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This paper studies the evolutionary planning strategies for mobile robots to move smoothly along efficient collision-free paths in known static environments. The cost of each candidate path is composed of the path length and a weighted sum of penetration depth to vertices of polygonal obstacles. The path is composed of a pre-specified number of cubic spiral segments with constrained curvature. Comparison of the path planning performance between two Pareto-optimal schemes, the parallel genetic algorithm scheme based on the island method (PGA) and the non-dominated sorting genetic algorithm (NSGA-II), are conducted in terms of success rate in separate runs and path length whenever collision-free paths are found. Numerical simulation results are presented for three types of obstacles: polygons, walls, and combinations of both.