Advanced sequential conservative integer programming for discrete-variable topology optimization involving multiple nonlinear constraints

doi:10.1016/j.compstruc.2026.108460

Advanced sequential conservative integer programming for discrete-variable topology optimization involving multiple nonlinear constraints

2026-09-19

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DOI：10.1016/j.compstruc.2026.108460

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Discrete-variable topology optimization (DVTO) effectively eliminates intermediate densities but inherently suffers from combinatorial complexity. The severity of this deficiency further increases when addressing problems involving multiple nonlinear constraints. This issue is addressed with the present paper which introduces the advanced sequential conservative integer programming (SCIP) method for DVTO problems with multiple nonlinear constraints. This technique integrates approximation based on the method of moving asymptotes (MMA) with the two-point fitting scheme of generalized MMA to construct a sequence of nonlinear subproblems, whose conservatism and accuracy are adaptively adjusted throughout the optimization process. A key novelty is the reformulation of these nonlinear integer subproblems into equivalent linear integer programming models with 0–1 design space. This approach achieves computational efficiency comparable to, or even surpassing, that of the techniques operating in continuous space for solving nonlinear subproblems by MMA. Consequently, the advanced SCIP successfully solves the Zhou-Rozvany problem, without resorting to mesh refinement or any auxiliary strategies. As another case study, the technique is applied to the design of the fully decoupled multi–input–multi–output (MIMO) compliant mechanisms under various boundary conditions. The numerical experiments validate that the advanced SCIP can generate hinge-free, fully decoupled MIMO compliant mechanisms with clear topology configurations, highlighting the method’s potential for tackling complex large-scale DVTO problems under multiple nonlinear constraints.

Keywords:

Topology optimization

Discrete-variable topology optimization

Sequential conservative integer programming

Compliant mechanisms

Multi-input-multi-output mechanisms

Zhou-Rozvany problem

Advanced sequential conservative integer programming for discrete-variable topology optimization involving multiple nonlinear constraints

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