Ubuntu 17.10 and later: can't change the input switching shortcut to alt+shift

You may use (GNOME) Tweaks to achieve your goal. First install it by running

sudo apt install gnome-tweaks

(on Ubuntu 18.04 and later) or

sudo apt install gnome-tweak-tool

Launch Tweaks and go to Keyboard & Mouse section. Click on the "Additional Layout Options".

A new window should pop up. Look for "Switching to another layout" and expand it. Then check the "Alt+Shift" option.

You can achieve this using gsettings (command-line configuration tool).

1. Set forward switch to Shift+Alt(left)

   gsettings set org.gnome.desktop.wm.keybindings switch-input-source "['<Shift>Alt_L']"
   

2. Set backward switch to Alt+Shift(left)

   gsettings set org.gnome.desktop.wm.keybindings switch-input-source-backward "['<Alt>Shift_L']"
   

To see the current setting value use get command:

gsettings get org.gnome.desktop.wm.keybindings switch-input-source
gsettings get org.gnome.desktop.wm.keybindings switch-input-source-backward

Examples of other key bindings:

<Primary>space, Alt_R, <Shift>Control_R, <Shift><Super>space

Changes will take effect immediately.

Ubuntu 20.20, gnome flashback, the gsettings option didn't work for me. This fixed the problem (copied from my other machine):

gsettings set org.gnome.desktop.input-sources xkb-options "['grp:alt_shift_toggle', 'grp_led:scroll', 'lv3:switch']"

Keyboard shortcuts still show Super+Space combination, and it still works, but Alt+Shift works as well.