An Efficient Implementation of the Robust Tabu Search Heuristic for Sparse Quadratic Assignment Problems

TL;DR

This paper presents a more efficient implementation of the robust tabu search heuristic tailored for sparse quadratic assignment problems, significantly reducing computational complexity from quadratic to near-linear for practical problem sizes.

Contribution

The authors introduce a novel implementation using priority queues and adjacency lists, lowering the complexity of the heuristic from O(N^2) to O(N log N) per iteration.

Findings

Complexity per iteration reduced to O(N log N)

Practical problem size complexity is O(N)

Implementation improves efficiency for sparse problems

Abstract

We propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems. The traditional implementation of the heuristic applicable to all quadratic assignment problems is of O(N^2) complexity per iteration for problems of size N. Using multiple priority queues to determine the next best move instead of scanning all possible moves, and using adjacency lists to minimize the operations needed to determine the cost of moves, we reduce the asymptotic complexity per iteration to O(N log N ). For practical sized problems, the complexity is O(N).