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Aquaculture is the fastest growing food production industry in terms of annual production growth and has become a significant contributor of essential macro-and micronutrients to the diets of the global population. [1][2][3] Increasing the consumption of farmed aquatic food products over land-raised animal meat could potentially reduce the amount of land required for growing feed crops for a global population expected to reach nine billion people by 2050. 4 However, there is a great deal of uncertainty in the further development of aquaculture due to the high and increasing pressure of environmental challenges and resource constraints. 2,5

We study the problem of maximizing an increasing function f : 2 N → R + subject to matroid constraints. Gruia Calinescu, Chandra Chekuri, Martin Pál and Jan Vondrák have shown that, if f is nondecreasing and submodular, the continuous greedy algorithm and pipage rounding technique can be combined to find a solution with value at least 1 − 1/e of the optimal value. But pipage rounding technique have strong requirement for submodularity. Chandra Chekuri, Jan Vondrák and Rico Zenklusen proposed a rounding technique called contention resolution schemes. They showed that if f is submodular, the objective value of the integral solution rounding by the contention resolution schemes is at least 1−1/e times of the value of the fractional solution. Let f : 2 N → R + be an increasing function with generic submodularity ratio γ ∈ (0, 1], and let (N , I) be a matroid. In this paper, we consider the problem max S∈I f (S) and provide a γ (1 − e −1 )(1 − e −γ − o(1))-approximation algorithm. Our main tools are the continuous greedy algorithm and contention resolution schemes which are the first time applied to nonsubmodular functions.