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Merge pull request #4 from rafaelmartinelli/expknap
Pisinger's Expanding Core Algorithm
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,18 @@ | ||
| struct KnapItem | ||
| weight::Int64 | ||
| profit::Int64 | ||
| end | ||
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| struct KnapData | ||
| capacity::Int64 | ||
| items::Vector{KnapItem} | ||
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| KnapData(capacity::Int64, items::Vector{KnapItem}) = new(capacity, items) | ||
| KnapData(capacity::Int64, weights::Vector{Int64}, profits::Vector{Int64}) = new(capacity, [ KnapItem(weights[i], profits[i]) for i in 1:length(weights) ]) | ||
| end | ||
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| function Base.show(io::IO, data::KnapData) | ||
| print(io, "Knapsack Data") | ||
| print(io, " ($(length(data.items)) items,") | ||
| print(io, " capacity = $(data.capacity))") | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,263 @@ | ||
| mutable struct Item | ||
| index::Int64 | ||
| weight::Int64 | ||
| profit::Int64 | ||
| solution::Bool | ||
| end | ||
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| struct Interval | ||
| first::Int64 | ||
| last::Int64 | ||
| weight::Int64 | ||
| end | ||
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| mutable struct GlobalData | ||
| items::Vector{Item} | ||
| capacity::Int64 | ||
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| br::Int64 | ||
| wsb::Int64 | ||
| psb::Int64 | ||
| z::Int64 | ||
| fsort::Int64 | ||
| lsort::Int64 | ||
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| stack1::Vector{Interval} | ||
| stack2::Vector{Interval} | ||
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| estack::Vector{Int64} | ||
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| GlobalData() = new([], 0, 0, 0, 0, 0, 0, 0, [], [], []) | ||
| end | ||
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| function solveKnapExpCore(data::KnapData) | ||
| n = length(data.items) | ||
| if n == 0 return 0, Int64[] end | ||
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| gd = GlobalData() | ||
| gd.items = [ Item(i, data.items[i].weight, data.items[i].profit, false) for i in 1:n ] | ||
| gd.capacity = data.capacity | ||
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| interval = partsort(gd, 1, n, 0) | ||
| gd.fsort = interval.first | ||
| gd.lsort = interval.last | ||
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| gd.z = heuristic(gd, 1, n) | ||
| heur = gd.z + gd.psb | ||
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| elebranch(gd, 0, gd.wsb - gd.capacity, gd.br - 1, gd.br) | ||
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| return gd.z + gd.psb, definesolution(gd) | ||
| end | ||
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| function det(a::Matrix{Int64}) | ||
| return a[1, 1] * a[2, 2] - a[1, 2] * a[2, 1] | ||
| end | ||
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| function partsort(gd::GlobalData, f::Int64, l::Int64, ws::Int64) | ||
| d = l - f + 1 | ||
| if d > 1 | ||
| m = f + d ÷ 2 | ||
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| if det([ gd.items[f].profit gd.items[f].weight; gd.items[m].profit gd.items[m].weight ]) < 0 | ||
| gd.items[f], gd.items[m] = gd.items[m], gd.items[f] | ||
| end | ||
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| if d > 2 | ||
| if det([ gd.items[m].profit gd.items[m].weight; gd.items[l].profit gd.items[l].weight ]) < 0 | ||
| gd.items[m], gd.items[l] = gd.items[l], gd.items[m] | ||
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| if det([ gd.items[f].profit gd.items[f].weight; gd.items[m].profit gd.items[m].weight ]) < 0 | ||
| gd.items[f], gd.items[m] = gd.items[m], gd.items[f] | ||
| end | ||
| end | ||
| end | ||
| end | ||
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| if d <= 3 | ||
| return Interval(f, l, ws) | ||
| else | ||
| mp = gd.items[m].profit | ||
| mw = gd.items[m].weight | ||
| i = f | ||
| j = l | ||
| wi = ws | ||
| while true | ||
| while true | ||
| wi += gd.items[i].weight | ||
| i += 1 | ||
| if det([ gd.items[i].profit gd.items[i].weight; mp mw ]) <= 0 break end | ||
| end | ||
| while true | ||
| j -= 1 | ||
| if det([ gd.items[j].profit gd.items[j].weight; mp mw ]) >= 0 break end | ||
| end | ||
| if i > j break end | ||
| gd.items[i], gd.items[j] = gd.items[j], gd.items[i] | ||
| end | ||
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| if wi > gd.capacity | ||
| push!(gd.stack2, Interval(i, l, wi)) | ||
| return partsort(gd, f, i - 1, ws) | ||
| else | ||
| push!(gd.stack1, Interval(f, i - 1, ws)) | ||
| return partsort(gd, i, l, wi) | ||
| end | ||
| end | ||
| end | ||
|
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| function heuristic(gd::GlobalData, f::Int64, l::Int64) | ||
| ps = 0 | ||
| ws = gd.capacity | ||
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| i = f | ||
| while gd.items[i].weight <= ws | ||
| ws -= gd.items[i].weight | ||
| ps += gd.items[i].profit | ||
