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运用混合整数线性规划法进行人类饮食规划。

Diet planning for humans using mixed-integer linear programming.

作者信息

Sklan D, Dariel I

机构信息

Faculty of Agriculture, Hebrew University, Rehovot, Israel.

出版信息

Br J Nutr. 1993 Jul;70(1):27-35. doi: 10.1079/bjn19930102.

DOI:10.1079/bjn19930102
PMID:8399108
Abstract

Human diet planning is generally carried out by selecting the food items or groups of food items to be used in the diet and then calculating the composition. If nutrient quantities do not reach the desired nutritional requirements, foods are exchanged or quantities altered and the composition recalculated. Iterations are repeated until a suitable diet is obtained. This procedure is cumbersome and slow and often leads to compromises in composition of the final diets. A computerized model, planning diets for humans at minimum cost while supplying all nutritional requirements, maintaining nutrient relationships and preserving eating practices is presented. This is based on a mixed-integer linear-programming algorithm. Linear equations were prepared for each nutritional requirement. To produce linear equations for relationships between nutrients, linear transformations were performed. Logical definitions for interactions such as the frequency of use of foods, relationships between exchange groups and the energy content of different meals were defined, and linear equations for these associations were written. Food items generally eaten in whole units were defined as integers. The use of this program is demonstrated for planning diets using a large selection of basic foods and for clinical situations where nutritional intervention is desirable. The system presented begins from a definition of the nutritional requirements and then plans the foods accordingly, and at minimum cost. This provides an accurate, efficient and versatile method of diet formulation.

摘要

人类饮食规划通常是通过选择饮食中要使用的食物项目或食物组,然后计算其成分来进行的。如果营养素的量未达到所需的营养要求,就更换食物或改变量,并重新计算成分。反复进行迭代,直到获得合适的饮食。这个过程既繁琐又缓慢,而且常常导致最终饮食成分的折衷。本文提出了一种计算机化模型,该模型以最低成本为人类规划饮食,同时满足所有营养需求,维持营养素之间的关系并保留饮食习惯。这是基于一个混合整数线性规划算法。为每种营养需求准备了线性方程。为了生成营养素之间关系的线性方程,进行了线性变换。定义了诸如食物使用频率、交换组之间的关系以及不同餐食的能量含量等相互作用的逻辑定义,并编写了这些关联的线性方程。通常以完整单位食用的食物项目被定义为整数。通过使用大量基本食物来规划饮食以及在需要营养干预的临床情况下,展示了该程序的使用。所提出的系统从营养需求的定义开始,然后以最低成本相应地规划食物。这提供了一种准确、高效且通用的饮食配方方法。

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引用本文的文献

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Mathematical Optimization to Explore Tomorrow's Sustainable Diets: A Narrative Review.数学优化探索明天的可持续饮食:叙事评论。
Adv Nutr. 2018 Sep 1;9(5):602-616. doi: 10.1093/advances/nmy049.
2
Food pattern modeling shows that the 2010 Dietary Guidelines for sodium and potassium cannot be met simultaneously.食物模式建模表明,2010 年饮食指南中的钠和钾的摄入量不能同时满足。
Nutr Res. 2013 Mar;33(3):188-94. doi: 10.1016/j.nutres.2013.01.004. Epub 2013 Feb 12.
3
Energy allowances for solid fats and added sugars in nutritionally adequate U.S. diets estimated at 17-33% by a linear programming model.
线性规划模型估计,美国营养充足饮食中的固体脂肪和添加糖的能量津贴为 17-33%。
J Nutr. 2011 Feb;141(2):333-40. doi: 10.3945/jn.110.131920. Epub 2010 Dec 22.