If you use Java 8, you can use Comparator.comparing(Double::parseDouble)to quickly create a comparator with parseDouble. This should (see below) call the function only once for each record, and not once for each pair.
List<String> list = Arrays.asList( "12", "3.5", "188", "33.03" );
list.sort(Comparator.comparing(Double::parseDouble));
System.out.println(list);
Conclusion:
[3.5, 12, 33.03, 188]
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