Multidomain Evolutionary Optimization on Combinatorial Problems in Complex Networks

TL;DR

This paper introduces a multi-domain evolutionary optimization framework that leverages shared characteristics of complex networks, such as power-law and small-world properties, to improve combinatorial problem solving across diverse real-world systems.

Contribution

The paper presents a novel multi-domain evolutionary optimization framework utilizing graph similarity, network alignment, and adaptive mechanisms for knowledge transfer across complex network domains.

Findings

Outperforms classical evolutionary methods in real-world network problems.

Effective knowledge transfer improves optimization efficiency.

Framework adapts to different domain characteristics successfully.

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.