Automatic termination of parallel optimization runs of stochastic global optimization methods in consensus or stagnation cases

Abstract

Dynamic models give detailed information about the influence of many parameters on the behaviour of the biochemical process of interest. Parameter optimization of dynamic models is used in parameter estimation tasks and in design tasks. A drawback of the popular family of global stochastic optimization methods is the stochastic nature of the convergence of the best value of objective function to the global optimum or a value close to that. Therefore the optimization can take long time until a stable value of objective function is reached. Even then the risk of stagnation far from global optimum remains. That sets force to look for efficient approaches to reduce optimization time and discover cases of poor performance of optimization methods. Parallel optimization runs of identical optimization tasks can be used to reduce the impact of stochastic processes used in stochastic optimization methods. Consensus and stagnation criteria are proposed to terminate a set of parallel optimization runs when it is assessed that no significant improvements of the best value of the objective function are expected. Four automatically detectable cases of behaviour of a group of parallel optimization runs are analysed: 1) reaching of consensus criterion (consensus case), 2) stagnation of all optimization runs without reaching the consensus criterion (stagnation case), 3) stagnation at the initial value of the objective function, 4) lack of feasible solution. The proposed approach can be used automating the termination of optimization process when no further progress of the best value of objective function is expected. Suitability of particular optimization method with its settings for particular optimization task can be assessed analysing the dynamics of objective function's best values of parallel runs.