This paper proposes a novel algorithm for solving combinatorial optimization problems using genetic algorithms (GA) with self-adaptive mutation. We selected the N-Queens problem (8 ≤ N ≤ 32) as our benchmarking test suite, as they are highly multi-modal with huge numbers of global optima. Optimal static mutation probabilities for the traditional GA approach are determined for each N to use as a best-case scenario benchmark in our conducted comparative analysis. Despite an unfair advantage with traditional GA using optimized fixed mutation probabilities, in large problem sizes (where N > 15) multi-objective analysis showed the self-adaptive approach yielded a 65% to 584% improvement in the number of distinct solutions generated; the self-adaptive approach also produced the first distinct solution faster than traditional GA with a 1.90% to 70.0% speed improvement. Self-adaptive mutation control is valuable because it adjusts the mutation rate based on the problem characteristics and search process stages accordingly. This is not achievable with an optimal constant mutation probability which remains unchanged during the search process.