Generalization, i.e., the ability of solving problem instances that are not available during the system design and development phase, is a critical goal for intelligent systems. A typical way to achieve good generalization is to learn a model from vast data. In the context of heuristic search, such a paradigm could be implemented as configuring the parameters of a parallel algorithm portfolio (PAP) based on a set of 'training' problem instances, which is often referred to as PAP construction. However, compared to the traditional machine learning, PAP construction often suffers from the lack of training instances, and the obtained PAPs may fail to generalize well. This article proposes a novel competitive co-evolution scheme, named co-evolution of parameterized search (CEPS), as a remedy to this challenge. By co-evolving a configuration population and an instance population, CEPS is capable of obtaining generalizable PAPs with few training instances. The advantage of CEPS in improving generalization is analytically shown in this article. Two concrete algorithms, namely, CEPS-TSP and CEPS-VRPSPDTW, are presented for the traveling salesman problem (TSP) and the vehicle routing problem with simultaneous pickup-delivery and time windows (VRPSPDTW), respectively. The experimental results show that CEPS has led to better generalization, and even managed to find new best-known solutions for some instances. © 1997-2012 IEEE.
Bibliographical noteThis work was supported in part by the Guangdong Provincial Key Laboratory under Grant 2020B121201001; in part by the Program for Guangdong Introducing Innovative and Entrepreneurial Teams under Grant 2017ZT07X386; in part by the Shenzhen Peacock Plan under Grant KQTD2016112514355531; in part by the Science and Technology Commission of Shanghai Municipality under Grant 19511120600; in part by the National Leading Youth Talent Support Program of China; and in part by the MOE University Scientific-Technological Innovation Plan Program.
- Algorithm configuration
- automatic parameter tuning
- parallel algorithm portfolios (PAPs)
- vehicle routing problems