The Kernighan-Lin Search Algorithm
Ali Dasdan
TL;DR
The paper generalizes the Kernighan-Lin variable-depth search mechanism into a Transferable Kernighan-Lin Search (KLS) framework for combinatorial optimization. It adds problem-aware variants (KLS1, KLS2) and compares KLS against hill climbing, simulated annealing, and genetic algorithms on seven benchmark functions, using a unified bit-string encoding and neighborhood defined by single-bit flips. Results show KLS achieving strong solution quality with favorable runtime tradeoffs, with KLS2 often delivering the best average rankings by exploiting problem structure, while SA and GA can be slower. The work demonstrates a transferable, general-purpose local-search approach with potential applicability beyond the TSP and GPP to a broad class of optimization problems.
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.