Optimizing Evolutionary Solver Parameters for Minimizing Total Tardiness in Single Machine Scheduling Problems

Core Concepts

The study explores the optimization of evolutionary solver parameters, including population size, mutation rate, and convergence rate, to enhance the efficiency of solving the NP-hard problem of minimizing total tardiness in single machine scheduling.

Abstract

The study investigates the optimization of evolutionary solver parameters to address the NP-hard problem of minimizing total tardiness in single machine scheduling. It examines various parameter combinations, including population sizes (100, 50, 25, 10), mutation rates (0.75, 0.075, 0.0075), and convergence rates (0.0001, 0.1), to identify an optimal generic set of parameters that can effectively solve this complex scheduling challenge.
The key findings are:

Using a population size of 50, mutation rate of 0.075, and convergence rate of 0.0001 yielded the best solutions within a runtime of 1-3 seconds.
Reducing the population size further to 25 or 10 resulted in the solver failing to find optimal solutions, even with adjustments to the mutation rate and convergence.
The study demonstrates the capability of the evolutionary solver in rapidly converging on different total tardiness values for various 10-job problems, with optimal solutions achieved in all 20 test cases when run for up to 42 seconds.
Future research will focus on extending the study to parallel machine scheduling scenarios with non-zero ready times and minimizing total weighted tardiness.

Stats

The processing times for the 10 jobs range from 10 to 20 units.
The due dates for the 10 jobs range from 50 to 150 units.

Quotes

"The impact of manufacturing scheduling on a company's operational performance, and consequently its sustainability, is significant, particularly when considering the correlation between tardiness and operational expenses."
"Evolutionary algorithms, a cornerstone of our approach, incorporate principles of natural evolution into the process of finding optimal solutions for Solver problems."

Key Insights Distilled From

Enhancing Evolutionary Solver Efficiency for NP Hard Single Machine Scheduling Problems

by Mohammed Alr... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19109.pdf

Deeper Inquiries

How can the insights from this study be applied to scheduling problems in other manufacturing or service industries

The insights gained from this study on optimizing evolutionary solver parameters for single machine scheduling problems can be applied to various scheduling challenges in other manufacturing or service industries. For instance, in the automotive industry, where production lines often involve complex sequences of tasks on different machines, the evolutionary solver's ability to minimize total tardiness can help streamline operations and reduce delays. Similarly, in the healthcare sector, where patient appointments, surgeries, and resource allocation need to be optimized, the evolutionary solver can be utilized to enhance scheduling efficiency and minimize waiting times. By adjusting the parameters such as population size, mutation rate, and convergence, tailored solutions can be developed to address specific scheduling requirements in different industries.

What are the potential limitations or challenges in extending the evolutionary solver approach to more complex scheduling scenarios with additional constraints or objectives

Extending the evolutionary solver approach to more complex scheduling scenarios with additional constraints or objectives may pose certain limitations and challenges. One potential limitation is the scalability of the solver when dealing with a large number of tasks or machines, which can lead to increased computational complexity and longer solution times. Moreover, incorporating multiple conflicting objectives, such as minimizing total tardiness while maximizing resource utilization, may require sophisticated multi-objective optimization techniques to balance trade-offs effectively. Additionally, the evolutionary solver's performance may be impacted by the presence of non-linear constraints, uncertain parameters, or dynamic environments, necessitating the development of robust algorithms to handle such complexities.

What other optimization techniques or hybrid approaches could be explored to further enhance the efficiency and solution quality for single machine scheduling problems

To further enhance the efficiency and solution quality for single machine scheduling problems, exploring other optimization techniques or hybrid approaches can be beneficial. One approach could involve integrating machine learning algorithms, such as reinforcement learning or neural networks, to adaptively learn from past scheduling decisions and improve decision-making over time. Additionally, metaheuristic algorithms like simulated annealing or particle swarm optimization could be combined with the evolutionary solver to explore a wider solution space and avoid local optima. Hybrid approaches that combine mathematical programming models with evolutionary algorithms or swarm intelligence methods could also offer a comprehensive optimization framework for tackling complex scheduling problems. By leveraging the strengths of different optimization techniques, a more robust and effective solution strategy can be developed for single machine scheduling scenarios.