Bosch
Bosch
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博世
DOI：
10.5860/choice.41-5084
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
B. Cornils
中科院分区：
文献类型：
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作者：
B. Cornils
优化是数学的一个分支，涉及寻找完成任务的最佳方法。当然，有些任务很简单，我们不需要依靠优化来解决它们。但许多其他问题要困难得多，以至于我们在没有优化的情况下令人满意地完成它们的希望非常渺茫，更不用说最佳地完成它们了。例如，假设我们的一位朋友为送餐服务项目做志愿者。她每周一次骑自行车去送餐车总部，领取餐食以及二十个姓名和地址的清单。然后，她坐上送餐车送餐，然后返回总部。她的目标是按照尽量减少出行里程的顺序送餐，因为这将最大限度地减少燃料消耗、污染物排放和工作时间。她的任务——规划她要走的路线——容易吗？这取决于。如果所有地址都在同一条路上，那就非常容易了；对于任何查看地图的人来说，最佳路线都是显而易见的。但如果不是，这可能会非常困难，特别是在地址似乎随机分散在城市各处的情况下。 （为什么？为什么不直接列出并评估每条路线？答案是有 20 条！2.43×1018 条路线，20 个地址的每一种排列都有一条。即使我们的朋友有一台每秒可以评估一万亿（1012）条路线的笔记本电脑，如果她想通过完整枚举找到最佳路线，她也必须运行大约 28 天！）顺便说一句，这个任务是旅行商问题的一个实例(TSP)，优化领域中最困难、最重要、研究最充分的问题之一。优化的应用范围似乎是无限的。它已在许多不同的学科中得到了很好的应用：广告、农业、生物学、商业、经济学、工程、制造、医学、电信和运输（仅举几例）。在本文中，我们通过描述艺术领域的一些应用来展示其惊人的实用性，乍一看似乎没有任何用处！
Optimization is the branch of mathematics concerned with finding the best way to complete a task. Certainly, some tasks are easy, and we need not rely on optimization to tackle them. But many others are much more difficult, so much so that we may have very little hope of completing them satisfactorily—let alone optimally—without optimization. For example, suppose a friend of ours does volunteer work for a Meals-on-Wheels program. Once a week she bikes to the Meals-on-Wheels headquarters and picks up meals and a list of twenty names and addresses. She then gets in the Meals-onWheels van, delivers the meals, and returns to headquarters. Her goal is to drop off the meals in an order that will minimize the number of miles she’ll travel, as this will minimize fuel consumption, pollutant emissions, and the amount of time she’ll spend on the job. Is her task—planning the route she’ll take—an easy one? It depends. If all of the addresses are on the same road, then it is extremely easy; the optimal route will be obvious to anyone who takes a look at a map. But if not, it can be extremely difficult, especially in the case in which the addresses appear to have been scattered about the city at random. (Why? Why not just list and evaluate every single route? The answer is that there are 20! 2.43×1018 routes, one for every permutation of the 20 addresses. Even if our friend has a laptop that can evaluate one trillion (1012) routes per second, she’ll have to run it for about 28 days if she wants to find the optimal route via complete enumeration!) Incidentally, this task is an instance of the Traveling Salesman Problem (TSP), one of the most difficult, important, and well-studied problems in the optimization field. Optimization has a seemingly unlimited number of applications. It has been put to good use in a large number of diverse disciplines: advertising, agriculture, biology, business, economics, engineering, manufacturing, medicine, telecommunications, and transportation (to name but a few). In this article, we showcase its amazing utility by describing some applications in the area of art, which at first glance would seem to have no use for it whatsoever!