View article

Algebraic variants of the Differential Evolution (DE) algorithm have been recently proposed to tackle permutation-based optimization problems by means of an algebraic framework, which allows to directly encode the solutions as permutations. The algebraic DE in the permutation space can be characterized by considering different neighborhood definitions such as swapping two adjacent items, swapping any two items, shifting an item to a given position. Here we propose the Variable Neighborhood Differential Evolution for Permutations (VNDEP), which adaptively searches the three neighborhoods together based on a method of dynamic reward. We provide an extensive and systematic analysis of the theoretical tools required in VNDEP, by studying the complexity of the proposed algorithmic components and by introducing the possibility to use a scale factor parameter larger than one. Experiments have been …