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http//www.iro.umontreal.ca/ferland/
http//www.researchandpractise.com/vrp/
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Capacitated Open Pit Mining Problem

• Semya Elaoud, Sfax University (Tunesia)
• Jacques A. Ferland, University of Montreal
• Jonathan Bellemare, University of Montreal
• Jorge Amaya, University of Chile
• 
  

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RIOT Mining Problem web site http//riot.ieor.ber
keley.edu/riot/Applications/OPM/OPMInteractive.htm
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the net value of extracting block i
objective function
Maximal Open Pit problem to determine the
maximal gain
expected from the extraction
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Maximal pit slope constraints to identify the set
Bi of predecessor blocks that have to be
removed before block i
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Maximal pit slope constraints to identify the set
Bi of predecessor blocks that have to be
removed before block i
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Maximal pit slope constraints to identify the set
Bi of predecessor blocks that have to be
removed before block i
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Use the open pit graph G (V, A) to specify the
maximal pit slope constraints
The maximal pit slope constraints
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• (MOP) equivalent to determine the maximal closure
  of G (V, A)
• Equivalent to determine the minimum cut
  of the associated
• Picards graph
• where

The maximal open pit is equal to N
(S s)
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Scheduling block extraction

• Account for operational constraints
• Ct the maximal weight that
  can be extracted during period t
• and for the discount factor during the
  extracting horizon
• discount rate
  per period

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pi weight of block i
the net value of extracting block i
N can be replaced by the maximal open pit
N (S s)
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Scheduling block extraction ? RCPSP

• Open pit extraction ? project
• Each block extraction ? activity
• Precedence relationship derived from the open pit
  graph

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Scheduling block extraction ? RCPSP
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Scheduling block extraction ? RCPSP
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Scheduling block extraction ? RCPSP

• Open pit extraction ? project
• Each block extraction ? activity
• Precedence relationship derived from the open pit
  graph
• Reward associated with activity (block) i depends
  of the extraction period t

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Solution encoding and decoding

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Decoding a block list into a schedule

• Serial decoding
• Initiate the first extraction period t 1
• During any period t
• - The next block to be extracted is the first
  block in the rest of the block list (including
  the blocks not extracted yet) having all their
  predecessors already extracted such that the
  capacity Ct is not exceeded by its extraction.
• Include this block in the newsol block
  list.
• - If no such block exists, then a new
  extraction period (t 1) is initiated.

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Metaheuristic solution approach

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Outline of the solution approach

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Initial solution

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First neighborhood moving one ore block

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Unique ore block process on cluster i

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Second neighborhood moving multiple ore blocks

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Multiple ore block process on cluster i

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Implementation of a metaheuristic procedure
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Numerical experimentation

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Second encoding of the solutionandParticle
Swarm Solution Approach
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Genotype representation of solution

• Similar to Hartmans priority value encoding
  for RCPSP
• priority of scheduling
  block i extraction

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Decoding of a representation PR into a solution x

• Serial decoding to schedule blocks sequentially
  one by one to be extracted
• To initiate the first extraction period t 1
• remove the block among those having no
  predecessor (i.e., in the top layer) having
  the highest priority.
• During any period t, at any stage of the decoding
  scheme
• the next block to be removed is one of those
  with the highest priority among those having all
  their predecessors already extracted such that
  the capacity Ct is not exceeded by its
  extraction.
• If no such block exists, then a new
  extraction period (t 1) is initiated.

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Priority of a block

• Consider its
• net value bi and
• impact on the extraction of
  other blocks in future periods
• Block lookahead value (Tolwinski and
  Underwood) determined by referring to the
  spanning cone SCi of block i

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Genotype priority vector generation

• Several different genotype priority vectors can
  be randomly generated with a GRASP procedure
  biased to give higher priorities to blocks i
  having larger lookahead values
• Several feasible solutions can be obtained by
  decoding different genotype vectors generated
  with the GRASP procedure.

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Particle Swarm Procedure

• Evolutionary process evolving in the set of
  genotype vectors to converge to an improved
  feasible solution
• Initial population P of M genotype vectors
  (individuals) generated using GRASP
• Denote
• the best achievement of the
  individual k up to the current iteration
• the best overall genotype
  vector achieved up to the current iteration

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Particle Swarm Procedure

• Denote
• the best achievement of the
  individual k up to the current iteration
• the best overall genotype
  vector achieved up to the current iteration
• Modification of the individual vector k at each
  iteration

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Particle Swarm Procedure

• Denote
• the best achievement of the
  individual k up to the current iteration
• the best overall genotype
  vector achieved up to the current iteration
• Modification of the individual vector k at each
  iteration

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Numerical experimentation