Evolutionary computation: toward a new philosophy of machine intelligence
Evolutionary computation: toward a new philosophy of machine intelligence
An introduction to genetic algorithms
An introduction to genetic algorithms
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Network design techniques using adapted genetic algorithms
Advances in Engineering Software
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
Constructing Railroad Blocking Plans to Minimize Handling Costs
Transportation Science
Fuzzy fixed charge solid transportation problem and algorithm
Applied Soft Computing
Logistics distribution centers location problem and algorithm under fuzzy environment
Journal of Computational and Applied Mathematics
Train timetable problem on a single-line railway with fuzzy passenger demand
IEEE Transactions on Fuzzy Systems
Random fuzzy programming with chance measures defined by fuzzy integrals
Mathematical and Computer Modelling: An International Journal
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The railway freight transportation planning problem under the mixed uncertain environment of fuzziness and randomness is investigated in this paper, in which the optimal paths, the amount of commodities passing through each path and the frequency of services need to be determined. Based on the chance measure and critical values of the random fuzzy variable, three chance-constrained programming models are constructed for the problem with respect to different criteria. Some equivalents of objectives and constraints are also discussed in order to investigate mathematical properties of the models. To solve the models, a potential path searching algorithm, simulation algorithms and a genetic algorithm are integrated as a hybrid algorithm to solve an optimal solution. Finally, some numerical examples are performed to show the applications of the models and the algorithm.