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Life sciences · Preprint
arXiv · August 10, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint proposes input convex neural networks (ICNNs) as surrogates for optimisation problems where the underlying response is convex or concave, and develops a branch-and-bound algorithm to exploit their structure. Three operational research case studies (humanitarian logistics, oil well routing, wine blending) report qualitative gains in computational speed and scalability relative to feedforward neural networks, but without peer review, statistical testing, or quantified effect sizes.
Methodological study with illustrative case studies. Optimisation problems in humanitarian logistics, petroleum engineering, and food product blending; not human subjects or clinical populations.. Intervention: Input convex neural network (ICNN) surrogate with LP-based reformulation and branch-and-bound solver.. Compared with: Feedforward neural network (FNN) with ReLU activations and mixed-integer programming reformulation..
ICNN-MIP formulation yields tighter LP relaxations than FNN-MIP, with no integrality gap in favourable instances ICNNs admit LP-based reformulation via epigraph representations of ReLU activations Case studies report ICNN surrogates match FNN accuracy and deliver gains in solve time and scalability
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A methodological proposal with computational case studies demonstrating technical feasibility, but no peer review, no clinical validation, and no comparison against established benchmarks with statistical significance testing.
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Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research. The prevailing approach uses feedforward neural networks (FNNs) with ReLU activations, whose piecewise-linear structure admits an exact but computationally intensive mixed-integer programming (MIP) reformulation as the networks grow. We advocate input convex neural networks (ICNNs) as structurally superior surrogates when the underlying response is approximately convex or concave. The convex architecture offers two computational advantages. First, the ICNN-MIP formulation tends to yield a tighter linear programming (LP) relaxation than its FNN-MIP counterpart, with no integrality gap in favourable instances. Second, ICNNs uniquely admit an LP-based reformulation via epigraph representations of ReLU activations, though this embedding is not always exact. When it is not, we exploit the properties of ICNNs to construct the strongest continuous relaxation over box domains, namely, the convex hull of the ICNN's graph, bounded below by the epigraph and above by the concave envelope; this construction is tractable under input convexity but hard for general ReLU networks. On this basis, we develop a branch-and-bound algorithm that builds this relaxation at each node, branches directly on input variables rather than intermediate variables as in MIP reformulations, and terminates at the root node whenever the epigraph embedding is valid. Case studies on humanitarian food aid, oil well routing, and wine blending show that ICNN surrogates match FNN accuracy and deliver gains in solve time and scalability, supporting ICNN as the default surrogate when the underlying function is convex, concave, or well-approximated as such.
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