INTEGER PROGRAMMING APPROACH TO CONTROL INVASIVE SPECIES SPREAD BASED ON CELLULAR AUTOMATON MODEL

We propose a new optimization model that captures the spatial dynamics of invaders by a cellular automaton model and finds the optimal solution to control its spread within a 0–1 integer programming framework. The model seeks a solution by minimizing the total costs to implement treatments for preventing the spread and damage caused by invaders’ colonization. By incorporating a cellular automaton model governed by state- and distance-dependent probability rule of colonization, the model is transformed into a linear model, so that a 0–1 integer programming formulation is used to evaluate and compare an optimal allocation of treatments on colonized and uncolonized areas. The study uses a hypothetical map to show that treatments on colonized cells are more effective when implemented at the front line of the invaders, while treatments on uncolonized areas are effective when conducted with some distance or buffer zone away from the front line. These buffer zones are likely to be colonized regardless of treatment. Under annual budget limits, treatments on colonized cells are implemented first. With heterogeneity in the invaders’ dynamics, the proposed optimization model provides an optimal allocation of treatments much different from the solution with homogeneous environment. However, treatment at the front line of the invading species is always recommended.