasting. The IT2IFLS utilises more indexes namely upper and lower non-membership functions. These additional parameters of IT2IFLS serve to refine the fuzzy relationships obtained from type-2 fuzzy models and ultimately improve the forecasting performance. Evaluation is made on the proposed system using three real world benchmark time series problems namely: Santa Fe, tree ring and Canadian lynx datasets. The empirical analyses show improvements of prediction of IT2IFLS over other approaches on these datasets.

Scheduling Airline Reserve Crew to Minimise Crew Related Delay Using Simulated Airline Recovery and a Probabilistic Optimisation Model

This paper addresses the problem of airline reserve crew scheduling for a single hub and spoke network. The proposed method involves a simulation parameter generation phase used to derive probabilities of crew related delay and associated expected delay durations. The parameter generation simulation simulates recovery from delays by searching for crew and aircraft swaps that absorb delays, therefore the probabilities of crew related delay are independent of the effects of reserve crew. The parameters generated in the simulation phase are stored in matrices which record the causal relationship of propagating crew related delays. The parameter matrices are then used to search for a reserve crew schedule that minimises the total expected crew related delay. The search method is based on calculating the effect a given reserve schedule has on the probabilities of crew related delays occurring. The experimental results indicate that the proposed model minimises crew related delay in comparison to a variety of alternative methods of reserve crew scheduling for the problem instances considered here.

Interval type-2 intuitionistic fuzzy logic systems: a comparative evaluation

Several fuzzy modeling techniques have been employed for handling uncertainties in data. This study presents a comparative evaluation of a new class of interval type-2 fuzzy logic system (IT2FLS) namely: interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK)-type with classical IT2FLS and its type-1 variant (IFLS). Simulations are conducted using a real-world gas compression system (GCS) dataset. Study shows that the performance of the proposed framework with membership functions (MFs) and non-membership functions (NMFs) that are each intervals is superior to classical IT2FLS with only MFs (upper and lower) and IFLS with MFs and NMFs that are not intervals in this problem domain.