Core Instances for Testing: A Case Study

Abstract

Data generation for computational testing of optimization algorithms is a key topic in experimental algorithmics. Recently, concern has arisen that many published computational experiments are inadequate respect to the way test instances are generated. In this paper we suggest a new research direction that might be useful to cope with the possible limitations of data generation. The basic idea is to select a finite set of instances which ‘represent’ the whole set of instances. We propose a measure of the representativeness of an instance, which we call ε-representativeness: for a minimization problem, an instance x ε is ε-representative of another instance x if a (1 + ε)-approximate solution to x can be obtained by solving x ε. Focusing on a strongly NP-hard single machine scheduling problem, we show how to map the infinite set of all instances into a finite set of ε-representative core instances. We propose to use this finite set of ε-representative core instances to test heuristics.

Supported by Swiss National Science Foundation project 20-63733.00/1, “Resource Allocation and Scheduling in Flexible Manufacturing”, and by the “Metaheuristics Network”, grant HPRN-CT-1999-00106.