Similarity of Continuous Optimization Problems from the Algorithm Performance Perspective
Yongwei Zhang, Saman Kumara Halgamuge · 2019
In the field of optimization, the performance of algorithms can be inferred by relating the problem features or properties to the past performance of algorithms on the tested instances of problems. However, the problem features or properties are usually strongly connected to the specific problem domain, which makes it difficult to apply the established feature-performance model in one problem domain to another. In our previous work, we tested 28 algorithms from different categories on a problem set consisting of 5562 instances and mapped the algorithm performance into a vector of 5562 elements via the proposed fractional ranking method. In this work, we propose to use the fractional ranking consisting of performance mapping of three unique criteria for finding similarity between continuous optimization problems. A feature vector consisting of 28 elements, derived from the performance of 28 algorithms, is used to compare the problems. This methodology enables comparison and visualizes differences of performance by the algorithms applied to the problems from different domains. The principal component analysis shows that the selected problem set has comprehensive coverage of the instance space. The clustering analysis shows that performance-wise speaking, the instances from different problem families or dimensions may be very close in the instance space.