Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm

Li, Chunlei; Deng, Libao; Yuan, Guanyu; Qiao, Liyan; Zhang, Lili; Chen, Chu

doi:10.3390/math13162679

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Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm

by

Chunlei Li

^1,2

,

Libao Deng

^1,*

,

Guanyu Yuan

¹,

Liyan Qiao

²

,

Lili Zhang

³

and

Chu Chen

¹

School of Information Science and Engineering, Harbin Institute of Technology, Weihai 264209, China

²

School of Electronics and Information Engineering, Harbin Institute of Technology, Harbin 150001, China

³

School of Computing, Dublin City University, D09 V209 Dublin, Ireland

^*

Author to whom correspondence should be addressed.

Mathematics 2025, 13(16), 2679; https://doi.org/10.3390/math13162679

Submission received: 21 July 2025 / Revised: 17 August 2025 / Accepted: 19 August 2025 / Published: 20 August 2025

(This article belongs to the Special Issue Intelligence Optimization Algorithms and Applications)

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Abstract

2.5D integrated circuits (ICs), which utilize an interposer to stack multiple dies side by side, represent a promising architecture for improving system performance, integration density, and design flexibility. However, the complex interconnect structures present significant challenges for post-fabrication testing, especially when scheduling test paths under constrained test access mechanisms. This paper addresses the test-path scheduling problem in interposer-based 2.5D ICs, aiming to minimize both total test time and cumulative inter-die interconnect length. We propose an efficient orthogonal learning-based differential evolution algorithm, named OLELS-DE. The algorithm combines the global optimization capability of differential evolution with an orthogonal learning-based search strategy and an elites local search strategy to enhance the convergence and solution quality. Comprehensive experiments are conducted on a set of benchmark instances with varying die counts, and the proposed method is compared against five state-of-the-art metaheuristic algorithms and CPLEX. Experimental results demonstrate that OLELS-DE consistently outperforms the competitors in terms of test cost reduction and convergence reliability, confirming its robustness and effectiveness for complex test scheduling in 2.5D ICs.

Keywords: 2.5D integrated circuits; test-path scheduling; differential evolution; orthogonal learning

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MDPI and ACS Style

Li, C.; Deng, L.; Yuan, G.; Qiao, L.; Zhang, L.; Chen, C. Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm. Mathematics 2025, 13, 2679. https://doi.org/10.3390/math13162679

AMA Style

Li C, Deng L, Yuan G, Qiao L, Zhang L, Chen C. Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm. Mathematics. 2025; 13(16):2679. https://doi.org/10.3390/math13162679

Chicago/Turabian Style

Li, Chunlei, Libao Deng, Guanyu Yuan, Liyan Qiao, Lili Zhang, and Chu Chen. 2025. "Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm" Mathematics 13, no. 16: 2679. https://doi.org/10.3390/math13162679

APA Style

Li, C., Deng, L., Yuan, G., Qiao, L., Zhang, L., & Chen, C. (2025). Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm. Mathematics, 13(16), 2679. https://doi.org/10.3390/math13162679

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Test-Path Scheduling for Interposer-Based 2.5D Integrated Circuits Using an Orthogonal Learning-Based Differential Evolution Algorithm

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