I don't use shuttles very often in Apex, but they can come in handy.
A feature that I recently needed was to sort both the left and right columns of the shuttle at all times. Some googling led me to this page where user jariola had a javascript solution that works fine. I just added a dynamic action to make life easier.

In the example above, Shuttle 1 is unsorted and Shuttle 2 is sorted, both with the same data, so you can see the difference when you try them both.
Note 1: The Ordering buttons still work as intended, as long as you don't add/remove any items - then the column(s) will sort again.
Note 2: The dynamic action makes calls for the left and right columns, so you can sort either column or both.
Note 3: Numbers are sorted as text here. If that's not what you want, take a look here.

Source: https://community.oracle.com/message/9570151#9570151

Page

Identification
	Page ID	1087
	Name	Apex - Shuttles - Shuttle Sorting
Javascript
	Function and Global Variable Declaration	function sortSelectOptions(pThis){ var t=$($x(pThis)); var o=t.children("option"); o.detach(); o.sort(function(a,b){ a=a.firstChild.nodeValue; b=b.firstChild.nodeValue; if(a==b){ return 0; } return (a>b)?1:-1; }); t.append(o); }

Item

Identification
	Sequence	10
	Name	P1087_SHUTTLE_1
	Display As	Shuttle
User Interface
	Region	Shuttle Sorting
List Of Values
	Display Extra Values	Yes
	Display Null Value	No
	List of values definition	select ename as d , ename as r from emp where rownum <= 7 union all select '1' as d, '1' as r from dual union all select '10' as d, '10' as r from dual union all select '2' as d, '2' as r from dual union all select '99' as d, '99' as r from dual union all select '3' as d, '3' as r from dual union all select '100' as d, '100' as r from dual -- note the weird sorting just to prove the point
Advanced
	Warn on Unsaved Changes	Page Default
Source
	Source Used	Only when current value in session state is null
	Source Type	Always Null

Item

Identification
	Sequence	20
	Name	P1087_SHUTTLE_2
	Display As	Shuttle
User Interface
	Region	Shuttle Sorting
List Of Values
	Display Extra Values	Yes
	Display Null Value	No
	List of values definition	select ename as d , ename as r from emp where rownum <= 7 union all select '1' as d, '1' as r from dual union all select '10' as d, '10' as r from dual union all select '2' as d, '2' as r from dual union all select '99' as d, '99' as r from dual union all select '3' as d, '3' as r from dual union all select '100' as d, '100' as r from dual -- note the weird sorting just to prove the point
Advanced
	Warn on Unsaved Changes	Page Default
Source
	Source Used	Only when current value in session state is null
	Source Type	Always Null

Dynamic Action

Identification
	Name	Sort Shuttle 2
Execution Options
	Sequence	10
When
	Event	Change
	Selection Type	Item
	Item(s)	P1087_SHUTTLE_2
Advanced
	Event Scope	Static
True Action
Identification
	Action	Execute JavaScript Code
Settings
	Code	sortSelectOptions('P1087_SHUTTLE_2_LEFT'); sortSelectOptions('P1087_SHUTTLE_2_RIGHT');
Execution Options
	Sequence	10
	Fire On Initialization	Yes