Metaheuristics Network

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• Metaheuristics Network
• Activities EuroBios

Thomas Bousonville EuroBios
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Overview

• Consumer Packed Goods Example
• Routing in Real Streetnetworks
• Experiment analysis environment

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Two-Stage Flow Shop
Demand
Mixers
Packing Lines
Intermediate Storage
Supply,
Supply,
Demand
Demand
Early
Delivery
Connectivity
Finished Good
Connectivity
Storage

of
PLs,
size
,
size
,
type,
capacity
Raw
Distribution
materials
Networks
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Two-Stage Flow Shop

• Constraints
• Run-rates
• Capacities
• Changeover
• Connectivity
• Precedence
• Maintenance

• Objective
• Minimizing makespan

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Two-Stage Flow Shop

• Linear programming appoaches
• Example (Jain and Grossmann 2000)
• Each product has a dedicated machine
• A tank can be connected to only one make and one
  pack machine at a time
• The size of an order does never exceed the tank
  capacity

• Solution
• Using a commercial MILP solver problems up to 15
  jobs could be solved to optimality

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Two-Stage Flow Shop
More formal problem description K1 machines make
stage K2 machines pack stage J jobs di duration
job i vi variant of job i im, ip make and pack
tasks of a job skij changeover times between the
jobs i, j on machine k operations of make task
of job i,
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Two-Stage Flow Shop
operations of make task of job i, start time
of operation duration of operation Objective
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Representation

• Direct representation is difficult because of
• Constraints
• Continuous nature of the decision variables
• Alternative

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Scheduler
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Scheduler
SP(j) schedules the maximal amount of job j on a
given resource combination (make, pack, tank)
without interruption this may lead to a
division of a job in different numbers of
operations in different schedules generally the
number of decision points during the algorithm is
not known in advance
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Representations
But if rki rli for all machines k,l of the
same stage any given job i tc is identical for
all tanks the number of generated operations
per jobs is invariant for all possible schedules
generated by the presented scheduler the
solution can also be represented by a fixed
length string of operations
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Local search

• No local evaluation of a neighbor solution
  possible
• After every local move the new solution has to
  reevaluated (beginning with the involved oper.)
• Only small (maximum quadratic) neighborhoods are
  useful for computational reasons

• Transpose neighborhood (linear)
• Insert neighborhood (quadratic)
• Block insert neighborhood (cubic)

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GA framework

• Operators
• Crossover OX operator
• Mutation two or four position exchanges
• Population management
• Stochastic universal sampling
• Constant population size
• all offspring are kept for the next generation
  and replace the worst individuals in the parent
  population

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Computational experiments

• Test problem
• 57 products, 20 variants
• 3 make lines, 7 pack lines, 5 tanks
• Genotype space size
• 476 (job rep.) vs. 2111 (operations rep.)
• Time limit
• 1000 seconds

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Computational experiments
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Computational experiments
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Computational experiments
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Conclusions - CPG

• Presentation of a real world problem from
  consumer packed goods
• Possible representations in combination with a
  scheduler
• The performance of different local search
  procedures and the combination within a Memetic
  Algorithm are compared
• Outlook broader evaluation by using further
  instances

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Routing in Garbage Collection
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Distribution of garbage
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Partition in districts
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Routing
Problem Determine the order in which to service
the street segmenst ... minimizing the total
length

• Take into account
• One way roads
• Turn restrictions
• Waiting times at crossings

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Model
Basemodel Mixed Rural Postman Problem on G
G(N,E,A,S,c,d) having c E?A ? ?, d S ? ?,
S ? (E ?A)
Extension Turn restrictions Tupel
with (j1, i1, j2), j1,j2?1,..,EA,
i1?1,..,N t T ? ?, T ? ( (E ?A) ? N ? (E ?A)
)
Mixed Rural Postman Problem with Turn penalties
MRPPTP
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Representation

• Reconstruction of a tour from the genotype
• Connect si and si1 with their shortest path
• Unique mapping
• Every edge has to have a logical direction (si,
  di)
• Shortest paths
• Turn restrictions andcosts are included

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Crossover Operator OX (Davis)

• Parents p1 ( 1 2 3 4 5 6 7 8 9 )
• p2 ( 4 5 2 1 8 7 6 9 3 )
• produce offsprings
• o1 ( x x x 4 5 6 7 x x )
• o2 ( x x x 1 8 7 6 x x )
• by trying to preserve the ordering of one parent
• o1 ( 2 1 8 4 5 6 7 9 3 )
• o2 ( 3 4 5 1 8 7 6 9 2 )

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Population management
r chromosomes are chosen for reproduction Stochas
tic Universal Sampling (Baker) Parents for
crossover or mutation are selected with a
probalility according to their relative
fitness popsize-r chromosomes are chosen to stay
unchanged
New population of popsize chromosomes
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Local Search
2-Opt 3-Opt
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Local Search
2-Opt 3-Opt
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Mutation
viewed as a local move
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Configuration
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Validation

• Testdata
• taken from literature (Corberan et al. (2001))
• 63 problems with sizes between 80 and 520 service
  edges
• Reference algorithm
• TabuSearch-Algorithm (Corberan 2001)
• Exact procedure for ATSP (only applicable for
  small instances)
• Experiments
• 6 runs in toal, 3 runs with 20 and 50 Individals
  respectively.

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Results

• For 24 instances the optimum is known
• EA reaches the optimum in 15 cases
• For the other cases max. 0,3 deviation
• For 53 out of 63 the EA performs better than the
  tabu search
• In average about 1 better solution quality
• but long running times

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GA Candidate list length
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GA vs.TabuSearch
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Experiment Analysis Environment

• Based on a database
• Graphical user interface
• Experiment organization
• Analysis definition

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DD-Example