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A specialized genetic algorithm is proposed in this paper for path planning of vehicles based on time-dependent optimization criterion. A variable signal encoding scheme is adopted to represent the path and a particular fitness function is investigated for time-dependent shortest path planning. Domain heuristic knowledge based crossover, mutation and deletion operators are also specifically designed to fit the vehicle path planning problem. Furthermore, a new fuzzy logic control algorithm is integrated to self-adaptively adjust the probabilities of crossover and mutation in the proposed genetic algorithm. Simulation for both off-line and on-line path planning under five different environments are carried out, and the comparative studies with Dijkstra and A* algorithm are presented. The simulation results show that the proposed genetic algorithm exhibits better performances such as rapid search speed and high search quality.