基于混合量子粒子群优化的癌症化疗最优控制
Optimal Control for Cancer Chemotherapy Using Hybrid Quantum Particle Swarm Optimization
- University of Texas at Arlington（阿灵顿得克萨斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对癌症化疗最优控制中肿瘤异质性和传统PMP方法依赖初值猜测的问题，提出基于正则化的混合量子粒子群优化方法，通过全局探索与细化逼近最优轨迹，并用数值案例验证了不同药物递送策略的肿瘤抑制效果。
AI中文摘要：
癌症化疗中的最优控制面临肿瘤异质性和突变带来的挑战，这些因素使治疗效果复杂化。传统方法，如庞特里亚金最大值原理（PMP），常因其对协态方程初值猜测的依赖而受到阻碍，影响精度和收敛性。为解决这些局限，本研究引入一种基于正则化的混合量子粒子群优化（QPSO）方法。QPSO用于全局探索以逼近最优控制轨迹，随后通过基于正则化的细化来确保平滑性及与最优性条件的一致性。利用哈密顿函数进行一阶和二阶最优性检验，验证解的质量。数值案例研究探讨了多种药物有效性函数，展示了周期性及局部药物递送在实现稳健肿瘤抑制中的作用，并提供了关于不同药物组合对最优化疗策略影响的见解。
英文摘要：
Optimal control in cancer chemotherapy is challenged by tumor heterogeneity and mutations, which complicate treatment effectiveness. Traditional methods, such as Pontryagin's maximum principle (PMP), are often hindered by their reliance on an initial guess for the costate equation, affecting accuracy and convergence. To address these limitations, this work introduces a hybrid quantum particle swarm optimization (QPSO) method based on regularization. QPSO is employed for global exploration to approximate the optimal control trajectory, followed by a regularization-based refinement to ensure smoothness and consistency with optimality conditions. The Hamiltonian function is used for first- and second-order optimality checks, verifying solution quality. Numerical case studies explore various drug effectiveness functions, demonstrating the role of periodic and localized drug delivery in achieving robust tumor suppression and providing insights into the impact of different drug combinations on optimal chemotherapy strategies.
