An efficient memetic, permutation-based evolutionary algorithm for real-world train timetabling

Train timetabling is a difficult and very tightly constrained combinatorial problem that deals with the construction of train schedules. We focus on the particular problem of local reconstruction of the schedule following a small perturbation, seeking minimisation of the total accumulated delay by adapting times of departure and arrival for each train and allocation of resources (tracks, routing nodes, etc.). We describe a permutation-based evolutionary algorithm that relies on a semi-greedy heuristic to gradually reconstruct the schedule by inserting trains one after the other following the permutation. This algorithm can be hybridised with ILOG commercial MIP programming tool CPLEX in a coarse-grained manner: the evolutionary part is used to quickly obtain a good but suboptimal solution and this intermediate solution is refined using CPLEX. Experimental results are presented on a large real-world case involving more than one million variables and 2 million constraints. Results are surprisingly good as the evolutionary algorithm, alone or hybridised, produces excellent solutions much faster than CPLEX alone

On the Benefits of Inoculation, an Example in Train Scheduling

The local reconstruction of a railway schedule following a small perturbation of the traffic, seeking minimization of the total accumulated delay, is a very difficult and tightly constrained combinatorial problem. Notoriously enough, the railway company's public image degrades proportionally to the amount of daily delays, and the same goes for its profit! This paper describes an inoculation procedure which greatly enhances an evolutionary algorithm for train re-scheduling. The procedure consists in building the initial population around a pre-computed solution based on problem-related information available beforehand. The optimization is performed by adapting times of departure and arrival, as well as allocation of tracks, for each train at each station. This is achieved by a permutation-based evolutionary algorithm that relies on a semi-greedy heuristic scheduler to gradually reconstruct the schedule by inserting trains one after another. Experimental results are presented on various instances of a large real-world case involving around 500 trains and more than 1 million constraints. In terms of competition with commercial math ematical programming tool ILOG CPLEX, it appears that within a large class of instances, excluding trivial instances as well as too difficult ones, and with very few exceptions, a clever initialization turns an encouraging failure into a clear-cut success auguring of substantial financial savings

Black-box optimization benchmarking of IPOP-saACM-ES on the BBOB-2012 noisy testbed

In this paper, we study the performance of IPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy. The algorithm was tested using restarts till a total number of function evaluations of $10^6D$ was reached, where $D$ is the dimension of the function search space. The experiments show that the surrogate model control allows IPOP-saACM-ES to be as robust as the original IPOP-aCMA-ES and outperforms the latter by a factor from 2 to 3 on 6 benchmark problems with moderate noise. On 15 out of 30 benchmark problems in dimension 20, IPOP-saACM-ES exceeds the records observed during BBOB-2009 and BBOB-2010.Comment: Genetic and Evolutionary Computation Conference (GECCO 2012) (2012

Computational Methods for Probabilistic Inference of Sector Congestion in Air Traffic Management

This article addresses the issue of computing the expected cost functions from a probabilistic model of the air traffic flow and capacity management. The Clenshaw-Curtis quadrature is compared to Monte-Carlo algorithms defined specifically for this problem. By tailoring the algorithms to this model, we reduce the computational burden in order to simulate real instances. The study shows that the Monte-Carlo algorithm is more sensible to the amount of uncertainty in the system, but has the advantage to return a result with the associated accuracy on demand. The performances for both approaches are comparable for the computation of the expected cost of delay and the expected cost of congestion. Finally, this study shows some evidences that the simulation of the proposed probabilistic model is tractable for realistic instances.Comment: Interdisciplinary Science for Innovative Air Traffic Management (2013

Multiobjective Tactical Planning under Uncertainty for Air Traffic Flow and Capacity Management

We investigate a method to deal with congestion of sectors and delays in the tactical phase of air traffic flow and capacity management. It relies on temporal objectives given for every point of the flight plans and shared among the controllers in order to create a collaborative environment. This would enhance the transition from the network view of the flow management to the local view of air traffic control. Uncertainty is modeled at the trajectory level with temporal information on the boundary points of the crossed sectors and then, we infer the probabilistic occupancy count. Therefore, we can model the accuracy of the trajectory prediction in the optimization process in order to fix some safety margins. On the one hand, more accurate is our prediction; more efficient will be the proposed solutions, because of the tighter safety margins. On the other hand, when uncertainty is not negligible, the proposed solutions will be more robust to disruptions. Furthermore, a multiobjective algorithm is used to find the tradeoff between the delays and congestion, which are antagonist in airspace with high traffic density. The flow management position can choose manually, or automatically with a preference-based algorithm, the adequate solution. This method is tested against two instances, one with 10 flights and 5 sectors and one with 300 flights and 16 sectors.Comment: IEEE Congress on Evolutionary Computation (2013). arXiv admin note: substantial text overlap with arXiv:1309.391

ATNoSFERES revisited

ATNoSFERES is a Pittsburgh style Learning Classifier System (LCS) in which the rules are represented as edges of an Augmented Transition Network. Genotypes are strings of tokens of a stack-based language, whose execution builds the labeled graph. The original ATNoSFERES, using a bitstring to represent the language tokens, has been favorably compared in previous work to several Michigan style LCSs architectures in the context of Non Markov problems. Several modifications of ATNoSFERES are proposed here: the most important one conceptually being a representational change: each token is now represented by an integer, hence the genotype is a string of integers; several other modifications of the underlying grammar language are also proposed. The resulting ATNoSFERES-II is validated on several standard animat Non Markov problems, on which it outperforms all previously published results in the LCS literature. The reasons for these improvement are carefully analyzed, and some assumptions are proposed on the underlying mechanisms in order to explain these good results