G53CLP Constraint Logic Programming

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G53CLPConstraint Logic Programming
Dr Rong Qu

• Constraint Optimisation Problems Demos in OPL
  Studio

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SEND MORE MONEY - model

• S E N D
• M O R E
• M O N E Y
• Variables
• Domain

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SEND MORE MONEY - model

• //.mod file
• //declaration
• //variables
• enum Letters S, E, N, D, M, O, R, Y
• //domain
• var int lLetters in 0..9

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SEND MORE MONEY - model

• //.mod file
• //declaration
• //problem - constraints
• solve
• alldifferent(l) onDomain
• lS ltgt 0
• lM ltgt 0
• ...

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SEND MORE MONEY - model

• //.mod file
• //declaration
• //problem - constraints
• solve
• ...
• 1000lS 100lE 10lN lD
• 1000lM 100lO 10lR lE
• 10000lM 1000lO 100lN 10lE
  lY

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SEND MORE MONEY - model
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SEND MORE MONEY decision tree
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SEND MOST MONEY model

• S E N D
• M O S T
• M O N E Y
• Variables
• Domain

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Smugglers Knapsack Problem

• A smuggler has a knapsack of capacity 9
• He can only make one trip
• He can smuggle
• Bottles of whisky size 4 profit 15
• Bottles of perfume size 3 profit 10
• Cartons of cigarettes size 2 profit 7
• He wants
• At least a profit of 30
• Maximise the profit

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Smugglers Knapsack Problem

• Variables
• W, P, C
• Domain
• 0, , 9
• Constraints
• 4W 3P 2C lt 9
• 15W 10P 7C gt30

Bottles of whisky size 4 profit
15 Bottles of perfume size 3 profit
10 Cartons of cigarettes size 2 profit 7
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Knapsack Problems

• Which items should be put in the bag to maximise
  the profit

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Knapsack Problems

• General problems
• Given a number of items with associated costs and
  values
• Determine the collection of items so that
• Total cost is minimised, or within a limit
• Total value is maximised

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Simple Assignment Problem

• In a factory
• 4 workers
• 4 products
• Profits of assigning workers to products
• Each worker has one product
• Each product is assigned to one worker
• At least total profit gt 19

p1 p2 p3 p4
w1 7 1 3 4
w2 8 2 5 1
w3 4 3 7 2
w4 3 1 6 3
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Simple Assignment Problem

• Variables
• li,j worker i assigned to product j
• Domain
• 0, 1
• Constraints
• sum (li) 1, i..4
• sum (weighti,j li,j) gt 19