Solving a Generalised VRP using Variable Neighbourhood Descent and MetaHeuristics

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Solving a Generalised VRP using Variable
Neighbourhood Descent and Meta-Heuristics

• Tore Dahl
• Geir Hasle
• Lars Magnus Hvattum
• Oddvar Kloster

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Contents

• Classical VRP and PDP
• Our model
• Order types
• Constraints and objectives
• Optimisation algorithm
• Initial solution construction
• Metaheuristics
• Operators
• Experimental results

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Classical VRP(TW)

• Deliveries from a depot
• Homogeneous fleet
• Sizes/capacities
• Single time windows

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Classical PDP(TW)

• Pickup and delivery at customer locations
• Homogeneous fleet
• Sizes/capacities
• Single time windows

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Model extensions

• Pure VRP and PDP are idealised
• To solve real world problems, richer models are
  needed
• Trade-off between model complexity and solving
  speed

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Generalisation of order types

• Any mix of
• Delivery
• Pickup
• Direct (PD)
• Service

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Other generalisations

• Non-homogenous fleet
• Arbitrary route start/end locations
• Non-Euclidean, asymmetric, dynamic travel times
• Multiple time windows (MTW)
• Capacity in multiple dimensions
• Compatibility order/route
• Orders on same or different routes
• Route chaining

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Cost elements

• Travel cost
• Route usage cost
• Cost for starting a route
• Cost per order on route
• Cost for unserviced order
• Waiting time cost

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Initial solution construction

• Best insertion
• Direct orders have more possibilities
• Solomons construction heuristic
• Builds one route at the time
• Selects order and insertion point based on time
  and cost calculations
• Extended to all order types

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Local search Descent

• Current solution

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Guided local search

• Metaheuristic
• Avoids being stuck in local minima
• When in local minimum
• Find solutions most costly features
• Penalise them
• Cost function is tilted
• Solution is no longer a local minimum
• Avoids similar solutions ? better search space
  exploration
• Features Edges between customers in route
• Keep best solution according to original cost
  function

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Neighbourhood operators

• Insert
• Relocate
• Two-opt
• Cross
• Exchange
• Deplete route

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The exchange operator

• Standard VRP version

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The exchange operator

• In our model

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Experimental results

• Benchmarks for the PDP, provided by Li Lim
• 100 customer cases 14 new best results, 36
  equal (of 56)
• Total 405 vehicles, travel distance 55220.09
  (ours) vs.
• Total 404 vehicles, travel distance 58403.6
  (theirs)
• 200 customer cases 33 new best results, 13
  equal (of 60)
• Total 636 vehicles, travel distance 151837.19
  (ours) vs.
• Total 640 vehicles, travel distance 155150.27
  (theirs)

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Further work

• More complex order types
• Work regulations
• Operators
• Metaheuristics