Differential adaptation: An operational approach to adaptation for solving numerical problems with CBR

Case-based reasoning relies on four main steps: retrieval, adaptation, revision and retention. This article focuses on the adaptation step; we propose differential adaptation as an operational formalization of adaptation for numerical problems. The solution to a target problem is designed on the basis of relations existing between a source case (problem and solution) and a target case. Differential adaptation relies on the metaphor of differential calculus where small variations on variable values are related to variations of function values. Accordingly, variations between problems correspond to variations between variable values and variations between solutions to variations between function values. Operators inspired from differential calculus are able to manipulate the variations and to support the whole adaptation process. Differential adaptation is operational and provides generic operators that can be reused for different real-world numerical situations.