| gd.items[i].solution = true | ||
| i += 1 | ||
| end | ||
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| gd.br = i | ||
| gd.wsb = gd.capacity - ws | ||
| gd.psb = ps | ||
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| dz = (gd.capacity - gd.wsb) * gd.items[gd.br].profit ÷ gd.items[gd.br].weight | ||
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| empty!(gd.estack) | ||
| gd.z = 0 | ||
| if gd.z == dz return gd.z end | ||
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| r = gd.capacity - gd.wsb | ||
| for i in gd.br:l | ||
| if (gd.items[i].weight <= r) && (gd.items[i].profit > gd.z) | ||
| empty!(gd.estack) | ||
| push!(gd.estack, gd.items[i].index) | ||
| gd.z = gd.items[i].profit | ||
| if gd.z == dz return gd.z end | ||
| end | ||
| end | ||
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| r = gd.wsb + gd.items[gd.br].weight - gd.capacity | ||
| pb = gd.items[gd.br].profit | ||
| for i in gd.br - 1:-1:f | ||
| if (gd.items[i].weight >= r) && (pb - gd.items[i].profit > gd.z) | ||
| empty!(gd.estack) | ||
| push!(gd.estack, gd.items[gd.br].index) | ||
| push!(gd.estack, gd.items[i].index) | ||
| gd.z = pb - gd.items[i].profit | ||
| if gd.z == dz return gd.z end | ||
| end | ||
| end | ||
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| return gd.z | ||
| end | ||
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| function reduce(gd::GlobalData, first::Int64, last::Int64) | ||
| pb = gd.items[gd.br].profit | ||
| wb = gd.items[gd.br].weight | ||
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| q = det([ gd.z + 1 gd.capacity - gd.wsb; pb wb ]) | ||
| i = first | ||
| j = last | ||
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| if i <= gd.br | ||
| k = gd.fsort - 1 | ||
| while i <= j | ||
| if det([ -gd.items[j].profit -gd.items[j].weight; pb wb ]) < q | ||
| gd.items[i], gd.items[j] = gd.items[j], gd.items[i] | ||
| i += 1 | ||
| else | ||
| gd.items[j], gd.items[k] = gd.items[k], gd.items[j] | ||
| j -= 1 | ||
| k -= 1 | ||
| end | ||
| end | ||
| if k == gd.fsort - 1 | ||
| gd.items[first], gd.items[k] = gd.items[k], gd.items[first] | ||
| k -= 1 | ||
| end | ||
| last = gd.fsort - 1 | ||
| first = k + 1 | ||
| else | ||
| k = gd.lsort + 1 | ||
| while i <= j | ||
| if det([ gd.items[i].profit gd.items[i].weight; pb wb ]) < q | ||
| gd.items[i], gd.items[j] = gd.items[j], gd.items[i] | ||
| j -= 1 | ||
| else | ||
| gd.items[i], gd.items[k] = gd.items[k], gd.items[i] | ||
| i += 1 | ||
| k += 1 | ||
| end | ||
| end | ||
| if k == gd.lsort + 1 | ||
| gd.items[last], gd.items[k] = gd.items[k], gd.items[last] | ||
| k += 1 | ||
| end | ||
| first = gd.lsort + 1 | ||
| last = k - 1 | ||
| end | ||
| return first, last | ||
| end | ||
|
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| function sorti(gd::GlobalData, stack::Vector{Interval}) | ||
| if isempty(stack) return false end | ||
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| interval = pop!(stack) | ||
| first, last = reduce(gd, interval.first, interval.last) | ||
| interval = partsort(gd, first, last, interval.weight) | ||
| if interval.first < gd.fsort gd.fsort = interval.first end | ||
| if interval.last > gd.lsort gd.lsort = interval.last end | ||
|
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| return true | ||
| end | ||
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| function elebranch(gd::GlobalData, ps::Int64, ws::Int64, s::Int64, t::Int64) | ||
| improved = false | ||
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| if ws <= 0 | ||
| if ps > gd.z | ||
| improved = true | ||
| gd.z = ps | ||
| empty!(gd.estack) | ||
| end | ||
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| while true | ||
| if t > gd.lsort && !sorti(gd, gd.stack2) break end | ||
| if det([ ps - (gd.z + 1) ws; gd.items[t].profit gd.items[t].weight ]) < 0 break end | ||
| if elebranch(gd, ps + gd.items[t].profit, ws + gd.items[t].weight, s, t + 1) | ||
| improved = true | ||
| push!(gd.estack, gd.items[t].index) | ||
| end | ||
| t += 1 | ||
| end | ||
| else | ||
| while true | ||
| if s < gd.fsort && !sorti(gd, gd.stack1) break end | ||
| if det([ ps - (gd.z + 1) ws; gd.items[s].profit gd.items[s].weight ]) < 0 break end | ||
| if elebranch(gd, ps - gd.items[s].profit, ws - gd.items[s].weight, s - 1, t) | ||
| improved = true | ||
| push!(gd.estack, gd.items[s].index) | ||
| end | ||
| s -= 1 | ||
| end | ||
| end | ||
|
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| return improved | ||
| end | ||
|
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| function definesolution(gd::GlobalData) | ||
| sort!(gd.items, by = x -> x.index) | ||
| for index in gd.estack | ||
| gd.items[index].solution = !gd.items[index].solution | ||
| end | ||
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| solution = Int64[] | ||
| for item in gd.items | ||
| if item.solution | ||
| push!(solution, item.index) | ||
| end | ||
| end | ||
| return solution | ||
| end |
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