Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics
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.
Versions
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BibTeX
@misc{kidane2026optimal,
title = {{Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics}},
author = {Bereket Sitotaw Kidane and Md Samiul Haque Motayed and Shuo Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11213},
eprint = {2609.11213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11213},
}
RIS
TY - UNPB
TI - Optimal chemo-immunotherapy scheduling: A hybrid QPSO-SQP approach with Michaelis-Menten pharmacodynamics
AU - Bereket Sitotaw Kidane
AU - Md Samiul Haque Motayed
AU - Shuo Wang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11213
UR - https://arxiv.org/abs/2609.11213
AB - 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.
ER -