A parallel multi-objective optimization algorithm for the calibration of mathematical models

Based on evolutionary computation techniques, we present a parallel, globally convergent, multi-objective optimization algorithm which extends the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). This approach enables identifying multiple global optima and multiple discontinuous Pareto set solutions of the optimization problem in a compact search space. After evaluating the algorithm with test functions, we apply our method to the identification of the parameters of a reaction–diffusion model of a genetic regulatory mechanism during Drosophila early development, our simulations being in agreement with the experimental data. Comparisons with a multi-objective version of the CMA-ES (MO-CMA-ES) on this dataset show that our algorithm outperforms largely the speed of convergence of MO-CMA-ES. We have identified an infinite number of accurate solutions of the model equations, associated with the Pareto set of the optimization problem. This non-unicity property of a biological developmental process explains phenotypic plasticity and resilience in biological systems.