Innovative Optimization Algorithms for Large-Sized Industrial Scheduling Problems

Abstract

The problem of minimizing total quadratic completion time in flow shops presents a significant challenge in industries such as chemical, metallurgical, and ceramic manufacturing. Initially investigated by Ren and coauthors (2016) [¹], this problem addresses the need to balance intermediate inventory reduction with maximizing resource utilization, particularly in multi-objective scenarios. We proposed two innovative metaheuristics (Covid and CHIO algorithms) and a mathematical optimization model. Evaluations were conducted across two industrial settings and three additional benchmarks from existing literature. Through the statistical analysis and performance profiling, our findings indicate that the Covid and CHIO algorithms outperform the Differential Evolution of Ren and coauthors (2016) [¹] and the Iterated Greedy Algorithm of Pan and Ruiz (2012) [²], as well as other techniques. Notably, the proposed Covid and CHIO algorithms achieved an average relative deviation from the optimal solution of 0.41% and 0.23%, respectively. Furthermore, they consistently outperformed other methods, securing the best solution in at least 12.5% of instances across all benchmarks, with their worst solutions closer to the best solutions than those produced by alternative approaches.

Keywords:
flow shop; metaheuristics; mathematical optimization; total quadratic completion time; stochastic local search

HIGHLIGHTS

Two new coronavirus-based metaheuristic algorithm was proposed.

A challenging nonlinear optimization problem is solved efficiently.

A mathematical optimization model is formulated to solve small instances.

Our algorithms outperform the main metaheuristics from the literature.