Integer programming for optimizing habitat network permeability

Abstract

Purpose

Negative effects of habitat isolation that arise from landscape fragmentation can be mitigated, by connecting natural areas through a network of habitat corridors. To increase the permeability of a given network, i.e. to decrease the resistance to animal movements through this network, often many developments can be made. The available financial resources being limited, the most effective developments must be chosen. This optimization problem, suggested in Finke and Sonnenschein, can be treated by heuristics and simulation approaches, but the method is heavy and the obtained solutions are sub‐optimal. The aim of the paper is to show that the problem can be efficiently solved to optimality by mathematical programming.

Design/methodology/approach

The moves of the individual in the network are modeled by an absorbing Markov chain and the development problem is formulated as a mixed‐integer quadratic program, then this program is linearized, and the best developments to make are determined by mixed‐integer linear programming.

Findings

First, the approach allows the development problem to be solved to optimality contrary to other methods. Second, the definition of the mathematical program is relatively simple, and its implementation is immediate by using standard, commercially available, software. Third, as it is well known with mixed‐integer linear programming formulation it is possible to add new constraints easily if they are linear (or can be linearized).

Research limitations/implications

With a view to propose a simple and efficient tool to solve a difficult combinatorial optimization problem arising in the improvement of permeability across habitat networks, the approach has been tested on simulated habitat networks. The research does not include the study of some precise species movements in a real network.

Practical implications

The results provide a simple and efficient decision‐aid tool to try to improve the permeability of habitat networks.

Originality/value

The joint use of mathematical programming techniques and Markov chain theory is used to try to lessen the negative effects of landscape fragmentation.

Citation

Billionnet, A. (2010), "Integer programming for optimizing habitat network permeability", Management of Environmental Quality, Vol. 21 No. 5, pp. 570-588. https://doi.org/10.1108/14777831011067890