An Analysis of Evolutionary Algorithms for Finding Approximation Solutions to Hard Optimisation Problems

In practice, evolutionary algorithms are often used to find good feasible solutions to complex optimisation problems in a reasonable running time, rather than the optimal solutions. In theory, an important question we should answer is that: how good approximation solutions can evolutionary algorithms produce in a polynomial time? This paper makes an initial discussion on this question and connects evolutionary algorithms with approximation algorithms together. It is shown that evolutionary algorithms can’t find a good approximation solution to two families of hard problems.