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A new hybrid heuristic for driver scheduling

This paper describes a new hybrid method based on the application of the Population Training Algorithm (PTA) and linear programming (LP) for generation of schedules for drivers in a public transport system. These methods are applied in an iterative way, where PTA is responsible for the generation of good columns (low cost and good covering of the tasks), and LP for solving a set partitioning problem formed by these columns. The PTA employs heuristics in fitness definition, guiding the population to settle down in search areas where the individuals cannot be improved by such heuristics. The driver schedules are represented by columns in a large-scale set partitioning problem, which are formed when solving the linear programming relaxation. The computational results are compared against a Simulated Annealing metaheuristic using randomly formed instances based on real problems.