Paradox-free analysis for comparing the performance of optimization algorithms

Numerical comparison serves as a major tool in evaluating the performance of optimization algorithms, especially nondeterministic algorithms, but existing methods may suffer from a ‘cycle ranking’ paradox and/or a ‘survival of the nonfittest paradox. This paper searches for paradox-free data analysis methods for numerical comparison. It is discovered that a class of sufficient conditions exist for designing paradox-free analysis. Rigorous modeling and deduction are applied to a class of profile methods employing a filter. It is thus further discovered and proven that algorithm-independent filter conditions can prevent cycle ranking and survival of non-fittest paradoxes from occurring. By adopting an algorithm-independent filter, popular profile methods such as the ‘modified data profile method’, ‘the accuracy profile method’, and ‘the operational characteristics zones method’ can be paradox free in comparing or bench-marking the performance of optimization algorithms.