Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning

TLDR

Simulated annealing was empirically studied for combinatorial optimization, with its performance compared to traditional algorithms. The study evaluates a generic simulated annealing implementation on graph partitioning and compares its results to standard methods. The authors implemented a parameterized generic simulated annealing algorithm, adapted it to graph partitioning, and optimized its parameters and basic algorithm. On sparse random graphs, the algorithm outperformed Kernighan‑Lin as vertex counts grew, despite higher runtime, but it performed poorly on geometrically structured graphs.

Abstract

In this and two companion papers, we report on an extended empirical study of the simulated annealing approach to combinatorial optimization proposed by S. Kirkpatrick et al. That study investigated how best to adapt simulated annealing to particular problems and compared its performance to that of more traditional algorithms. This paper (Part I) discusses annealing and our parameterized generic implementation of it, describes how we adapted this generic algorithm to the graph partitioning problem, and reports how well it compared to standard algorithms like the Kernighan-Lin algorithm. (For sparse random graphs, it tended to outperform Kernighan-Lin as the number of vertices become large, even when its much greater running time was taken into account. It did not perform nearly so well, however, on graphs generated with a built-in geometric structure.) We also discuss how we went about optimizing our implementation, and describe the effects of changing the various annealing parameters or varying the basic annealing algorithm itself.