问题
I was working on an application last night and came across a particular problem which I'm sure probably has an efficient algorithm to solve it. Could anyone suggest?
Problem:
TL;DR: Maybe a picture will help: http://www.custom-foam-inserts.com/ . I have lots of items which fit in a range of compartments: and I want to minimise the number of cases I need to take.
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I have a set of N items of expensive electronic equipment which I want to pack into specially designed protective boxes. These boxes each have many compartments which can each fit a single item: some of which are designed specially to fit a particular item (ie, a camera shaped hole) and some of which are generic (a rectangular hole). I know in advance that there are C different sizes of compartment and what sizes these are.
These boxes come in L different layouts, each with at least one compartment. A layout might be ‘two large rectangular compartments and 4 small circular compartments’.
Each compartment size is present on at least one layout, but I have items which don’t suit any compartment size. Each item fits at least one compartment and may fit into multiple different compartments: for example, my DSLR camera might be a tight fit in a ‘medium rectangle’ compartment, a loose fit in a ‘large rectangle’ and a perfect fit in a ‘DSLR camera compartment’, but won’t fit in a ‘small circle’. To this end I’ve made a list of which compartments are suitable for each item.
The items are moderately heterogeneous – for example there may be 50 items of one size and 20 items of another size.
Each box has two costs Volume and Dollars (however D ~proportional to V). I need to minimise one or both of these costs whilst fitting ALL of my items into the boxes. Due to the layouts of the boxes, the optimal solution may contain unused compartments. If two solutions have equal volume, select the one with the most unused compartments. Because each compartment is present on at least one layout and each item fits in at least one compartment, there is always a solution which fits all items.
Number of items: <=2000, average case 150. Number of compartments: <= 1000. Number of layouts: <= 1000.
Any ideas on this one? I've looked a bit at Knapsack and Bin Packing algorithms and I'm not sure they're the way to go. Help much appreciated.
回答1:
From the problem description this does indeed seem to be knapsack problem since you have to maximise your space available while keeping in mind the weight of your options.
Depending on what you are after, you could also consider using a Genetic Algorithm. Since this problem is NP Complete the running time will eventually explode should you need to add more items, so I would go with this primarily if I need the best solution available irrelevant of the time it takes.
On the other hand, the Genetic Algorithm should be able to provide with some solution in a relatively small period of time, however, the solution it provides might not be as good as the one provided by the Knapsack algorithm, so I would choose a GA if I have restrictions on the time I need to provide some solution and I do not care if it is the not absolute best.
来源：https://stackoverflow.com/questions/10430981/what-kind-of-algorithm-is-this-box-packing-knapsack