Re-labeling Differential Evolution for combinatorial optimization

In this paper, the authors propose a new differential evolution (DE) technique called Re-labeling Differential Evolution for combinatorial optimization. DE was proposed in 1995 by Stone and Price. DE is one of the techniques of evolutionary computation (EC), and efficiently solves optimization problems using difference vectors between individuals in continuous space. DE can efficiently solve problems using information about the landscape of objective functions obtained by difference vectors between individuals. However, in problems whose solution candidates (individuals in EC terminology) are sets of integer values which are used to identify several different things, the information about the landscape of objective functions can not be obtained by difference vectors. For example, in a route selection problem where routes are distinguished by integer valued indices, such as route 1, route 2 and so on, although route 1 and route 2 have indices numerically close to each other, length of these routes are not necessarily similar to each other. In order to apply the DE to such problems, Re-labeling DE re-labels indices so that difference vectors are small between two individuals whose fitness values are close to each other. The proposed Re-labeling DE is compared with genetic algorithms (GA) and normal DE in the performance when applied to example route selection problems which are simple combinatorial optimization problems, and usefulness of Re-labeling DE is confirmed.