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.

Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to automatically learn effective solvers for CO. The resultant new paradigm is termed neural combinatorial optimization (NCO). However, the advantages and disadvantages of NCO relative to other approaches have not been empirically or theoretically well studied. This work presents a comprehensive comparative study of NCO solvers and alternative solvers. Specifically, taking the traveling salesman problem as the testbed problem, the performance of the solvers is assessed in five aspects, i.e., effectiveness, efficiency, stability, scalability, and generalization ability. Our results show that the solvers learned by NCO approaches, in general, still fall short of traditional solvers in nearly all these aspects. A potential benefit of NCO solvers would be their superior time and energy efficiency for small-size problem instances when sufficient training instances are available. Hopefully, this work would help with a better understanding of the strengths and weaknesses of NCO and provide a comprehensive evaluation protocol for further benchmarking NCO approaches in comparison to other approaches.

Since automatic algorithm configuration methods have been very effective, recently there is increasing research interest in utilizing them for automatic solver construction, resulting in several notable approaches. For these approaches, a basic assumption is that the given training set could sufficiently represent the target use cases such that the constructed solvers can generalize well. However, such an assumption does not always hold in practice since in some cases, we might only have scarce and biased training data. This article studies effective construction approaches for the parallel algorithm portfolios that are less affected in these cases. Unlike previous approaches, the proposed approach simultaneously considers instance generation and portfolio construction in an adversarial process, in which the aim of the former is to generate instances that are challenging for the current portfolio, while the aim of the latter is to find a new component solver for the portfolio to better solve the newly generated instances. Applied to two widely studied problem domains, that is, the Boolean satisfiability problems (SAT) and the traveling salesman problems (TSPs), the proposed approach identified parallel portfolios with much better generalization than the ones generated by the existing approaches when the training data were scarce and biased. Moreover, it was further demonstrated that the generated portfolios could even rival the state-of-the-art manually designed parallel solvers.

Over the past few years, various word-level textual attack approaches have been proposed to reveal the vulnerability of deep neural networks used in natural language processing. Typically, these approaches involve an important optimization step to determine which substitute to be used for each word in the original input. However, current research on this step is still rather limited, from the perspectives of both problem-understanding and problem-solving. In this paper, we address these issues by uncovering the theoretical properties of the problem and proposing an efficient local search algorithm (LS) to solve it. We establish the first provable approximation guarantee on solving the problem in general cases. Extensive experiments involving 5 NLP tasks, 8 datasets and 26 NLP models show that LS can largely reduce the number of queries usually by an order of magnitude to achieve high attack success rates. Further experiments show that the adversarial examples crafted by LS usually have higher quality, exhibit better transferability, and can bring more robustness improvement to victim models by adversarial training.