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We present a nonparametric comparative efficiency analysis of urban public transport systems (UPTS) in Shanghai (2004-2012). The UPTS include urban public bus transit system (UPBTS) and urban public rail transit system (UPRTS). We apply data envelopment analysis (DEA) to assess the technical, pure technical and scale efficiencies of UPBTS and UPRTS over years. We find the performance of UPBTS and UPRTS are good in general but still have a potential scope for improvement. We also quantitatively analyze the reasons for inefficiency of them in some years and provide potential improvements for inefficient units. Moreover, we observe the efficiency of UPBTS is better despite a good development trend in the efficiency of the UPRTS. We demonstrate the UPRTS during the period 2006-2011 works on decreasing returns to scale (DRS), which indicates the authorities should adjust the UPRTS structure and improve the operational services without blindly expanding the levels of inputs. Our work may help in evaluating the possible enhancement of the operations of the UPTS.

An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.