Author: Community

Evolutionary Computation, Volume 29, Issue 1, Page 129-155, Spring 2021.

Evolutionary Computation, Volume 29, Issue 1, Page 107-128, Spring 2021.

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The complex network is an important tool to represent relational data in nature and human society, which has been widely applied in various real-world application scenarios. A key issue for analyzing the features of networks is to represent the characteristic information in the network with rationality. Network embedding, attracting plenty of attention recently, aims to convert network information into a low-dimensional space while maintaining the structure and properties of the network maximally. Most of the existing network embedding methods intend to preserve the pairwise relationship or similarity between nodes, but the community structure, which is one of the most important features of complex networks, is largely ignored. In this article, we propose a novel network embedding method based on evolutionary algorithm (EA), termed as EA-NE_Community, which can preserve both the local proximity of nodes and the community structure of the network by optimizing a carefully designed objective function. The number of communities in the network can be automatically determined without any prior knowledge. Moreover, taking the intrinsic properties of the network embedding problems in mind, we design a local search operator based on multidirectional search which can effectively find feasible solutions. In the experiments, we first visualize the embedding representation obtained by different algorithms, and then use the problems of node clustering, node classification, and link prediction to further validate the quality of the embedding representation obtained. The experimental results show that EA-NE_Community outperforms other state-of-the-art algorithms on both the real life and synthetic networks.

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Multi-solution problems extensively exist in practice. Particularly, the traveling salesman problem (TSP) may possess multiple shortest tours, from which travelers can choose one according to their specific requirements. However, very few efforts have been devoted to the multi-solution problems in the discrete domain. In order to fill this research gap and to effectively tackle the multi-solution TSP, we propose a niching memetic algorithm in this article. The proposed algorithm is characterized by a niche preservation technique to enable the parallel search of multiple optimal solutions; an adaptive neighborhood strategy to balance the exploration and exploitation; a critical edge-aware method to provide effective guidance to the reproduction; and a selective local search strategy to improve the search efficiency. To evaluate the performance of the proposed algorithm, we conduct comprehensive experiments on a recently published multi-solution optimization test suite. The experimental results show that our algorithm outperforms other compared algorithms. Furthermore, the proposed algorithm is adopted to tackle problems from the well-known TSPLIB library to obtain a set of distinct but good solutions.

Hypervolume (HV) is one of the most commonly used metrics for evaluating the Pareto front (PF) approximations generated by multiobjective evolutionary algorithms. Even so, HV is a resultant of a complex interplay between the PF shape, number of objectives, and user-specified reference points which, if not well understood, may lead to misinformed inferences about benchmarking performance. In order to understand this behavior, some previous studies have investigated such interactions empirically. In this letter, a new and unconventional approach is taken for gaining further insights about HV behavior. The key idea is to develop theoretical formulas for certain linear (equilateral simplex) and quadratic (orthant) PFs in two specific orientations: 1) regular and 2) inverted. These PFs represent a large number of problems in the existing DTLZ and WFG suites commonly used for benchmarking. The numerical experiments are presented to demonstrate the utility of the proposed work in benchmarking, and in understanding the contributions of the different regions of the PFs, such as corners, edges, as well explaining the contrast between the HV behaviors for regular versus inverted PFs. This letter provides a foundation and computationally fast means to undertake parametric studies to understand various aspects of HV.

Uncertainty is an important feature abstracted from real-world applications. Multiobjective optimization problems (MOPs) with uncertainty can always be characterized as robust MOPs (RMOPs). Over recent years, multiobjective optimization evolutionary algorithms (EAs) have demonstrated the success in solving MOPs. However, most of them do not consider disturbance in the design. In order to handling the uncertainty in the optimization problem, we first give a thorough analysis of three important issues on robust optimization. Then, a novel EA called multiobjective optimization EA with robustness enhancement is developed, where the seamless integration of robustness and optimality is achieved by a proposed novel archive updating mechanism applied on the evolutionary process as well as the new robust optimal front building strategy designed to construct the final robust optimal front. Furthermore, the new designed archive updating mechanism makes the robust optimization process free of the enormous computational workload induced from sampling. The experimental results on a set of benchmark functions show the superiority of the proposed design in terms of both solutions’ quality under the disturbance and computational efficiency in solving RMOPs.

Many real-world optimization problems lead to multimodal domains and require the identification of multiple optima. Crowding methods have been developed to maintain population diversity, to investigate many peaks in parallel and to reduce genetic drift. We present the first rigorous runtime analyses of probabilistic crowding and generalized crowding, embedded in a ( $mu +1$ ) EA. In probabilistic crowding the offspring compete with their parent in a fitness-proportional selection. Generalized crowding decreases the fitness of the inferior solution by a scaling factor during selection. We consider the bimodal function TwoMax and introduce a novel and natural notion for functions with bounded gradients. For a broad range of such functions we prove that probabilistic crowding needs exponential time with overwhelming probability to find solutions significantly closer to any global optimum than those found by random search. Even when the fitness function is scaled exponentially, probabilistic crowding still fails badly. Only if the exponential’s base is linear in the problem size, probabilistic crowding becomes efficient on TwoMax. A similar threshold behavior holds for generalized crowding on TwoMax with respect to the scaling factor. Our theoretical results are accompanied by experiments for TwoMax showing that the threshold behaviors also apply to the best fitness found.