A Variable Neighborhood Search for solving a real life waste collection problem

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A Variable Neighborhood Search for solving a
real life waste collection problem
R. Aringhieri, M. Bruglieri (speaker),
T.Davidovic , M. Nonato t D.E.I. Politecnico
di Milano, Italy D.T.I. Università di Milano,
Italy t D. I. Università di Ferrara, Italy
M.I. Serbian Academy of Arts and Sciences,
Belgrade, Yugoslavia
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Problem description
Disposal plant metal, glass
Collection center
Disposal plant paper, wood
Disposal plant paper, glass
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Problem description operations

• Users convey waste to their nearest collection
  center (CC) and dispose it into an appropriate
  container
• Once a container is full, a service request is
  issued
• bring the full container to a disposal plant to
  be emptied
• bring back to the CC an empty container of the
  same type
• The swap takes place when the CC is closed to the
  users

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The particular VRP

• Given
• Locations of CCs, disposal plants, depot
• Travel times matrix,
• Additional empty skips at the depot,
• The set of full skips

• the problem consists of ROUTING the vehicles s.t.
• full skips are loaded and brought to a plant to
  be emptied,
• empty skips alike replace the full ones,
• without exceeding maximum route duration T

Goal minimize number of vehicles and global
travelled time
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Differences with other VRP
Capacitated VRP
serve n customers with requests q1, , qn with a
fleet of k vehicles each with capacity Q located
at a depot.
It consists of two indipendent decision
problems
i) clustering (which vehicle to send to which
customer)
ii) routing (in what sequence each vehicle
should visit the customers
assigned to it)
The problem we consider is not a capacitated
VRP the request of each customer saturates
the capacity of the vehicle (1 container at a
time)
The actual capacity of the vehicle is the
maximum duration allowed for a route
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Related problems in the literature
1 C. Archetti, M.G. Speranza, Collection
of waste with single load trucks a real case,
www.eco.unibs.it/dmq/speranza 2
L. Bodin, A. Mingozzi, R. Baldacci, M. Ball,
The Rollon-Rolloff Vehicle Routing Problem,
Transportation Science 34 (3) 271-288 (2000).
1 disposal plant 3 L. De Meulemeester,
G.Laporte, F.V.Louveaux, and F. Semet,
Optimal Sequencing of Skip Collections and
Deliveries, Journal of Operational
Research Society 48, 57-64 (1997). unbounded
number of spare containers
no container circulation
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Vehicle Routing graph construction
Nodes
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Vehicle Routing graph construction
Arcs
Physical graph
Vehicle
VR Graph
Cost of the arc
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Vehicle routing tours and routes
Tour close path on the depot
Alternating sequence of loaded and unloaded arcs
Route sequence of tours
Feasible route route not exceeding maximum
duration time

Feasible solution set of feasible routes
covering all the non dummy nodes and possibly
the dummy ones
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From tours to routes
We heuristically solve the bin packing problem
associated to the assignment of tours to route
through the Best Fit Decreasing algorithm
Performing the algorithm we take into account
of possible savings merging two tour
Case 2
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Constructing a feasible solution
Modified Clarke and Wright
1) Saving computation
for each pair (i,j) of compatible
nodes sijcij-ci0-c0j
2) Sort the savings in non increasing order
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3) Greedy phases
Phase 1
consider the savings in the order make the
shortcuts that decrease the infeasibilities
(i.e. decrease the use of spare containers)
i
j
0 spare container
1 spare container
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Improving the solution Local Search
5 different types of neighborhoods considering
move inter-tour, move intra-tour
some moves are customization of classical VRP
moves (Van Breedam 94), others have been tailored
for this specific network
N1 String Cross Exchange
S1
S1, S2 both odd
t1
t2
S2
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Evaluation of a move
The move have impact on routes feasibility
If the move m generates an infeasible tour then
m is refused Else if the move generates an
infeasible route then call Best Fit obtaining
the route set R EndIF f(m) ?a?A ca - ?a? A-
ca a( ?r?R (max (0, ?a?r ca-T))-
?r?R (max (0, ?a?r ca-T)))
saving on the duration
saving on the infeasibility
A is the set of arcs added and A- the set of
arcs removed from the original route set
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GRASP

• The modified CW is randomized by choosing at
  random among the q1 best savings
• Then a LS is applied
• exhaustive search in each neighborhood and
  selection of the best improvement

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Tabu Search

• We just use 3 kinds of neighborhoods
• Two tabu lists of fixed length are used
• - L1 avoids moves involving nodes used in the
  previous
• L1 moves
• - L2 avoids a node to return to the tour from
  which
• it was removed for L2 moves
• (Clearly L1ltL2)
• Variable objective function to tackle
  infeasibility
• Intensification the tours of the shortest route
  are spreaded on the other routes, whenever
  BestFit decreases
• Diversification the longest tours are split
  into smaller ones

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VNS

• Ideas for Shaking
• Nk is obtained applying k times a same type of
  move
• Nk is String Cross Exchange where at most k nodes
  are jumped (i.e. Sk)
• Nk is Scarr2Carr considering at most k containers
  available at the depot
• RGVNS J.Puchingher R.Raidl

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Results on Random Instances
Different numbers of available spare
containers T0 none T1 one for each type Tdef an
intermediate number T? large number of container