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An Efficient Evolutionary Algorithm for Diversified Top-k (Weight) Clique Search Problems

Jiongzhi Zheng, Jinghui Xue, Kun He, Chu-Min Li, Yanli Liu

TL;DR

This work tackles Diversified Top-$k$ Clique problems by introducing DiverTEAM, a two-stage hybrid algorithm that first uses a focused local search to generate diverse, high-quality cliques and then applies an efficient genetic algorithm to propagate promising genes across a population, aided by pseudo graph reduction and tabu-search-based diversity controls. The method achieves near-optimal performance on both DTkC and DTkWC across real-world, dense DIMACS, and random graphs, with ablations showing the value of each component. Key contributions include a specialized crossover for clique-based genes, a scalable solution-based tabu mechanism, and postprocessing techniques that enhance final solutions without sacrificing non-worsening guarantees. The results demonstrate strong, robust improvements and suggest the framework can be adapted to other DTk problems defined on graphs.

Abstract

In many real-world problems and applications, finding only a single element, even though the best, among all possible candidates, cannot fully meet the requirements. We may wish to have a collection where each individual is not only outstanding but also distinctive. Diversified Top-k (DTk) problems are a kind of combinatorial optimization problem for finding such a promising collection of multiple sub-structures, such as subgraphs like cliques and social communities. In this paper, we address two representative and practical DTk problems, DTk Clique search (DTkC) and DTk Weight Clique search (DTkWC), and propose an efficient algorithm called Diversified Top-k Evolutionary AlgorithM (DiverTEAM) for these two problems. DiverTEAM consists of a local search algorithm, which focuses on generating high-quality and diverse individuals and sub-structures, and a genetic algorithm that makes individuals work as a team and converge to (near-)optima efficiently. Extensive experiments show that DiverTEAM exhibits an excellent and robust performance across various benchmarks of DTkC and DTkWC.

An Efficient Evolutionary Algorithm for Diversified Top-k (Weight) Clique Search Problems

TL;DR

This work tackles Diversified Top- Clique problems by introducing DiverTEAM, a two-stage hybrid algorithm that first uses a focused local search to generate diverse, high-quality cliques and then applies an efficient genetic algorithm to propagate promising genes across a population, aided by pseudo graph reduction and tabu-search-based diversity controls. The method achieves near-optimal performance on both DTkC and DTkWC across real-world, dense DIMACS, and random graphs, with ablations showing the value of each component. Key contributions include a specialized crossover for clique-based genes, a scalable solution-based tabu mechanism, and postprocessing techniques that enhance final solutions without sacrificing non-worsening guarantees. The results demonstrate strong, robust improvements and suggest the framework can be adapted to other DTk problems defined on graphs.

Abstract

In many real-world problems and applications, finding only a single element, even though the best, among all possible candidates, cannot fully meet the requirements. We may wish to have a collection where each individual is not only outstanding but also distinctive. Diversified Top-k (DTk) problems are a kind of combinatorial optimization problem for finding such a promising collection of multiple sub-structures, such as subgraphs like cliques and social communities. In this paper, we address two representative and practical DTk problems, DTk Clique search (DTkC) and DTk Weight Clique search (DTkWC), and propose an efficient algorithm called Diversified Top-k Evolutionary AlgorithM (DiverTEAM) for these two problems. DiverTEAM consists of a local search algorithm, which focuses on generating high-quality and diverse individuals and sub-structures, and a genetic algorithm that makes individuals work as a team and converge to (near-)optima efficiently. Extensive experiments show that DiverTEAM exhibits an excellent and robust performance across various benchmarks of DTkC and DTkWC.
Paper Structure (14 sections, 3 figures, 4 tables, 5 algorithms)

This paper contains 14 sections, 3 figures, 4 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The DiverTEAM Evolutionary Algorithm
  4. Main Process of DiverTEAM
  5. Pseudo Graph Reduction Preprocessing
  6. Local Search Process
  7. Genetic Algorithm
  8. Tabu Search in the Genetic Algorithm
  9. Postprocessing
  10. Experimental Results
  11. Experimental Setup
  12. Performance Evaluation
  13. Ablation Study
  14. Conclusion

Figures (3)

  • Figure 1: An instance for the DT$k$WC problem.
  • Figure 2: Comparison of DiverTEAM and DT$k$C baselines. A point with coordinates $(x,y)$ represents a DT$k$C instance that the best result obtained by DiverTEAM is $x$ and the baseline algorithm is $x \times y$ in 10 runs. (a) DiverTEAM vs. HEA-D on Real-world graphs; (b) DiverTEAM vs. HEA-D on 2nd DIMACS and random graphs; (c) DiverTEAM vs. TOPKLS on Real-world graphs; (d) DiverTEAM vs. TOPKLS on 2nd DIMACS and random graphs.
  • Figure 3: Comparison of DiverTEAM and DT$k$WC baselines. A point with coordinates $(x,y)$ represents a DT$k$WC instance that the best result obtained by DiverTEAM is $x$ and the baseline algorithm is $x \times y$ in 10 runs. (a) DiverTEAM vs. HEA-D on Real-world graphs; (b) DiverTEAM vs. HEA-D on 2nd DIMACS and random graphs; (c) DiverTEAM vs. TOPKWCLQ on Real-world graphs; (d) DiverTEAM vs. TOPKWCLQ on 2nd DIMACS and random graphs.