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arXiv · 2609.11213

Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics

Bereket Sitotaw Kidane·Md Samiul Haque Motayed·Shuo Wang
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Abstract

Optimal scheduling of combined chemo-immunotherapy is often formulated as a control-affine optimal control problem, which generically yields boundary-selected (bang-bang-type) protocols unless singular arcs occur. This structure, while convenient, neglects saturating pharmacodynamics at high dose rates. We incorporate Michaelis-Menten saturation directly into the therapy channels, making the dynamics non-control-affine and the Hamiltonian nonlinear in each control. With strictly positive exposure penalties, the Hamiltonian admits an explicit three-regime pointwise minimization law: each input is chosen at the lower bound, the upper bound, or as a unique interior minimizer. On interior intervals the strict Legendre condition holds, so continuously modulated dosing arises as a regular interior extremal rather than a singular-arc or smoothing artifact. The resulting transcription is nonconvex; we therefore use a hybrid Quantum Particle Swarm Optimization (QPSO)-Sequential Quadratic Programming (SQP) pipeline, where QPSO provides a constraint-aware warm start and SQP enforces feasibility and Karush-Kuhn-Tucker (KKT) optimality on a collocation grid. Costate reconstruction corroborates the Pontryagin Minimum Principle (PMP) structure and the predicted boundary/interior regime transitions.

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Bereket Sitotaw Kidane, Md Samiul Haque Motayed, Shuo Wang. 2026-09-10. Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics. https://doi.org/10.3934/dcdsb.2026072

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