A brief overview on an air transportation system (ATS)

The worldwide Air Transport System (ATS) has a huge impact on the global economy and is expected to grow annually in size and operational costs. This impact has led the ATS to attract the attention of researchers worldwide. This article aims to provide an operational insight into the ATS by discussing the major stages of the flight planning process, which is commonly known as airline scheduling, and elaborates how the traversal of flights takes place in the ATS after the filing of flight plan. The reader will also see references to other research which can provide further information, in the hope that this article can be of use to those who are beginning to look into this area

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 parame- ters 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

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

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 Australia’s 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

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

Hybrid learning for interval type-2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

This paper presents a novel application of a hybrid learning approach to the optimisation of membership and non-membership functions of a newly developed interval type-2 intuitionistic fuzzy logic system (IT2 IFLS) of a Takagi-Sugeno-Kang (TSK) fuzzy inference system with neural network learning capability. The hybrid algorithms consisting of decou- pled extended Kalman filter (DEKF) and gradient descent (GD) are used to tune the parameters of the IT2 IFLS for the first time. The DEKF is used to tune the consequent parameters in the forward pass while the GD method is used to tune the antecedents parts during the backward pass of the hybrid learning. The hybrid algorithm is described and evaluated, prediction and identification results together with the runtime are compared with similar existing studies in the literature. Performance comparison is made between the proposed hybrid learning model of IT2 IFLS, a TSK-type-1 intuitionistic fuzzy logic system (IFLS-TSK) and a TSK-type interval type-2 fuzzy logic system (IT2 FLS-TSK) on two instances of the datasets under investigation. The empirical comparison is made on the designed systems using three artificially generated datasets and three real world datasets. Analysis of results reveal that IT2 IFLS outperforms its type-1 variants, IT2 FLS and most of the existing models in the literature. Moreover, the minimal run time of the proposed hybrid learning model for IT2 IFLS also puts this model forward as a good candidate for application in real time systems

A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

Airlines operate in an uncertain environment for many reasons, for example due to the efects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence and journey time uncertainty for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. Given an airline's crew schedule and aircraft routings we propose a Mixed Integer Programming approach to scheduling the airline's reserve crew. A simulation of the airline's operations with stochastic journey time and crew absence inputs and without reserve crew is used to generate disruption scenarios for the MIPSSM formulation (Mixed Integer Programming Simulation Scenario Model). Each disruption scenario corresponds to a record of all of the disruptions in a simulation for which reserve crew use would have been beneficial. For each disruption in a disruption scenario there is a record of all reserve crew that could have been used to solve or reduce the disruption. This information forms the input to the MIPSSM formulation, which has the objective of finding the reserve schedule that minimises the overall level of disruption over a set of scenarios. Additionally, modifications of the MIPSSM are explored, and a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed Mixed Integer Programming Simulation Scenario Model or MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as ensuring that enough disruption scenarios are added to the MIPSSM

A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

Airlines operate in an uncertain environment for many reasons, for example due to the efects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence and journey time uncertainty for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. Given an airline's crew schedule and aircraft routings we propose a Mixed Integer Programming approach to scheduling the airline's reserve crew. A simulation of the airline's operations with stochastic journey time and crew absence inputs and without reserve crew is used to generate disruption scenarios for the MIPSSM formulation (Mixed Integer Programming Simulation Scenario Model). Each disruption scenario corresponds to a record of all of the disruptions in a simulation for which reserve crew use would have been beneficial. For each disruption in a disruption scenario there is a record of all reserve crew that could have been used to solve or reduce the disruption. This information forms the input to the MIPSSM formulation, which has the objective of finding the reserve schedule that minimises the overall level of disruption over a set of scenarios. Additionally, modifications of the MIPSSM are explored, and a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed Mixed Integer Programming Simulation Scenario Model or MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as ensuring that enough disruption scenarios are added to the MIPSSM

Scheduling airline reserve crew using a probabilistic crew absence and recovery model

Airlines require reserve crew to replace delayed or absent crew, with the aim of preventing consequent flight cancellations. A reserve crew schedule specifies the duty periods for which different reserve crew will be on standby to replace any absent crew. For both legal and health-and-safety reasons the reserve crew's duty period is limited, so it is vital that these reserve crew are available at the right times, when they are most likely to be needed and will be most effective. Scheduling a reserve crew unnecessarily, or earlier than needed, wastes reserve crew capacity. Scheduling a reserve crew too late means either an unrecoverable cancellation or a delay waiting for the reserve crew to be available. Determining when to schedule these crew can be a complex problem , since one crew member could potentially cover a vacancy on any one of a number of different flights, and flights interact with each other, so a delay or cancellation for one flight can affect a number of later flights. This work develops an enhanced mathematical model for assessing the impact of any given reserve crew schedule, in terms of reduced total expected cancellations and any resultant reserve induced delays, whilst taking all of the available information into account, including the schedule structure and interactions between flights, the uncertainties involved, and the potential for multiple crew absences on a single flight. The interactions between flights have traditionally made it very hard to predict the effects of cancellations or delays, and hence to predict when best to allocate reserve crew and lengthy simulation runs have traditionally been used to make these predictions. This work is motivated by the airline industry's need for improved mathematical models to replace the time-consuming simulation-based approaches. The improved predictive probabilistic model which is introduced here is shown to produce results that match a simulation model to a high degree of accuracy, in a much shorter time, making it an effective and accurate surrogate for simulation. The modelling of the problem also provides insights into the complexity of the problem that a purely simulation based approach would miss. The increased speed enables potential deployment within a real time decision support context, comparing alternative recovery decisions as disruptions occur. To illustrate this, the model is used in this paper as a fitness function in meta-heuristics algorithms to generate disruption minimising reserve crew schedules for a real airline schedule. These are shown to be of a high quality, demonstrating the effectiveness and reliability of the proposed approach