Packing (knapsack) problem (packing Problem) __ Packing problem

Source: Internet
Author: User

Packing problem is also called knapsack problem, in simple terms, is to put small goods into a large box, how to install more. Personal common experience is "install refrigerator", very interesting phenomenon is often feel the refrigerator can no longer fit, but after a toss after the magic of the installed.


From the business point of view is to try to make each container (warehouses, vehicles, containers, ships, etc.) as much as possible, can save the cost of the enterprise. Usually, the loading rate is about 85%, after using the packing optimization method, can reach 90~95% or so. Haier has done a sea-boxing project, saving a lot of freight. Japan's car companies also attach great importance to the problem of packing, they are transported by sea in the car parts box almost every corner will be filled, and often improve its packing scheme.


Boxing problem is a typical NP difficult problem, generally using heuristic algorithm-greedy algorithm, ant colony algorithm, Tabu search, Genetic algorithm, NF (Next fit) approximation algorithm, FF (the one Fit) approximation algorithm, FFD (the decreasing) approximation algorithm, BF ( Best Fit), BFD (best fit deceasing) and more.


Packing problem can be divided into one-dimensional, two-dimensional, three-dimensional, multi-dimensional and so on.


One-dimensional packing problem is the most common, consider only one factor, such as weight, volume, length and so on. Problem Description: Packing problem can be summarized as follows: equipped with

Number is 1,2, ..., N of n items, volume is V1, v2, ..., vn. Load these n items into a number of boxes with a capacity of V. The contract for these n kinds of goods

The volume is not more than V, that is, for 1≤i≤n, there are 0


Two-dimensional packing problem takes into account a couple of factors-given a rectangular piece of paper (cloth, leather) that requires a given shape to be clipped from the sheet.

, a shearing method is made to minimize the total area of the cut waste. Frequently asked questions include space in the yard to consider the length and width of the functional area division, parking location

Division, Packaging materials to consider how to cut to make material waste at least, clothing cloth cut, leather shoes in the production of cutting and so on.


Three-dimensional packing problem considers three factors-----------long, wide and high. loading, loading, loading containers, etc. to consider these three dimensions can not exceed.


Multiple factors are considered in the multidimensional packing problem-for example, the length, width, height, and weight of the volume factor are included.

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