Multidomain Evolutionary Optimization on Combinatorial Problems in Complex Networks

TL;DR

This paper introduces Multi-Domain Evolutionary Optimization (MDEO), a framework for transferring solutions across network domains that share structural properties, enabling improved optimization of graph-structured combinatorial problems. It integrates four components—graph similarity, graph embedding via a graph autoencoder, network alignment, and many-network evolutionary optimization—along with a self-adaptive transfer mechanism and a knowledge-guided mutation to harness cross-domain insights. Empirical evidence on eight real-world networks shows MDEO consistently outperforms single-domain evolutionary optimization and other baselines in adversarial community deception and, more broadly, node-level tasks like influence maximization, highlighting its generality and practical impact. The work highlights cross-domain knowledge transfer as a viable path to tackle complex network problems with improved efficiency and robustness, while outlining future directions for bidirectional transfer and scalability across heterogeneous network sizes.

Abstract

Knowledge transfer-based evolutionary optimization has garnered significant attention, such as in multi-task evolutionary optimization (MTEO), which aims to solve complex problems by simultaneously optimizing multiple tasks. While this emerging paradigm has been primarily focusing on task similarity, there remains a hugely untapped potential in harnessing the shared characteristics between different domains. For example, real-world complex systems usually share the same characteristics, such as the power-law rule, small-world property and community structure, thus making it possible to transfer solutions optimized in one system to another to facilitate the optimization. Drawing inspiration from this observation of shared characteristics within complex systems, we present a novel framework, multi-domain evolutionary optimization (MDEO). First, we propose a community-level measurement of graph similarity to manage the knowledge transfer among domains. Furthermore, we develop a graph learning-based network alignment model that serves as the conduit for effectively transferring solutions between different domains. Moreover, we devise a self-adaptive mechanism to determine the number of transferred solutions from different domains, and introduce a knowledge-guided mutation mechanism that adaptively redefines mutation candidates to facilitate the utilization of knowledge from other domains. To evaluate its performance, we use a challenging combinatorial problem known as adversarial link perturbation as the primary illustrative optimization task. Experiments on multiple real-world networks of different domains demonstrate the superiority of the proposed framework in efficacy compared to classical evolutionary optimization.

Figures (5)

• Figure 1: The diagram of multi-domain evolutionary optimization. Four networks representing different systems (brain network, power network, social network, communication network) are optimized simultaneously. The transfer of knowledge across networks is achieved through the trained network alignment model. $e^{i}_j$ denote the $j$-th edge in $i$-th network and $M_{i \rightarrow j}$ is the edge mapping from the $i$-th network to the $j$-th network. The solution shown in yellow represents the transferred solution, while the light red color represents the elite solution from other networks. The red edge is the mutated edge that will be replaced by the edge of elite solutions of other networks. The knowledge exchange occurs when a series of conditions are met, and only elite solutions will be utilized to assist the optimization of other networks.
• Figure 2: The optimization curve of MDEO and SDEO on eight tested networks for the illustrative task of community deception, with FastGreedy as the attacker.
• Figure 3: The optimization curve of MDEO and SDEO on eight tested networks for the illustrative task of community deception, with WalkTrap as the attacker.
• Figure 4: Average running time of MDEO under different parameter settings when optimizing eight real-world networks simultaneously.
• Figure 5: The optimization curve of MDEO and SDEO in addressing the node-level problem of influence maximization.

Theorems & Definitions (5)

• Definition 1
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• Definition 5