Mid-term bio-economic optimization of multi-species fisheries

TL;DR

This paper develops a method to optimize harvesting strategies in multi-species fisheries over a mid-term horizon, balancing economic gains with ecological constraints using advanced control techniques.

Contribution

It introduces a novel algorithm combining Pontryagin's Maximum Principle, cyclic coordinate descent, and the shooting method for multi-species fisheries management.

Findings

The method effectively handles inter-species competition and predator-prey dynamics.

Numerical examples demonstrate the algorithm's versatility and robustness.

Parameter studies reveal key factors influencing optimal strategies.

Abstract

In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. For its solution, we combine techniques derived from Pontryagin's Maximum Principle, cyclic coordinate descent and the shooting method. The algorithm we develop can solve problems both with inter-species competition and with predator-prey behaviors. Several numerical examples are presented to illustrate the different possibilities of the method and a study of the dependence of the behavior on some parameters is performed.