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stackdump/knapsack2.ipynb

Created January 3, 2025 21:59
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Analyzing Knapsack outcomes when suppressing 1 of the items
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knapsack2.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "eea2cfe5-61d4-4b58-a4c6-21fa6f526fe7",
"metadata": {},
"source": [
"This script models a knapsack problem using Petri nets in Julia, simulating the dynamic inclusion of items based on their weights and values. By excluding specific transitions, it explores how each item's absence impacts the knapsack's value over time, providing insights through differential equation-based simulations and annotated plots.\n",
"\n",
"\n",
"[![pflow](https://pflow.dev/img/zb2rheXF9ikouRESRNsR2d1ZcidxdvLuv6zuvxc7ERA5KfM5X.svg)](https://pflow.dev/p/zb2rheXF9ikouRESRNsR2d1ZcidxdvLuv6zuvxc7ERA5KfM5X/)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fa9d67b9-0cc2-463b-9910-f846f52911f5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Petri\n",
"using LabelledArrays\n",
"using Plots\n",
"using OrdinaryDiffEq\n",
"\n",
"# Define the states (places in Petri net)\n",
"states = [\n",
" :item0, :item1, :item2, :item3, :weight, \n",
" :value, :capacity, :max\n",
"]\n",
"\n",
"# Define the transitions (steps in Petri net)\n",
"transitions = LVector(\n",
" txn0=(LVector(item0=1, capacity=2), LVector(weight=2, value=10)),\n",
" txn1=(LVector(item1=1, capacity=4), LVector(weight=4, value=10)),\n",
" txn2=(LVector(item2=1, capacity=6), LVector(weight=6, value=12)),\n",
" txn3=(LVector(item3=1, capacity=9), LVector(weight=9, value=18)),\n",
")\n",
"\n",
"# Create the Petri net model\n",
"knapsack_model = Petri.Model(states, transitions)\n",
"\n",
"# Define a function to create rates\n",
"function create_rates(success_rate, exclude=[])\n",
" rates = LVector(\n",
" txn0=success_rate,\n",
" txn1=success_rate, \n",
" txn2=success_rate,\n",
" txn3=success_rate, \n",
" )\n",
" for key in exclude\n",
" rates[key] = 0\n",
" end\n",
" return rates\n",
"end\n",
"\n",
"# Define the initial state\n",
"initial_state = LVector(\n",
" item0=1, item1=1, item2=1, item3=1, \n",
" weight=0, value=0, capacity=15, max=0\n",
")\n",
"\n",
"# Define the simulation function\n",
"function simulate_petri_net(model, initial_state, rates, time_max)\n",
" tspan = (0.0, time_max)\n",
" prob = ODEProblem(model, initial_state, tspan, rates)\n",
" return solve(prob, Tsit5(), saveat=0.1)\n",
"end\n",
"\n",
"# Simulation parameters\n",
"time_max = 5.0\n",
"success_rates = [1] # Different success rates for testing\n",
"\n",
"# exclude each txn in turn\n",
"exclusions = [:none, :txn0, :txn1, :txn2, :txn3] # REVIEW: shouldn't excluding 0 and 1 produce the same result?\n",
"\n",
"# Run simulations\n",
"solutions = Dict()\n",
"for exclusion in exclusions\n",
" if exclusion == :none\n",
" rates = create_rates(1)\n",
" else\n",
" rates = create_rates(1, [exclusion])\n",
" end\n",
" sol = simulate_petri_net(knapsack_model, initial_state, rates, time_max)\n",
" solutions[exclusion] = sol\n",
"end\n",
"\n",
"plot(title=\"Knapsack with Exclusions\", xlabel=\"Time\", ylabel=\"Tokens\", lw=2)\n",
"# Plot results\n",
"for (excluded, sol) in solutions\n",
" #plot!(sol.t, sol[5, :], label=\"Weight\", linestyle=:dash)\n",
" #plot!(sol.t, sol[6, :], label=\"Value\", linestyle=:dash)\n",
" #plot!(sol.t, sol[7, :], label=\"Capacity\", linestyle=:dash)\n",
"\n",
" # max value with exclusion\n",
" #plot!(sol.t, sol[8, :], label=\"exclude: $excluded\", linestyle=:dash)\n",
"\n",
" # value with exclusion\n",
" plot!(sol.t, sol[6, :], label=\"exclude: $excluded\", linestyle=:dash)\n",
"\n",
" # get time index at t=4\n",
" idx = findfirst(x -> x == 4, solutions[excluded].t)\n",
"\n",
" # annotate values at t=4\n",
" #weight = round(solutions[excluded][5, idx], digits=3)\n",
" value = round(solutions[excluded][6, idx], digits=3)\n",
" #capacity = round(solutions[excluded][7, idx], digits=3)\n",
" max_value = round(solutions[excluded][8, idx], digits=3)\n",
"\n",
" #annotate!(3, weight, text(\"Weight: $weight\", :left))\n",
" #annotate!(3, value, text(\"Value: $value\", :left))\n",
" #annotate!(3, capacity, text(\"Capacity: $capacity\", :left))\n",
" #annotate!(3, max_value+5, text(\"Max: $max_value\", :left))\n",
"\n",
" # plot max value at t=4\n",
" #scatter!([4], [max_value], label=\"$excluded: $max_value\", markersize=5)\n",
"\n",
" # plot value at t=4\n",
" scatter!([4], [value], label=\"$excluded: $value\", markersize=5)\n",
"end\n",
"\n",
"plot!()"
]
},
{
"cell_type": "markdown",
"id": "bb58d911-bbd1-4214-b517-1e111e885217",
"metadata": {},
"source": [
"\n",
"The simulation's observation that excluding txn2 increases the knapsack value aligns with the Python-based branch-and-bound algorithm's results. In the Python implementation, items are assessed based on their value-to-weight ratio and explored to maximize the knapsack's total value.\n",
"\n",
"The algorithm reveals that Item(12, 6, 2)—analogous to txn2 in the Petri net model—may not contribute optimally to the solution, as its inclusion can lead to a suboptimal allocation of capacity.\n",
"\n",
"This consistency across methodologies underscores the robustness of these findings and highlights the value of complementary approaches to analyze and refine decision-making in knapsack problems."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.2",
"language": "julia",
"name": "julia-1.11"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.2"
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"nbformat": 4,
"nbformat_minor": 5
}
@stackdump
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The post above is an iteration on the original model https://gist.github.com/stackdump/7351cba2958626fe6196b566069ccb1e

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stackdump commented Jan 4, 2025 •
edited
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It's possible the ODE solver approach is more similar to the fractional knapsack problem since we it's continuous and evaluates all places at once.

https://www.geeksforgeeks.org/fractional-knapsack-problem/

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Screenshot 2025-01-04 at 9 58 42 AM

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