From Twomax To The Ising Model: Easy And Hard Symmetrical Problems

The paper shows that there is a key dividing line between two types of symmetrical problems: problems for which a genetic algorithm (GA) benefits from the fact that genetic drift chooses between equally good partial solutions, and problems for which all equally good partial solutions have to be preserved to find an optimum. By analyzing in detail the search process of a selectorecombinative GA optimizing a TwoMax and comparing this search process with that of a one-dimensional Ising model, the paper investigates the difference between these two types of symmetrical problems. For the first type of problems, naively adding a niching technique to the genetic algorithm makes the problem harder to solve. For the last type of problems, niching is necessary to find an optimum.