最优捕鱼策略问题

最优捕鱼策略问题

摘要

问题一，我们考虑渔场生产过程中的各年龄组鱼群数量的制约因素，将其分为两大类，第1,2龄鱼群为一类，该鱼群数量变化只受自然死亡率制约；第3,4龄鱼群为一类，其数量变化在前8个月受捕捞强度和自然死亡率影响，后4个月只受自然死亡率的制约；可写出在某时刻各鱼群的数量表达式。捕捞只在前8个月进行，则年捕捞量为前8个月各时刻鱼群数量的积分。最后建立年总捕捞量的函数与生产过程中满足的关系式，转化为非线性规划模型，利用matlab 软件求解。

问题二，我们利用问题一中所得到的迭代方程，可迭代地求出第i 年初各年龄组鱼群的数量；再根据问题一中的捕捞量表达式，可写出5年的捕捞总量表达式，以5年捕捞总量最大为前提，利用matlab 软件求解出此时的捕捞强度，然后再验证在此捕捞强度下会不会使5年后鱼群的生产能力有太大的破坏。

最后得出以下结论：可持续捕获条件下，捕捞强度为17.36时，达到最大捕捞总质量g 1088.311⨯； 5年后鱼群的生产能力不会有太大的破坏条件下，捕捞强度为()17.5,17.8k ∈，达到最大最大捕捞总质量g 1064.112⨯。

关键词：渔业；最大收益；捕捞策略；生产能力；生长率；matlab

Optimal Fishing Strategy

ABSTRACT

One problem,meet the function of integral quantity expressions; we consider fisheries production process in the age group of fish number of constraints, it is divided into two major categories, on the 1st and 2nd instar fish as a class, the number of fish change only by natural mortality rate control; the 3,4 years old fish as a class, the number of changes in the first eight months of fishing intensity and natural mortality, after 4 months only by natural mortality constraints can be written in a moment the fish. Fishing only in the first eight months, then the annual catches in the first eight months each time stocks. Finally a total fishing volume and production process, is transformed into a nonlinear programming model by MATLAB software solution.

Two problem,we exploit the problem in the iterative equation that can be iterated to calculate the number of fish in each age group at the beginning of the i-th; according to the problems in catches of expression, can write with 5 years of fishing aggregate expressions, in 5 years of total fishing maximum as the premise, at this time the fishing intensity was obtained by using MATLAB software, which are then validated in this fishing intensity does not make 5 years after fish production capacity has too much damage.

Finally draws the following conclusion: Sustainable capture conditions, fishing intensity of 17.36 to achieve maximum catch total quality ; 5 years after fish production capacity will not have too much damage conditions, the fishing intensity , achieve the maximum total fishing quality.

Key word：Fisheries；Maximum benefit; Fishing strategy; Throughput；Growth rate; Matlab

目录

1 绪论 (4)

1.1 研究背景及目的 (4)

1.2 研究方法 (4)

2 最优捕鱼策略问题分析求解 ......................................................................................... - 1 -

2.1 问题的提出................................................................................................................... - 1 -

2.2 问题假设....................................................................................................................... - 1 -

2.3 符号说明....................................................................................................................... - 2 -

2.4题中术语理解................................................................................................................ - 2 -

2.4.1自然死亡率........................................................................................................ - 2 -

2.4.2 捕捞强度系数................................................................................................... - 2 -

2.4.3 成活率............................................................................................................... - 3 -

2.5 问题分析....................................................................................................................... - 3 -

2.5.1 问题一分析....................................................................................................... - 3 -

2.5.2 问题二分析....................................................................................................... - 3 -

2.6 模型建立....................................................................................................................... - 4 -

2.6.1问题一模型........................................................................................................ - 4 -

2.6.2 问题二模型....................................................................................................... - 6 -

2.7模型求解........................................................................................................................ - 6 -

2.7.1问题一求解........................................................................................................ - 6 -

2.7.2 问题二求解....................................................................................................... - 8 -

2.8 模型评价..................................................................................................................... - 10 - 参考文献 .................................................................................................................................. - 10 - 附录源程序清单 .................................................................................................................. - 10 -