# An improved Ant Colony System for the Sequential Ordering Problem

## TL;DR

This paper enhances the Ant Colony System for the Sequential Ordering Problem by integrating Simulated Annealing, leading to improved solution quality and convergence, and achieving new best results on benchmark instances.

## Contribution

It introduces a novel hybrid approach combining ACS with SA and local search, significantly improving solution quality for SOP.

## Key findings

- ACS-SA and EACS-SA outperform original algorithms in solution quality
- EACS-SA with SOP-3-exchange-SA finds 10 new best solutions
- Achieved best or improved solutions in 41 of 48 cases

## Abstract

It is not rare that the performance of one metaheuristic algorithm can be improved by incorporating ideas taken from another. In this article we present how Simulated Annealing (SA) can be used to improve the efficiency of the Ant Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering Problem (SOP). Moreover, we show how the very same ideas can be applied to improve the convergence of a dedicated local search, i.e. the SOP-3-exchange algorithm. A statistical analysis of the proposed algorithms both in terms of finding suitable parameter values and the quality of the generated solutions is presented based on a series of computational experiments conducted on SOP instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed ACS-SA and EACS-SA algorithms often generate solutions of better quality than the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with the proposed SOP-3-exchange-SA local search was able to find 10 new best solutions for the SOP instances from the SOPLIB2006 repository, thus improving the state-of-the-art results as known from the literature. Overall, the best known or improved solutions were found in 41 out of 48 cases.