Make MultipleShooting more robust with different initial guess

[ErikQQY]

Fix: #347

[github-actions]

Benchmark Results

Click to check benchmark results

	master	0b8378e...	master / 0b8378e...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.616 ± 0.013 s	0.623 ± 0.022 s	0.99 ± 0.041
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	14.2 ± 0.58 ms	14.1 ± 0.69 ms	1.01 ± 0.064
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	3.2 ± 0.2 ms	3.17 ± 0.15 ms	1.01 ± 0.079
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	9.49 ± 1.3 ms	9.47 ± 1.3 ms	1 ± 0.19
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.66 ± 0.29 ms	1.64 ± 0.29 ms	1.01 ± 0.25
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.85 ± 0.66 ms	1.87 ± 0.64 ms	0.989 ± 0.49
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	3.12 ± 0.99 ms	3.14 ± 0.97 ms	0.992 ± 0.44
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0682 ± 0.013 s	0.0679 ± 0.012 s	1 ± 0.26
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0838 ± 0.016 s	0.081 ± 0.021 s	1.03 ± 0.33
Simple Pendulum/IIP/Shooting(Tsit5())	0.234 ± 0.074 ms	0.239 ± 0.081 ms	0.977 ± 0.45
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.772 ± 0.016 s	0.78 ± 0.0059 s	0.99 ± 0.022
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	17.2 ± 6.1 ms	17.2 ± 5.1 ms	1 ± 0.46
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	3.66 ± 0.18 ms	3.67 ± 0.18 ms	0.996 ± 0.069
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	11 ± 2 ms	11.1 ± 0.99 ms	0.998 ± 0.2
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.91 ± 0.17 ms	1.91 ± 0.16 ms	1 ± 0.12
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.56 ± 2.9 ms	3.65 ± 2.9 ms	0.976 ± 1.1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	5.98 ± 5.2 ms	6.13 ± 5.5 ms	0.976 ± 1.2
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.12 ± 0.021 s	0.118 ± 0.013 s	1.02 ± 0.21
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.141 ± 0.019 s	0.145 ± 0.02 s	0.973 ± 0.19
Simple Pendulum/OOP/Shooting(Tsit5())	0.633 ± 0.044 ms	0.634 ± 0.046 ms	0.997 ± 0.1
time_to_load	4.74 ± 0.022 s	4.81 ± 0.023 s	0.985 ± 0.0066

### Benchmark Plots A plot of the benchmark results has been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).