Optimization of short-haul aircraft schedule recovery problems using a hybrid multiobjective genetic algorithm
Introduction
Aircraft schedule recovery problems arise when the original flight plan is disrupted by various occasional events, e.g. severe weather and mechanical problems, and should be rescheduled by delaying certain flights, swapping aircraft or taking other actions to minimize the negative effects. The operation coordinators who manage the daily airline situations have to carefully consider the practical conditions and try to make a suitable plan to narrow down the disturbance impact. Usually, a practical trade-off should be considered among the decision criteria (Luo & Yu, 1998) such as minimizing the number of delayed flights, minimizing the maximum delay, minimizing the total passenger delay, and so on. The difficulty for solving most of them is NP-complete, that is, no polynomial algorithms exist for the solutions.
Most studies for this kind of recovery problems only solve the objectives (or criteria) one by one or propagate a linear-sum on objectives to convert them into the single one. For example, Arguello, Jonathan, and Gang (1997) provided a greedy randomized adaptive search procedure (GRASP) which uses a randomized neighborhood search technique to reconstruct aircraft routings. Gu and Chung (1999) used a genetic algorithm to search the extra minimum delay time on the gate reassignments. Rosenberger, Johnson, and Nemhauser (2003) provided a set-packing model and solve it by an aircraft selection heuristic (ASH) method. Andersson (2006) presents two meta-heuristics, a tabu search and a simulated annealing approach, to solve the recovery problems efficiently. However, the single objective solution can not reflect the true cases with practical multiobjective needs, as stated by Fieldsend and Singh (2005).
Multiobjective evolutionary algorithms with global search capabilities have been successfully applied in aircraft schedule planning cases (Adachi et al., 2004, Chou et al., 2008). But, there are very few literature to study the multiobjective optimization problems of the aircraft schedule recovery. Although Lee, Lee, and Tan (2007) ever considered the schedule recovery problem under disturbance as a multiobjective optimization problem, and developed a multiobjective genetic algorithm (MOGA) to improve the robustness and operational cost of an existing flight schedule based on a simulation tool, SIMAIR 2.0, however, this approach consumes quite long computation time and may mainly be applicable for monthly schedules according to their conclusion. Clearly, it can not suit the short-haul recovery problems which require a short-time response in the daily work.
Summing up the above statements and reasons, the purpose of this paper is to formulate the daily short-haul recovery problems into multiobjective combinational optimization equations, and to develop a hybrid evolutionary algorithm which employs an adaptive evaluated vector (AEV) to guide the solution search and uses the method of inequality-based multiobjective genetic algorithm (MMGA) for globally searching for the Pareto solutions with regard to the performance. Besides, a simulated disturbance experiment, temporal airport closure, is made to validate the proposed approach.
Section snippets
Problem definition and formulation
The aircraft schedule recovery problem considered in this paper contains several hard and soft constraints. Flight connection is the main hard constraint which ensures the arrival airport does not have conflicts with the next flight departure airport. Turn-around period is another hard constraint which requests the legal minimization time gap between two adjacent flights of an aircraft. In addition, the soft constraints can be formulated into objectives which contain the minimal total delay
Solution by using hybrid MMGA (HMMGA)
Genetic algorithms, first introduced by Holland (Holland, 1975), were later improved by many researchers (Leung and Wang, 2001, Tsai et al., 2004) to serve as the global explorer for the single objective (Tsai, Chou, & Liu, 2006) or multiobjective optimization problems. For most well-designed multiobjective genetic algorithms (Chou et al., 2008, Deb et al., 2002, Horn et al., 1994, Zitzler and Thiele, 1999), Pareto-based or similar scenario guides the search for the variety and tries to explore
HMMGA algorithm
The flow chart of the hybrid algorithm is summarized in Fig. 1. Just like the general multiobjective genetic algorithm (MOGA), the evolutionary population should be operated by iterations through initialization, fitness computation, multiobjective evaluation, crossover to generate offspring, mutation and selection for elimination. However, the method used to measure objectives differs greatly from the general MOGA.
Case study
In this study, a larger disturbance event, airport temporal closure in the afternoon due to bad weather (which usually happens in the summer in Taiwan), is simulated by directly assigning a disruption time period on the flight schedule. The simulated scenario from a practice expects to prioritize the total flight delay time objective first and then measure the other objectives. This makes the recovery problem become more complex containing hard constraints, one prioritized objective and four
Experimental results
The customized parameters are chosen through repeating experiments for good performance: population size 100, off-spring size 80, crosser rate 1.0, mutation rate 0.3, and AEV separation ratio 0.8. For the hardware and software environment, the specifications are an Intel P4 3.2G CPU, 1G memory, XP SP2 OS and Dev-C++4.9.9.2 complier.
Conclusions
Aircraft recovery problems usually involve many practical objectives and should be solved within the short time limitations. Most multiobjective evolutionary algorithms mainly search for the Pareto solutions prior to considering performance constraints. Such methods may not fit the practical recovery needs especially when the response time is required to be short enough. Hence, a hybrid multiobjective genetic algorithm is proposed in this paper to provide an optimal or sub-optimal recovery
Acknowledgement
This work was supported by the National Science Council, Taiwan, Republic of China, under Grant numbers NSC 96-2221-E-327-027, NSC 96-2221-E-327-005-MY2, and NSC 96-2628-E-327-004-MY3.
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