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Vehicle Routing in a Forestry Commissioning Operation using Ant

Colony OptimisationEdward Kent

Jason AtkinRong Qi

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ContentsVehicle Routing Problem VRP in Forestry CommissioningLoading Bay ConstraintsAnt Colony Optimisation Handing Loading BaysLower Bound CalculationResults Conclusions

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Vehicle Routing Problem• Graph of Points (Customers, with one point being the

Depot)

• Vehicles Originate at the Depot

• Customers have a demand

• Vehicles have a capacity

• Objective: Fulfil all customer demand in the least cost

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Vehicle Routing Problem• Variants

• Time windows• Heterogeneous Fleets• Limited Route Distance• Multiple Depots

• Methods of Solving• Exact algorithms (Column generation, relaxations based

on matchings and trees etc) • Heuristics (SA, GA, Savings Algorithms, Tabu Search .. )

• Aims:• Save Fuel, Money, Time

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VRP In Forestry commissioning Logs are cut using large chain-saw like machines into different sizes at

different forests

Different forests have different log cuts as well as different species of wood

An ordering system is used where sawmills/power plants or pulp plants order specific cuts and species from particular forests. (consignments)

Aim & Objective : Get the wood from the forests to the sawmills in the least amount of cost

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VRP In Forestry commissioning• Consignment: An a priori pairing of a forest

to a sawmill• Represents a sawmill’s order of a truck

load of wood from a forest

• Trucks drive from the forest directly to the sawmill to deliver wood

• Time windows (Forest and sawmill)

• Re model problem into a Graph of Consignments (matrix given from distances between consignments)

• Asymmetric, non-euclidean, triangle rule does not apply

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Loading Bay Constraints Many vehicles can arrive at a forest/sawmill

at once

Only a limited number of vehicles are allowed to be serviced simultaneously

These constraints are non-linear Arrival time vehicle 1 > departure time of

vehicle 2 OR Arrival Time vehicle 2 > departure time of

vehicle 1

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Ant Colony Optimisation A population based search that’s robust and versatile

Example for solving TSP problems

Set of cooperating agents “ants”

One ant, one solution

Ants build solution with decisions made based on Length of the arc between the cities Amount of “pheromone” on the arcs Visited before by the Ant

Ants leave “pheromone” on the arcs – good solutions leave more pheromone than bad ones

Pheromone evaporated at a rate of rho

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Ant Colony Optimisation• Over time, Pheromone on arcs strengthen

on good solutions

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Ant Colony Optimisation• How to apply ACO to the Forestry Commissioning routing problem

• Consignments = Cities

• Ant is synonymous to a Vehicle• Ants keep track of their own time

• Ant group represents a solution

• Consignments that will violate a constraint are invisible

• Return to Depot when no more consignments are available

? ?

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Handling Loading Bays• Handle Loading bays in 3 ways:

• Repair loading bay constraint violations• Solution is created, ignoring loading bays• Attempt re-arranging solution to abolish violations

• Avoid consignments that have no loading bays available• Make consignments that have no loading bays invisible• Ants will only go to “free” consignments

• Make vehicles wait for loading bays to be free• Assign a penalty multiplier on the waiting time and driving time

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Handling Loading BaysExpected:

(1) – Waiting/Queuing(2) – Avoid Queuing

Calculating loading bay spreadCluster LB usage togetherRatio of total usage and total length of cluster

Determine how “busy” loading bays are.

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Lower Bound Calculation• a-TSP Lower Bound Relaxation

• Column generation on sub-tour elimination constraints

• CPLEX runs out of memory

• “Weak” lower bound

• Results in large optimality gap

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Results6 Datasets generated from 2 large real-world datasetsAll datasets have at least one “busy period”Various parameters tried :

Rho: 0.99, 0.95, 0.9 ): (0.5, 5), -> (~0.7,~1.5)

Limited Time: Iterations = 1000, Ant Groups = Number of ConsignmentsTime: 20-30 minutes (30 minutes capped)

Testing: LB Constraints RelaxedW1 & W2Avoiding Queuing

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ResultsConsignments: 300 – 500Vehicles constant at 40 per dataset (100 in

the real world sets) Weak lower bounds means large gap

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Results2 out of 6 datasets could not be scheduled with

the “avoid queuing” method.Time windows could not be metConsignments left too late

Ignoring constraints gives a better objectiveLoading bays relaxed, less constrainedNo waiting recorded and no diversions

Avoid queuing method causes bad objective values

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ResultsMann-Whitney U Test Results

Objective: 5/6 datasets had better objectives when setting W2 to 2 vs

setting W2 to 0. 4/6 datasets had better objectives when setting W2 to 1 vs

setting W2 to 0. Similar results were found (objectives worse) when setting W1

to 2 ( making waiting time less penalised than driving time) Objectives are better when penalising waiting time with 1 or

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Loading bay spread:Avoiding queuing produced more manageable solutions

but worse objectives

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ConclusionThe forestry Commissioning routing problem

was explainedRe-formulated into a VRP model with time

windows and loading bay constraintsAnt colony optimisation heuristic was used

Possible adaptations were explained, avoiding queuing or penalising waiting time in the ant’s visibility

Results show best objectives from using the penalising waiting times methodSet waiting time penalty to 1 or 2