An Efficient Multi-Objective Optimization Method for Use in the Design of Marine Protected Area Networks

Alan D Fox,David W Corne,C Gabriela Mayorga Adame,J Murray Roberts,Jeff A Polton,Lea-Anne Henry

doi:10.3389/fmars.2019.00017

Abstract

An efficient connectivity-based method for multi-objective optimisation applicable to the design of marine protected area networks is described. Multi-objective network optimisation highlighted previously unreported step changes in the structure of optimal subnetworks for protection associated with minimal changes in cost or benefit functions. This emphasises the desirability of performing a full, unconstrained, multi-objective optimisation for marine spatial planning. Brute force methods, examining all possible combinations of protected and unprotected sites for a network of sites, are impractical for all but the smallest networks as the number of possible networks grows as 2^m, where m is the number of sites within the network. A metaheuristic method based around Markov Chain Monte Carlo methods is described which searches for the set of Pareto optimal networks (or a good approximation thereto) given two separate objective functions, for example for network quality or effectiveness, population persistence, or cost of protection. The optimisation and search methods are independent of the choice of objective functions and can be easily extended to more than two functions. The speed, accuracy and convergence of the method under a range of network configurations are tested with model networks based on an extension of random geometric graphs. Examination of two real-world marine networks, one designated for the protection of the stony coral Lophelia pertusa, the other a hypothetical man-made network of oil and gas installations to protect hard substrate ecosystems, demonstrates the power of the method in finding multi-objective optimal solutions for networks of up to 100 sites. Results using network average shortest path as a proxy for population resilience and gene flow within the network supports the use of a conservation strategy based around highly connected clusters of sites.

Highlights

Connectivity of marine ecosystems is fundamental to survival, growth, spread, recovery from damage and adaptation to changing conditions, on ecological and evolutionary timescales (James et al, 2002; Cowen and Sponaugle, 2009; Burgess et al, 2014)
As we discovered in preliminary experiments, this was more successful than using a standard Markov Chain Monte Carlo (MCMC) approach; individual walks have an increased chance of wandering away from promising areas, this is balanced by the repeated restarts, which emphasise exploitation of the current Pareto set
Each optimal solution is built around a core of the best connected nodes, gradually expanding with the addition of nodes as costs are increased, with the poorly connected sites on the edges selected last

Summary

Introduction

Connectivity of marine ecosystems is fundamental to survival, growth, spread, recovery from damage and adaptation to changing conditions, on ecological and evolutionary timescales (James et al, 2002; Cowen and Sponaugle, 2009; Burgess et al, 2014). For marine conservation there is ongoing debate (see Cabral et al, 2016) over the relative merits of prioritizing site protection by network structure and connectivity (Kininmonth et al, 2011; Watson et al, 2011; Berglund et al, 2012), or by intrinsic patch characteristics such as habitat quality and extent (Carson et al, 2011; López-Duarte et al, 2012; Cabral et al, 2016). Cabral et al (2016) found the most effective way to maximize adult population was to base conservation on extent and quality of habitat, ignoring connectivity. Kininmonth et al (2011) used a quality measure based on metapopulation persistence to advocate prioritizing groups of highly connected reserves (hubs)

Methods

Results

Conclusion