A cancer-inspired metaheuristic applied to optimal control of breast cancer treatment
The authors present the Cancer Improvement Optimizer (CIO), a new bio‑inspired metaheuristic that mimics tumor‑immune dynamics. After benchmarking CIO against standard optimization algorithms, they use it to solve a nonlinear optimal‑control model that integrates chemotherapy, immunotherapy, anti‑cancer drugs and a ketogenic diet for breast cancer. The computational results suggest that the CIO‑driven framework can generate treatment schedules that suppress tumor growth while preserving healthy cells and limiting toxicity.
Study and findings
The paper describes the development of the Cancer Improvement Optimizer (CIO), a metaheuristic algorithm whose design is motivated by five biological processes: tumor proliferation, immune surveillance, therapeutic intervention, dormancy, and recurrence. CIO balances global exploration and local exploitation to avoid premature convergence. Its performance was first evaluated on a suite of continuous benchmark functions (unimodal, multimodal, separable, non‑separable), where it achieved solution quality and convergence speed comparable to or better than several state‑of‑the‑art algorithms. The authors then applied CIO to an optimal control problem (OCP) for breast cancer. The OCP models tumor‑immune dynamics with ordinary differential equations and includes control variables for chemotherapy, immunotherapy, anti‑cancer drug dosing, and a ketogenic diet. Using a collocation method based on Boubaker scaling functions, the OCP was transformed into a finite‑dimensional nonlinear programming problem solved by CIO. Numerical simulations indicated that the CIO‑derived treatment schedules reduced tumor volume, maintained healthy cell counts, enhanced immune activity, and kept treatment‑related toxicity within acceptable limits.
Clinical interpretation
Because the study is entirely computational, the findings cannot be directly extrapolated to patient care. Nonetheless, the results illustrate that a metaheuristic grounded in cancer biology can efficiently explore complex, multi‑objective treatment spaces. The inclusion of a ketogenic diet as a control variable demonstrates that dietary interventions can be mathematically integrated with pharmacologic therapies, potentially informing future in‑silico trial designs. The reported ability of CIO to balance tumor suppression with preservation of healthy tissue aligns with clinical goals of maximizing efficacy while minimizing adverse effects, but clinical validation would require prospective studies in animal models or patients.
Limitations and open questions
The analysis relies on a deterministic ODE model that simplifies many aspects of tumor heterogeneity, patient variability, and pharmacokinetics. No experimental or clinical data were used to calibrate or validate the model parameters, limiting confidence in the quantitative predictions. The study does not compare CIO‑generated schedules with those derived from standard clinical protocols, so the relative clinical advantage remains uncertain. Future work should test the algorithm on validated preclinical models, explore stochastic extensions to capture biological variability, and assess whether the inclusion of a ketogenic diet yields measurable benefits in vivo.
Source
Ebrahimzadeh et al., Mathematical Biosciences, 2026.