Relative Position Indexing Approach

Abstract

We introduce some standard types of combinatorial optimization problems, and indicate ways in which one might attack them using Differential Evolution. Our main focus will be on indexing by relative position (also known as order based representation); we will describe some related approaches as well. The types of problems we will consider, which are abstractions of ones from engineering, go by names such as knapsack problems, set coverings, set partitioning, and permutation assignment. These are historically significant types of problems, as they show up frequently, in various guises, in engineering and elsewhere. We will see that a modest amount of programming, coupled with a sound implementation of Differential Evolution optimization, can lead to good results within reasonable computation time.We will also show how Differential Evolution might be hybridized with other methods from combinatorial optimization, in order to obtain better results than might be found with the individual methods alone.