Optimizing my solution for problem #23 - project Euler
I would like to optimize my solution.

Really? It's already pretty fast and there isn't much to gain, given that Java has some start up overhead. I'd save my power for later Eulers.
Set&lt;Integer&gt; abundantNumSet = new LinkedHashSet&lt;Integer&gt;();

Do you need &quot;Linked&quot;? I don't think so, so we've a tiny optimization.
    abundantNumSet.add(12);
    for (int i = 13; i &lt; 28124; ++i) {
        if (isAbundant(i)) {
            abundantNumSet.add(i);
        }
    }

I really wouldn't do it. You're testing nearly 30k numbers, so is it worth to optimize the first 13? Moreover, the saved tests are the fastest.
You should use no magic constants like 12, 13, 28124. Define constants and give them proper names. This will help you to avoid unworthy optimizations. :D
    int total = 276; // sigma 23, since 24 = 12 * 2
    for (int i = 25; i &lt; 28124; ++i) {

Another unworthy optimization, more magic numbers. What's worse, a repeated magic number. One day, in a big project you save a second by copying some numbers instead of defining constants. Another day, you change them all (it's easy, isn't it?). Yet another day, you'll be hunting a bug caused by having changed a completely unrelated number which by accident had the same value.
        boolean isRep = false;

The loop body is big enough for an own method. Then you can drop the variable, instead of spending time on naming it properly (isRep is not properly).
            // iterating through half of the numbers in the set is enough

This is a promise, you didn't keep. No problem, as this part takes much less time than the other, so speeding it twice helps nothing.
I'd go for a method like this (untested):
private boolean isSumOfTwoAbundants(int n) {
    for (int i : abundantNumSet) {
         if (i &gt; n - i) {
             break;
         }
         if (abundantNumSet.contains(n - i)) {
             return true;
         }
    }
    return false;
}

When using things like this
    int end = (int) Math.sqrt(n);

be aware of how it get rounded. I always prefer Guava's
   IntMath.sqrt(int, RoundingMode)

as it's explicit about it.
    if (sum &gt; n) {
        return true;
    }

    return false;

Do you really mean return sum &gt; n?
I guess, isAbundant could be sped up by factorization:

Similarly to the Sieve of Eratosthenes, you can precompute one factor for all numbers up to 28124.
For every number n, you get one factor, which you can divide out and get another number and another factor etc., till you have the factorization of n.
Having all prime factors (with their exponents), you can trivially compute the number of divisors.

This would probably help a lot, however, your code is already more then fast enough. While I love optimizing, I did about nothing for this problem and it took one second only (yours is about 10 times faster, do I care?).
Summary
You can optimize, but now it's time to learn not to optimize. Otherwise you can get quickly lost in the root of all evil.