Philosophical proposition optimizer (ΦPO)

Philosophical Proposition Optimizer (ΦPO), a simple and parameter-free optimization algorithm is presnted.

The implementation of the Philosophical Proposition Optimizer (ΦPO) follows a modular and transparent structure that directly reflects its epistemic inspiration. Each candidate solution is treated as a philosophical proposition characterized by one of three belief states: Justified True Belief (JTB), Possibly False Belief (PFB), or Unjustified True Belief (UTB). The algorithm initializes a population of propositions uniformly within the variable bounds and assigns belief states based on solution quality.

During each iteration, propositions are updated using three deterministic operators: Providing Justification (PJ), which intensifies search around promising solutions; Raising Metaphysical Skepticism (RMS), which perturbs beliefs to challenge potentially misleading optima; and Raising Epistemic Skepticism (RES), which promotes exploration by revisiting under-justified but potentially valuable regions. These operators are applied without adaptive parameters or control coefficients, ensuring a fully parameter-free implementation.

The code evaluates objective functions directly, updates belief states based on comparative fitness, and retains the best-performing propositions across iterations. Termination is controlled solely by the maximum number of function evaluations or iterations. The overall structure emphasizes simplicity, interpretability, and reproducibility, making the implementation easy to extend to other optimization problems, including engineering design applications.Cite as:

Talatahari, S., Bayazidi, H. & Sareh, P. Philosophical proposition optimizer (ΦPO): an epistemology-inspired algorithm for numerical optimization. Artif Intell Rev 58, 405 (2025). https://doi.org/10.1007/s10462-025-11383-8