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Open Access

ARTICLE

An Adaptive Imperialist Competitive Algorithm with Cooperation for Flexible Jobshop and Parallel Batch Processing Machine Scheduling

Jie Wang, Deming Lei*
School of Automation, Wuhan University of Technology, Wuhan, China
* Corresponding Author: Deming Lei. Email: email
(This article belongs to the Special Issue: Swarm-Based Optimization and its Cross-Disciplinary Applications in Modern Engineering)

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.076202

Received 16 November 2025; Accepted 29 December 2025; Published online 16 March 2026

Abstract

Both flexible jobshop scheduling and parallel batch processing machine scheduling have been extensively considered; however, the flexible jobshop and parallel batch processing machine scheduling problem (FJPBPMSP) is prevalent in real-life manufacturing processes and is seldom investigated. In this study, FJPBPMSP is examined, where flexible processing and batch processing are performed sequentially. An adaptive imperialist competitive algorithm with cooperation (CAICA) is proposed to minimize makespan and total energy consumption simultaneously. In CAICA, a four-string representation is adopted, and initial empires with novel structures are formed by uniformly dividing the population. An adaptive assimilation and revolution are designed. An adaptive assimilation and revolution are designed. An adaptive imperialist competition with cooperation is provided. Search strategies, imperialists, and colonies are also renewed by new procedures. Computational experiments are conducted on 50 instances. The computational results show that the new strategies of CAICA are effective, and CAICA can provide better results than its comparative algorithms in solving FJPBPMSP.

Keywords

Flexible jobshop scheduling; parallel batch processing scheduling; imperialist competition algorithm; cooperation

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