Simulation of diets for dairy goats and growing doelings using nonlinear optimization procedures

ABSTRACT The objective of this study was to simulate total dry matter intake and cost of diets optimized by nonlinear programming to meet the nutritional requirements of dairy does and growing doelings. The mathematical model was programmed in a Microsoft Excel(r) spreadsheet. Increasing values of body mass and average daily weight gain for growing doelings and increasing body mass values and milk yield for dairy does were used as inputs for optimizations. Three objective functions were considered: minimization of the dietary cost, dry matter intake maximization, and maximization of the efficiency of use of the ingested crude protein. To solve the proposed problems we used the Excel(r) Solver(r) algorithm. The Excel(r) Solver(r) was able to balance diets containing different objective functions and provided different spaces of feasible solutions. The best solutions are obtained by least-cost formulations; the other two objective functions, namely maximize dry matter intake and maximize crude protein use, do not produce favorable diets in terms of costs.摘要 本研究旨在模拟经非线性规划（nonlinear programming）优化、满足泌乳母山羊与生长青年母山羊营养需求的日粮总干物质采食量（total dry matter intake）与成本。本研究在Microsoft Excel（注册商标）电子表格中搭建了数学模型，以生长青年母山羊的体重、平均日增重的递增取值，以及泌乳母山羊的体重、产奶量的递增取值作为优化输入参数。本次研究共设置三类目标函数：日粮成本最小化、总干物质采食量最大化，以及摄入粗蛋白质（crude protein）利用效率最大化。本研究采用Excel（注册商标）Solver（注册商标）算法求解所构建的优化问题。该算法可针对不同目标函数完成日粮配比优化，并可生成不同的可行解空间。最优解可通过最低成本日粮配方获得；其余两类目标函数，即总干物质采食量最大化与粗蛋白质利用效率最大化，在成本维度下均无法生成经济性优良的日粮方案。