GAbased Multiobjective Workforce Scheduling

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GA-based Multi-objective Workforce Scheduling

• Nic Colledge
• Peter Cowling
• Keshav Dahal
• Stephen Remde

Work Sponsored by
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The Problem Model
Quantity
Connect New Customer
Competency
Cabling
Jointing
Erect New Pole
Polling
Possess
Require
Resources
Skills
Tasks
Location (Start Finish) Working Hours
(Time Windows) Travel Speed Name ID
Location (Start Finish) Precedence
Constraints Assist Constraints Time
Windows Release Date Due Date Priority Name ID
Name ID
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Heuristic Scheduler
A task is scheduled by first selecting a group of
resources for it, this is Resource Selection.
Then once the resources to be used for the task
are known, the task is inserted into the
schedule, this is Task Insertion.
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Resource Selection

• For each of the skills required by the task the
  resources with that skill are compared and the
  best is used for the work.
• Once the resources are chosen the tasks duration
  is known and the task is inserted as early as
  possible.

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The Best Resource
Preceding Task
Resource A
2 hours
Resource B
1.5 hours

• 2 hours x 0.9 competency 1.8 score
• 1.5 hours x 1.5 competency 2.25 score
• Resource B will be chosen for the work

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Optimal Task Order?

• The order in which tasks are scheduled with this
  method greatly effects the resulting schedule.
• Can the task order be optimised using a Genetic
  Algorithm?

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GA / Scheduler Pseudo Code
Generate initial population randomly with Zero
Knowledge For each Generation or until population
converged Select pairs from population for
crossover and/or mutation For each pair
selected Crossover and mutate chromosomes Run
Scheduler on all new / mutated chromosomes Resou
rce Selection Task Insertion Fitness
Assessment Replace population using
replacement strategy Return best solution from
final population
Done By Scheduler
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GA / Scheduler Interaction
Genetic Algorithm
Returns Fitness Values
Returns Fitness Values
Task Order Chromosome 1
Task Order Chromosome n

Scheduler builds schedule
Scheduler builds schedule
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Weighted Sum Objectives

• The most popular method for combining different
  objectives.
• Used with traditional mating selection and
  replacement mechanisms like elitist replacement
  and binary tournament selection
• For example one of our GAs used

f scheduled priority 2(schedule cost)
6(travel time)
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Problems With Weighted Sum

• Population is often converged and not diverse
• Few non-dominated solutions in population
  (solutions that are not beaten in all respects)
• Finding correct set of weights for a problem is
  difficult and is often guesstimated.

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Multiple objective methods

• Actual fitness of an individual is not considered
  directly by GA
• Non-domination and distribution used to score
  individuals instead of fitness value
• Two popular multi objective algorithms
• SPEA2 (Strength Pareto Evolutionary Algorithm)
• NSGA-II (Non-dominated Sorting Genetic Algorithm)

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NSGA-II

• Sorts population into fronts
• Uses crowding distance as a tie-breaker

Minimise Unscheduled Tasks Objective
Front 3
Front 2
Front 1 (non-dominated)
Minimise Cost Objective
How are fronts identified?
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NSGA-II Crowding Distance
Then for each individual i in the front I and for
each objective m. The distance is calculated by
Iidistance Iidistance (Ii1.m -
Ii-1.m)
Minimise Unscheduled Tasks Objective
(i 1)
Individual being considered (i)
(i 1)
Sum of these distances is the Crowding Distance
Minimise Cost Objective
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Diversity at What Cost

• What is the difference in the quality of the best
  solution found by multi-objective methods
  compared with a weighted sum method, when
  assessed by that single weighted sum method?

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Results

• Fitness of multi-objective methods within 2 of
  weighted sum method despite knowing nothing of
  the weights.
• Population approximately 40 more diverse by Max
  Spread measure and 70 more diverse by Morrison
  and De Jong diversity measure.