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

Abstract

Train timetabling is a difficult and very tightly constrained combinatorial prob lem that deals with the construction of train schedules. We focus on the particu lar problem of local reconstruction of the schedule following a small perturbati on, seeking minimisation of the total accumulated delay by adapting times of dep arture and arrival for each train and allocation of resources (tracks, routing n odes, etc.). We describe a permutation-based evolutionary algorithm that relies on a semi-gre edy heuristic to gradually reconstruct the schedule by inserting trains one afte r the other following the permutation. This algorithm can be hybridised with ILO G commercial MIP programming tool CPLEX in a coarse-grained manner: the evolutio nary part is used to quickly obtain a good but suboptimal solution and this inte rmediate 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