SeqTG: Scalable Combinatorial Test Generation via Sequential Integer Linear Programming

2026-03-14

AI Summary

This work addresses the NP-hard problem of generating minimum covering arrays under complex constraints, where existing greedy approaches often introduce redundancy in later stages of coverage. To overcome this limitation, the authors propose SeqTG, a novel framework that, for the first time, integrates exact integer linear programming (ILP) into combinatorial testing. SeqTG employs a three-stage pipeline—constraint-prioritized grouping, incremental optimization, and global refinement—augmented with Warm-Start initialization and graph partitioning techniques to significantly enhance both scalability and solution quality. Extensive experiments on standard benchmarks and 200 large-scale configurations demonstrate that SeqTG consistently produces the most compact test suites to date while strictly preserving constraint satisfaction accuracy.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Programming
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Combinatorial Testing (CT) is essential for detecting interaction-triggered faults, yet generating minimal Covering Arrays under complex constraints remains an unresolved NP-hard challenge. Current greedy algorithms are highly scalable but suffer from severe ``diminishing returns'': they efficiently cover initial interactions but produce bloated, redundant test suites when struggling to pack the final few difficult pairs. While exact mathematical programming could theoretically address this inefficiency, it has historically been intractable due to combinatorial explosion. In this paper, we pioneer the application of exact mathematical modeling to CT by introducing SeqTG, a scalable framework based on Sequential Integer Linear Programming (ILP). To circumvent the scalability barrier, SeqTG employs a novel Warm-Start strategy: a rapid greedy initialization first clears the ``easy'' interactions, allowing the rigorous ILP solver to exclusively optimize the fragmented, difficult-to-cover remainder. The pipeline operates in three stages: (1) a Constraint-First phase grouping must-include requirements via graph partitioning; (2) an Incremental Optimization phase targeting the remaining interactions with sequential ILP; and (3) a Global Minimization phase eliminating redundancies via set-covering. Extensive evaluations across standard benchmarks and 200 large-scale configurations validate the framework's efficacy. The results demonstrate that SeqTG effectively eradicates late-stage bloat, achieving state-of-the-art test suite compactness and strict constraint adherence.

Problem

• Combinatorial Testing
• Covering Arrays
• NP-hard
• Test Suite Minimization
• Constraints

Innovation

• Sequential Integer Linear Programming
• Combinatorial Testing
• Warm-Start Strategy
• Covering Arrays
• Scalable Optimization