# Exploiting Promising Sub-Sequences of Jobs to solve the No-Wait Flowshop Scheduling Problem

## TL;DR

This paper introduces a novel approach that leverages common sub-sequences called super-jobs to improve solutions for the NP-hard no-wait flowshop scheduling problem, significantly enhancing solution quality.

## Contribution

It proposes IG-SJ, an innovative algorithm that exploits super-jobs within the Iterated Greedy framework to better solve the no-wait flowshop scheduling problem.

## Key findings

- IG-SJ finds 64 new best solutions on benchmark instances.
- Exploiting super-jobs improves solution quality for the no-wait flowshop.
- The approach effectively captures problem structure to enhance optimization.

## Abstract

The no-wait flowshop scheduling problem is a variant of the classical permutation flowshop problem, with the additional constraint that jobs have to be processed by the successive machines without waiting time. To efficiently address this NP-hard combinatorial optimization problem we conduct an analysis of the structure of good quality solutions. This analysis shows that the No-Wait specificity gives them a common structure: they share identical sub-sequences of jobs, we call super-jobs. After a discussion on the way to identify these super-jobs, we propose IG-SJ, an algorithm that exploits super-jobs within the state-of-the-art algorithm for the classical permutation flowshop, the well-known Iterated Greedy (IG) algorithm. An iterative approach of IG-SJ is also proposed. Experiments are conducted on Taillard's instances. The experimental results show that exploiting super-jobs is successful since IG-SJ is able to find 64 new best solutions.