Adaptive hybrid optimization strategy for calibration and parameter estimation of physical process models

• Authors: Velimir V. Vesselinov;Dylan R. Harp
• Venue: Computers & Geosciences
• Year: 2012

A new adaptive hybrid optimization strategy, entitled squads, is proposed for complex inverse analysis of computationally intensive physics-based models. Typically, models are calibrated and model parameters are estimated by minimization of the discrepancy between model simulations characterizing the system and existing observations requiring a substantial number of model evaluations. Squads is designed to be computationally efficient and robust in identification of the global optimum (i.e. maximum or minimum value of an objective function). It integrates global and local optimization using Adaptive Particle Swarm Optimization (APSO) and Levenberg-Marquardt (LM) optimization using adaptive rules based on runtime performance. The global strategy (APSO) optimizes the location of a set of solutions (particles) in the parameter space. The local strategy (LM) is applied only to a subset of the particles at different stages of the optimization based on the adaptive rules. After the LM adjustment of the subset of particle positions, the updated particles are returned to APSO. Therefore, squads is a global strategy that utilizes a local optimization speedup. The advantages of coupling APSO and LM in the manner implemented in squads is demonstrated by comparisons of squads performance against Levenberg-Marquardt (LM), Particle Swarm Optimization (PSO), Adaptive Particle Swarm Optimization (APSO; i.e. TRIBES), and an existing hybrid optimization strategy (hPSO). All the strategies are tested on 2D, 5D and 10D Rosenbrock and Griewank polynomial test functions and a synthetic hydrogeologic application to identify the source of a contaminant plume in an aquifer. Tests are performed using a series of runs with random initial guesses for the estimated parameters. The performance of the strategies are compared based on their robustness, defined as the percentage of runs that identify the global optimum, and their efficiency, quantified by a statistical representation of the number of function evaluations performed prior to identification of the global optimum. Squads is observed to have better performance than the other strategies for the test functions and the hydrogeologic application when both robustness and efficiency are taken into consideration.