# Enhancing the best-first-search F with incremental search and restarts for large-scale single machine scheduling with release dates and deadlines

## TL;DR

This paper introduces a new scheduling algorithm that efficiently handles large-scale job scheduling with deadlines and release dates.

## Contribution

The novel contribution is a heuristic search method combining incremental search and restarts for improved scalability.

## Key findings

- The new method outperforms IBM ILOG CP and CPLEX solvers on large-scale instances.
- It finds feasible solutions for 100,000-job instances in under a minute.

## Abstract

This paper presents a new heuristic search \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {F}_{IR}$$\end{document}FIR that determines the feasibility of scheduling a set of jobs on a single machine where each job is characterized by its release date, processing time, and deadline. \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {F}_{IR}$$\end{document}FIR uses incremental search and restart strategies to scale the best-first-search heuristic F (Laalaoui and M’Hallah, in: IEEE symposium on evolutionary scheduling and combinatorial optimisation (SSCI) 2022, IEEE, Singapore, 2022). Experimental results provide computational evidence of the superiority of \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {F}_{IR}$$\end{document}FIR for large-scale instances. In fact, \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {F}_{IR}$$\end{document}FIR outperforms the IBM ILOG CP constraint programming solver, the CPLEX mixed integer programming solver, and existing heuristics. It finds feasible solutions for many instances with 100,000 jobs in less than one minute.