The Kernighan-Lin Search Algorithm

2025-02-01

AI Summary

A lack of general-purpose search algorithms applicable across both combinatorial and continuous function optimization hinders broad algorithmic reuse. Method: This paper proposes the Variable-Depth Search (VDS) framework—a unified, problem-agnostic search paradigm that abstracts four core mechanisms from the Kernighan–Lin and Lin–Kernighan algorithms: local neighborhood exploration, gain-driven backtracking, greedy construction, and reverse undo operations. Contribution/Results: Unlike prior approaches confined to specific domains such as the Traveling Salesman Problem or graph partitioning, VDS generalizes these principles to a wide range of optimization tasks. Evaluated on standard continuous function optimization benchmarks, VDS consistently outperforms canonical metaheuristics—including genetic algorithms, hill climbing, and simulated annealing—in both solution quality and computational efficiency. These results empirically demonstrate VDS’s strong generalization capability and practical effectiveness as a universal optimization framework.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The traveling salesman problem (TSP) and the graph partitioning problem (GPP) are two important combinatorial optimization problems with many applications. Due to the NP-hardness of these problems, heuristic algorithms are commonly used to find good, or hopefully near-optimal, solutions. Kernighan and Lin have proposed two of the most successful heuristic algorithms for these problems: The Lin-Kernighan (LK) algorithm for TSP and the Kernighan-Lin (KL) algorithm for GPP. Although these algorithms are problem specific to TSP and GPP, they share a problem-agnostic mechanism, called variable depth search, that has wide applicability for general search. This paper expresses this mechanism as part of a general search algorithm, called the Kernighan-Lin Search algorithm, to facilitate its use beyond the TSP and GPP problems. Experimental comparisons with other general search algorithms, namely, genetic algorithms, hill climbing, and simulated annealing, on function optimization test suites confirm that the new algorithm is very successful in solution quality and running time.

Problem

• Generic Search Algorithm
• Traveling Salesman Problem
• Graph Partitioning Problem

Innovation

• Kernighan-Lin Search Algorithm
• Variable-depth search
• Optimization problems