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We are a group of first-year students studying computer science.

We are working on a project called "The electronical diet plan" (directly translated)

We want to make a program in C# that on a weekly basic calculate a diet plan that fullfiels/satisfies some criteria:

Your daily energy intake should not exceed the calculated calorie needs. (Ex. If we calculate that a person should eat 2000 calories per day, the diet plan should plan approximately 2000 calories)

The daily energy (calories) should be distributed as follows:

  • Fat 25-35%
  • Carbohydrates 50-60%
  • Proteins 10-20%

We have a "database" with food and how much fat, carbohydrates and proteins it contains + the approximate price. And we have a "database" with recipies and how much time it takes to cook it.

SO: We want to make a program that on a weekly basic calculate a good diet plan which satisfies the daily energy need (and how it should be distributed (fat, carbohydrates, proteins)). The program should also plan a diet plan that not takes a lot of time and not cost to much (the user defines a upper bound for the price pr. week).

SO.. We want help to find a method/algorithm that can combinate 3-6 dishes per day which satisfied this ^^ We have been looking at a lot of combinational optimizations algorithms/problems but mostly "The knapsack problem".

But these algorithms/problem is only satisfying one criteria or trying to find the "cheapest" solution. -> We want to satisfy a lot of criteria and want to find the best solution (not cheapest.. ex. fat has to be between 25-35%, not just be the lowest value)

We hope that some of you can help us with a good algorithm.

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当谈到寻找“最便宜”的解决方案而不是“最好的”时，您只需要重新定义“便宜”。

在优化理论中，通常指的是要最小化的成本函数-在您的情况下，“成本”可能是“与 30% 的脂肪百分比差异”，即吃 30% 的脂肪不需要任何成本，而吃 20% 作为 40%。当然，为了使方法更复杂，你可以称重，这样吃太多脂肪比吃太少更“昂贵”。

现在，如果您为每个标准创建成本，您还必须一起权衡它们，正如 mellamokb 在评论中指出的那样；为此，只需计算加权总成本。你最终会得到类似下面的东西：

饮食成本=（价格的重要性）*价格+（时间的重要性）*时间+（脂肪的重要性）*（与脂肪目标的偏差）+等...

如果你想让它不可能超出预算（花费的钱），你可以添加一些术语，比如
over budget ? infinity : 0让算法在预算内找到解决方案。您还可以限制用餐的重复等 - 或多或少是您的想象力（和计算能力）设置了限制。

现在您有了成本函数，您可以开始着手解决问题：最小化饮食成本。突然间，所有那些找到“最便宜”解决方案的算法都变得有意义了……；）

请注意，制定此成本函数通常是困难的部分。根据您权衡成本的方式，您会找到非常不同的解决方案；并非所有这些都是有用的（实际上它们中的大多数可能不会有用）。

于 2013-04-17T19:46:03.200 回答