[Paper Review] Squeeze-and-Breathe Evolutionary Monte Carlo Optimisation with Local Search Acceleration and its application to parameter fitting

Mariano Beguerisse-Díaz, Baojun Wang+2 more|arXiv (Cornell University)|Jul 14, 2011

Advanced Multi-Objective Optimization Algorithms4 citations

TL;DR

This paper proposes a novel Squeeze-and-Breathe Evolutionary Monte Carlo (SBE-MC) optimization algorithm that integrates evolutionary strategies, sequential Monte Carlo, and local search to efficiently fit parameters in nonlinear biological models. By iteratively refining parameter distributions through local optimization and adaptive resampling from a historical prior, the method achieves robust convergence even with unknown parameter ranges or orders of magnitude, outperforming standard heuristics in complex, noisy, and high-dimensional biological parameter estimation problems.

ABSTRACT

Motivation: Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in the biological setting. Results: In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimisation. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimisation combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.

Motivation & Objective

• To address the challenge of parameter estimation in nonlinear biological models where data is sparse, noisy, and parameters span unknown orders of magnitude.
• To overcome limitations of traditional optimization methods—such as local minima trapping, high computational cost, or reliance on accurate priors—common in systems biology.
• To develop a robust, globally convergent method that does not require prior knowledge of parameter ranges or initial distributions.
• To enable efficient and reliable parameter fitting in models governed by ordinary differential equations with nonlinear parameter dependencies.
• To close the modeling-experiment loop by supporting predictive modeling, model selection, and experimental design guidance.

Proposed method

• The method employs an iterative framework that alternates between 'squeeze' (local optimization) and 'breathe' (resampling from a historical prior) steps to refine parameter distributions.
• It combines evolutionary algorithms for global exploration with local search to accelerate convergence toward low-error parameter sets.
• A historical prior is dynamically updated across iterations, capturing the support of all previously sampled parameter sets to guide future exploration.
• Sequential Monte Carlo principles are used to map a prior distribution to a posterior through weighted resampling, focusing on low-error regions.
• The algorithm avoids explicit cost function computation by using simulation-based error evaluation, making it suitable for models with no analytical solutions.
• Parameter updates are guided by a combination of mutation, selection, and local refinement, ensuring both diversity and convergence.

Experimental results

Research questions

• RQ1 Can a hybrid optimization framework combining evolutionary, Monte Carlo, and local search strategies improve parameter fitting in nonlinear biological models with limited data?
• RQ2 How does the method perform when the true parameter values lie outside the initial prior support, particularly when the order of magnitude is unknown?
• RQ3 To what extent does local search acceleration improve convergence speed compared to standard evolutionary or Monte Carlo methods?
• RQ4 Can the method reliably estimate parameters in models with nonlinear parameter dependencies, such as Michaelis-Menten kinetics, without requiring linearity or explicit cost functions?
• RQ5 How does the historical prior mechanism enhance exploration and prevent premature convergence in high-dimensional, multimodal parameter spaces?

Key findings

• The SBE-MC algorithm successfully estimates parameters in nonlinear ODE models even when the initial prior spans orders of magnitude wider than the true parameter values, avoiding the need for overly broad priors.
• The method achieves efficient convergence in both simulated and real experimental data, including a GFP expression model with 10 time points and 10 ligand concentrations, demonstrating robustness to noise.
• Local search acceleration significantly reduces the number of iterations required to reach low-error solutions, outperforming standard evolutionary or pure Monte Carlo approaches in convergence speed.
• The algorithm reliably identifies parameter sets that minimize model-data discrepancy, enabling cross-validation and predictive modeling in systems biology.
• The historical prior mechanism enables effective exploration of complex, multimodal error surfaces without prior knowledge of the true parameter range.
• In the GFP model, the method achieved consistent parameter estimates across multiple replicates (e.g., fluorescence measurements at t=360 with mean ~7910.6 and standard deviation ~387.8), indicating stability and reproducibility.