Enhanced global optimization methods applied to complex fisheries stock assessment models

[Abstract] Statistical fisheries models are frequently used by researchers and agencies to understand the behavior of marine ecosystems or to estimate the maximum acceptable catch of different species of commercial interest. The parameters of these models are usually adjusted through the use of optimization algorithms. Unfortunately, the choice of the best optimization method is far from trivial. This work proposes the use of population-based algorithms to improve the optimization process of the Globally applicable Area Disaggregated General Ecosystem Toolbox (Gadget), a flexible framework that allows the development of complex statistical marine ecosystem models. Specifically, parallel versions of the Differential Evolution (DE) and the Particle Swarm Optimization (PSO) methods are proposed. The proposals include an automatic selection of the internal parameters to reduce the complexity of their usage, and a restart mechanism to avoid local minima. The resulting optimization algorithms were called PMA (Parallel Multirestart Adaptive) DE and PMA PSO respectively. Experimental results prove that the new algorithms are faster and produce more accurate solutions than the other parallel optimization methods already included in Gadget. Although the new proposals have been evaluated on fisheries models, there is nothing specific to the tested models in them, and thus they can be also applied to other optimization problems. Moreover, the PMA scheme proposed can be seen as a template that can be easily applied to other population-based heuristics.Xunta de Galicia; ED431C 2017/04Xunta de Galicia; R2016/0

Multiple time–scale dynamics of stage structured populations and derivative–free optimization

The parent-progeny (adult fish–juvenile) relationship is central to understanding the dynamics of fish populations. Management and harvest decisions are based on the assumption of a stock-recruitment function that relates the number of adults to their progeny. Multi-stage population dynamic models provide a modelling framework for understanding this relationship, since they describe the dynamics of fish in several life stages (such as adults, eggs, larvae, and juveniles). Biological processes at various life stages usually evolve at distinct time scales. This thesis contains three papers, which address challenges in modelling and parameter estimation for multiple time-scale dynamics of stage structured populations. A major question is, whether a multi-stage population dynamic model supports the assumption of a stock-recruitment function. In the first paper, we address the parent-progeny relationship admitted by slow-fast systems of differential equations that model the dynamics of a fish population with two stages. We introduce a slow-fast population dynamic model which replicates several well-known stock-recruitment functions. Traditionally, the dynamics of fish populations are described by difference equations. In the second paper, discrete time models for several life stages are formulated. We demonstrate that a multi-stage model may not admit a stock-recruitment function. Sufficient conditions for the validity of two hypotheses about the existence and structure of a parent-progeny function are established. Parameters in population dynamic models can be estimated by minimizing a function of the solution of the ordinary differential equations and available data. Efficient and accurate methods for the solution of differential equations usually evaluate conditional statements. In this case, the objective function may be noisy, instead of continuously differentiable. Furthermore, an algorithm which is used to evaluate the objective function may unexpectedly fail to return a (plausible) value. Then, the optimization problem includes constraints which are only implicitly stated and hidden from the problem formulation. We demonstrate that derivative-free optimization methods find sufficiently accurate solutions for the challenging optimization problems. In the third paper, we compare the performances of several derivative-free methods for a set of optimization problems. We find that a derivative-free trust-region method is most robust to the choice of the initial iterate, but is in general outperformed by direct search methods. Additional numerical simulations in the thesis reveal that direct search methods which approximate a gradient or Hessian find the most accurate solutions. We observe that the optimization problems considered in this thesis are more challenging than a set of noisy benchmark problems. The thesis includes scientific contributions in addition to the results from the three papers