Smutje gave you the answer how to do this in Java 5 to 7. With Java8 you can make use of the functional interfaces and lambda expressions. So your sorting method would reduce to

Arrays.sort(objectArray, Comparator.<YourObject>comparing(YourObject::getDate)
        .thenComparing(YourObject::getString));

Write a Comparator<YourObject> which first compares dates and, if the dates are equal, the names and sort the array

Example

YourObject

public class YourObject {

    private Date date;

    private String string;

    public Date getDate() {
        return date;
    }

    public void setDate(Date date) {
        this.date = date;
    }

    public String getString() {
        return string;
    }

    public void setString(String string) {
        this.string = string;
    }
}

Sorting

Arrays.sort(new YourObject[]{}, new Comparator<YourObject>() {

        @Override
        public int compare(YourObject o1, YourObject o2) {
            final int dateComparisonResult = o1.getDate().compareTo(o2.getDate());
            final int yourObjectComparisonResult;

            if (dateComparisonResult == 0) {
                yourObjectComparisonResult = o1.getString().compareTo(o2.getString());
            } else {
                yourObjectComparisonResult = dateComparisonResult;
            }

            return yourObjectComparisonResult;
        }
    });

Object[] obj = {obj1,obj2,obj3};

your array like this right

you just convert this into `java.util.List` , because it's having helpful API(classes & interfaces), so that you can easily access that API instead of your own tough coding

Step-1: List l = Arrays.asList(obj);

once you get the reference of List you can sort out the list by using `Collections.sort(Collection)`

Step-2: like, Collections.sort(l);

if you want your own sort technique like, By date or By name you just simply use java.util.Comparator interface

for example, Byname basis sorting the code snippet like this,

class ByName implements Comparator<String>{

    @Override
    public int compare(String str1, String str2) {
        // TODO Auto-generated method stub
        if(str1.length > str2.length)
           return 1;
        else
           return -1;
    }
}