Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://reference.wolfram.com/language/ref/KnapsackSolve.html below:

KnapsackSolve—Wolfram Language Documentation

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technology expertise.

• Data & Computational Intelligence
• Model-Based Design
• Algorithm Development
• Wolfram|Alpha for Business
• Blockchain Technology
• Education Technology
• Quantum Computation

WolframConsulting.com

• See Also
  • LinearOptimization
  • ArgMax
  • Maximize
  • NMaximize
  • FindMaximum
  • FrobeniusSolve
• Related Guides
  • Diophantine Equations
  • Optimization
  • Discrete Mathematics

KnapsackSolve[{cost₁,cost₂,…},maxtotalcost]

solves the knapsack problem of finding the maximum number of items associated with each of the cost_i, subject to the constraint that the total cost is not larger than maxtotalcost.

KnapsackSolve[{{payoff₁,cost₁},{payoff₂,cost₂},…},maxtotalcost]

finds a number of items that maximizes the total payoff, while satisfying the constraint on the total cost.

KnapsackSolve[{{payoff₁,cost₁,maxcount₁},…},maxtotalcost]

allows at most maxcount_i copies of item i.

KnapsackSolve[items,{maxtotalpayoff,maxtotalcost}]

finds a result that gives a total payoff not larger than maxtotalpayoff.

KnapsackSolve[items,{maxtotalpayoff,maxtotalcost,maxtotalcount}]

adds the constraint of having no more than maxtotalcount items in total.

KnapsackSolve[label₁itemspec₁,…,maxtotals]

labels each type of item and gives the result as an association.

• KnapsackSolve finds a list {c₁,c₂,…} of non-negative integer counts c_i≤maxcount_i that maximizes the total payoff and satisfies the constraints specified by maxtotals.
• All payoffs and costs must be non-negative real numbers or Quantity objects. Counts must be non-negative integers or Infinity.
• Possible specifications for the constraints maxtotals are: maxtotalcost, {maxtotalcost}, {maxtotalpayoff,maxtotalcost}, and {maxtotalpayoff,maxtotalcost,maxtotalcount}.
• By default, payoff_i is taken to be 1, and maximum constraints are taken to be Infinity.
• KnapsackSolve solves the unbounded knapsack problem if the maxcount_i are omitted or Infinity, the bounded knapsack problem if they are non-negative integers, and the 0-1 knapsack problem if they are all 1.
• Each collection {payoff_i,cost_i,maxcount_i} can alternatively be given as <|"Payoff"->payoff_i,"Cost"->cost_i,"MaxCount"->maxcount_i|>, where the entries "Payoff" and "MaxCount" are optional.
• The constraint parameters {maxtotalpayoff,maxtotalcost,maxtotalcount} can alternatively be given as <|"MaxTotalPayoff"->maxtotalpayoff,"MaxTotalCost"->maxtotalcost,"MaxTotalCount"->maxtotalcount|>, where the entries "MaxTotalPayoff" and "MaxTotalCount" are optional.

Find the numbers of items c_i maximizing the total count c₁+c₂+c₃ and satisfying :

Find the numbers of items c₁ and c₂ maximizing the total payoff 3c₁+2c₂ and satisfying :

Solve the knapsack problem for two sets of payoffs, costs, and maximum counts:

Solve the problem with additional constraints on the total payoff and total count:

Use an association to label the sets of items:

Solve the knapsack problem by specifying costs only:

Omitted payoffs are set to 1 by default:

Solve the knapsack problem, specifying values for payoffs and costs:

The 0-1 knapsack problem is obtained by setting all maximum individual counts to 1:

Name the payoffs, costs, and maximum individual counts:

The key-value pairs can be given in any order:

Use Association instead of a list of rules:

Name the sets of items:

Use Association instead of a list of rules:

Name both the sets of items and the payoffs, costs, and maximum individual counts:

Solve the knapsack problem with a constraint on the total cost:

Specify constraints on the total payoff and total cost:

Constrain the total payoff, total cost, and total count:

Name the constraints:

The key-value pairs can be given in any order:

Use Association instead of a list of rules:

Use Quantity objects to specify the payoffs or costs:

Compatible units are automatically converted:

Solve a knapsack problem with QuantityArray objects:

Use Dataset objects to specify the collection of items:

Maximize the calorie content of fruits in a grocery list of a limited amount of money:

This is the calorie contribution from each of the fruit types, and the total:

This is the cost for each fruit type and the total cost:

KnapsackSolve is equivalent to a form of LinearProgramming:

If not specified, the values of the total payoff and total count are set to Infinity:

Setting maxtotalpayoff to Infinity will return the maximum total a solution can reach:

The costs and payoffs can be non-negative real numbers, but the counts must be positive integers:

KnapsackSolve returns only one solution satisfying the constraints:

But other solutions can exist:

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4