Superior Genetic Algorithms for the Target Set Selection Problem Based on Power-Law Parameter Choices and Simple Greedy Heuristics

TL;DR

This work addresses the NP-hard Target Set Selection (TSS) problem, seeking a minimum seed set that activates all vertices under a threshold diffusion. It replaces costly offline parameter tuning with on-the-fly parameter choices drawn from capped power-law distributions and augments a BRKGA with a simple TSS-specific ReverseMDG pruning heuristic. Empirically, these lightweight modifications often match or outperform state-of-the-art methods (including BRKGA, MMAS, and MMAS-Learn) on hard instances, with statistical significance in many cases, while avoiding expensive preprocessing. The findings suggest that parameterless or parameter-light randomized strategies coupled with problem-specific reductions can surpass more complex approaches, with potential applicability to broader combinatorial optimization problems. The approach emphasizes practical efficiency and ease of use without sacrificing solution quality, highlighting a path toward more robust, scalable heuristics in diffusion-based graph problems.

Abstract

The target set selection problem (TSS) asks for a set of vertices such that an influence spreading process started in these vertices reaches the whole graph. The current state of the art for this NP-hard problem are three recently proposed randomized search heuristics, namely a biased random-key genetic algorithm (BRKGA) obtained from extensive parameter tuning, a max-min ant system (MMAS), and a MMAS using Q-learning with a graph convolutional network. We show that the BRKGA with two simple modifications and without the costly parameter tuning obtains significantly better results. Our first modification is to simply choose all parameters of the BRKGA in each iteration randomly from a power-law distribution. The resulting parameterless BRKGA is already competitive with the tuned BRKGA, as our experiments on the previously used benchmarks show. We then add a natural greedy heuristic, namely to repeatedly discard small-degree vertices that are not necessary for reaching the whole graph. The resulting algorithm consistently outperforms all of the state-of-the-art algorithms. Besides providing a superior algorithm for the TSS problem, this work shows that randomized parameter choices and elementary greedy heuristics can give better results than complex algorithms and costly parameter tuning.