[Paper Review] Recent Progress on Graph Partitioning Problems Using Evolutionary Computation

Hyejin Kim, Yong-Hyuk Kim|arXiv (Cornell University)|May 4, 2018

VLSI and FPGA Design Techniques20 references3 citations

TL;DR

This paper surveys recent advances (2011–2018) in solving the NP-hard graph partitioning problem (GPP) using evolutionary computation (EC). It reviews diverse EC approaches—including genetic algorithms, memetic algorithms, quantum-inspired evolution, particle swarm optimization, ant colony optimization, and harmony search—highlighting innovations in encoding schemes, local search integration, multi-level heuristics, and hybridization that yield competitive, high-quality solutions for real-world applications like circuit design and community detection.

ABSTRACT

The graph partitioning problem (GPP) is a representative combinatorial optimization problem which is NP-hard. Currently, various approaches to solve GPP have been introduced. Among these, the GPP solution using evolutionary computation (EC) is an effective approach. There has not been any survey on the research applying EC to GPP since 2011. In this survey, we introduce various attempts to apply EC to GPP made in the recent seven years.

Motivation & Objective

• To provide a comprehensive, up-to-date survey of evolutionary computation (EC) applications to the NP-hard graph partitioning problem (GPP), filling a gap since the last major review in 2011.
• To analyze and categorize recent EC techniques for GPP, including novel encoding strategies, local search integration, and hybridization with multi-level heuristics.
• To evaluate the effectiveness of various EC algorithms—such as quantum-inspired, memetic, and parallel GAs—in achieving high-quality, scalable solutions for large-scale graph partitioning.
• To identify trends and methodological innovations in EC-based GPP solving, particularly in improving convergence, avoiding local optima, and enhancing solution diversity.
• To support future research by organizing and summarizing key developments in EC for GPP, emphasizing practical performance and algorithmic design principles.

Proposed method

• Proposes and evaluates edge-set encoding based on spanning trees, which guarantees feasible solutions without repair mechanisms, differing from traditional vertex-based GA encoding.
• Integrates local search heuristics—such as the Fiduccia-Mattheyses algorithm—into quantum-inspired evolutionary algorithms (QEA) to refine solutions and improve convergence.
• Employs multi-level graph partitioning techniques with EC, using coarsening, partitioning, and uncoarsening phases to enhance scalability and solution quality.
• Applies hybrid EC frameworks, including memetic algorithms and cultural algorithms, to guide search using knowledge and population diversity, improving global exploration.
• Utilizes alternative EC paradigms such as particle swarm optimization (PSO) with link density-based multi-objective models, ant colony optimization (ACO) for energy-aware partitioning, and harmony search for efficient global search with fewer parameters.
• Introduces novel mechanisms like simulated catalytic reaction and niching in QEA to enhance convergence speed, avoid genetic drift, and locate multiple global optima.

Experimental results

Research questions

• RQ1 How have encoding strategies in evolutionary computation evolved to improve feasibility and solution quality in graph partitioning?
• RQ2 What role does local search play when integrated with metaheuristics like quantum-inspired GA or memetic algorithms in solving GPP?
• RQ3 How effective are multi-level heuristics when combined with EC operators such as crossover and mutation in large-scale graph partitioning?
• RQ4 To what extent do alternative EC paradigms—such as PSO, ACO, and harmony search—outperform or complement traditional genetic algorithms in GPP?
• RQ5 What are the key design principles and performance trade-offs in hybrid EC frameworks for solving the graph partitioning problem?

Key findings

• Edge-set encoding based on spanning trees produces only feasible solutions, eliminating the need for repair procedures and improving efficiency in GA-based GPP solvers.
• Hybridization with local search, especially Fiduccia-Mattheyses in quantum-inspired GAs, significantly enhances solution quality and convergence speed.
• Multi-level memetic algorithms with effective recombination and mutation operators achieve high-quality partitions, demonstrating strong performance on both synthetic and real-world graphs.
• Parallel and nonlinear mixed-integer programming-based GAs successfully solve large-scale, real-world GPP instances, showing scalability and robustness.
• Ant colony optimization and PSO-based approaches achieve competitive results in energy-aware and community detection applications, with PSO generating uniformly distributed Pareto sets for multi-objective GPP.
• Harmony search and cultural algorithms outperform standard GAs in terms of convergence speed and parameter sensitivity, with fewer parameters required and better global search capability.