PERFORMANCE COMPARISON OF SIXEFFICIENT PURE HEURISTICS FOR

SCHEDULING META-TASKS ONHETEROGENEOUS DISTRIBUTED

ENVIRONMENTS

Hesam Izakian, Ajith Abraham, Vaclav Snasel

PresenterRadu Stoenescu

Problem Formulation

• Resources: M = {m1, m2, …, mm}• Performance of machine i on task j: Estimated

Completion Time (ECT(i, j))• Tasks performed in First-Come First-Served fashion

• Tasks: T = {t1, t2, … , tn}• Assumptions:

• No preemption• Tasks are independent• The environment (resources available) is invariable

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Performance Metrics

• Notations• E(i, j) – Time to execute tj on mi

• W(i) – Existing workload on mi• C(i) = W(i) + – Total completion time of all tasks

assigned to mi • Metrics

• Flowtime F(T, M) = • Makespan MK(T,M) =

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Problem Instance Example

M1 M2T1T2WScheduling:i) T1 M1, T2 M2: F = 4 + 5 = 9 MK = max{7,7} = 7ii) T1 M2, T2 M1: F = 4 + 3 = 7 MK = max{6,6} = 6

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Challenge

• NP-Complete, takes exponential time• The task scheduling algorithm should• Offer a solution as close as possible to the

optimal• Yield a result in a timely manner

• Would be a plus to use one algorithm for optimizing under more than one metric

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Min-min

• While there are unscheduled, tasks schedule the task with a minimum completion time out the set of unscheduled tasks

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Max-min

• While there are unscheduled tasks, for every task find the shortest completion time. Schedule the task with the longest completion time out of the above set.

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Longest Job to Fastest Resource – Shortest Job to Fastest Resource (LJFR-SJFR)

• A mix between Min-min and Max-min• While there are tasks unscheduled, compute for

each set the shortest completion time.• LJFR is the task with the longest time in the

above set.• SJFR is the task with the shortest time in the

above set.• Schedule first m tasks in LJFR fashion, then

alternate.10

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Max-min

Min-min

Max-min

Sufferage heuristic

• At each step, for each task compute the sufferage as the difference in time to complete the task on the best resource vs. on the second-best resource.

• Schedule the task with the highest sufferage.• The intuition is that we would like to schedule task

that show an affinity for a certain resource with priority.

• Works well when the variance in completion times is high.

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Work Queue

• When a resource (machine) is available assign it a task chosen randomly from the set of unscheduled tasks.

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Min-max

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C

Benchmark

• 512 tasks, 16 machines• Each test consists of an ECT matrix labeled using the

format u-yy-zz-x– u means uniform distribution used in generating the

matrices– yy indicates the heterogeneity of the tasks; hi means high

and lo means low– zz represents the heterogeneity of the machines; hi means

high and lo means low– shows the type of inconsistency; c means consistent, i

means inconsistent, and p means partially-consistent

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Makespan(lower is better)

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Flowtime(lower is better)

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Can we do better?

• Improve previously obtained results using a meta-heuristic approach– Genetic Algorithms– Simulated Annealing– Tabu Search– Colony Optimization

• They heavily depend on the quality of the initial candidate

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Simulated annealing

• Begin with a candidate• At each step:– Slightly modify this candidate randomly– If the new result is an improvement, replace the

candidate– If not, probabilistically replace the candidate

• The probability is higher at the beginning and it gets smaller and smaller

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Makespan improvement(lower is better)

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Makespan improvement(lower is better)

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Observations

• Starting with a good candidate constantly offers better results than a randomly assigned one

• Simulated annealing does not offer huge improvements compared to pure-heuristic

• Usually one can not improve both Makespan and Flowtime

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Conclusions

• Scheduling is a hard problem with great implications

• Min-min helps reducing Flowtime• Min-Max helps reducing Makespan• Meta-heuristics can be used to further

improve a result

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Questions