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 traditional machine learning, PAP construction often suffers from the lack of training instances, and the obtained PAPs may fail to generalize well. This paper 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 paper. 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. Experimental results show that CEPS has led to better generalization, and even managed to find new best-known solutions for some instances.
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