To what extent evolutionary algorithms can benefit from a longer search?

In many comparison papers Evolutionary Algorithms are stopped after a pre-defined number of function calls, which is a code-independent measure of computational time. This number of function calls is either defined by the inventors of particular benchmark problems, or set subjectively by the user for the specific problem. The question how much improvement could be achieved by Evolutionary Algorithms if they were given much more time is surprisingly rarely asked. In the present study we analyze improvements obtained by thirty Evolutionary Algorithms on four different benchmark sets, including one composed of 22 real-world problems, when the allowed number of function calls is extended ten times with respect to the values defined in the comparison criteria for the specific benchmark sets. We analyze how the prolonged search would affect the ranking of algorithms, how much improvement could be obtained by Evolutionary Algorithms in general, on what kind of problems the improvement will be achieved, and which type of algorithms would benefit most from such an extended search. We show that the improvements obtained in prolonged search are higher for real-world problems than for mathematical functions, and such improvements are mainly achieved by similar kinds of adaptive algorithms proposed relatively recently. Many metaheuristics fail to benefit from the extended search on most benchmark problems, or benefit only marginally.