Towards a Multi-Objective Capital Allocation within Data Centres

Towards a Multi-Objective Capital

Allocation within Data Centres

Takfarinas Saber Anthony VentresqueXavier Gandibleux Liam Murphy

July 15, 2014

Saber et al. − IFORS’14 — Slide 1 of 24

Lero c© 2014 THE IRISH SOFTWARE ENGINEERING RESEARCH CENTRE

Outline of the Presentation

1 Multi-Objective Machine Reassignment Problem

2 Evaluation of State of the Art Techniques

3 Modification of GRASP

4 Next step of our Work: Hybrid Technique for MOMRP

5 Conclusion



Outline for Section 1





5 Conclusion



Data Centre Optimisation

Capital allocators and other sort of operators in data centresperform optimisations of the infrastructure on a regular basis(e.g., every month).A high number of constraints apply on the placement ofservices (Capacity, conflicts, . . . ), which makes the data centreoptimisation a difficult problem: find the best possible solution.Even worse than that, the question we should ask is: what is agood solution?E.g., minimising the power consumption? The salary cost?The environmental impact? The reliability? Etc.→ need for a Multi-Objective Machine Reassignmentsolution.



Problem Overview



Problem Formulation

We manage a set of VMs v ∈ V with different resourcerequirements dv ,r , initially hosted on machinesM0(v) ∈M with a capacity QM0(v),r .

Objective: assigning every VM v to a new machine M(v)(live migration).

We want to provide the decision-maker solutions (i.e.,reassignments) respecting the set of hard constraints &optimising the objectives



Constraints (1)

Capacity

Ensures that the capacity of the machine m ∈M satisfies therequirements of the VMs it hosts:∑

v∈V | M(v)=m

dv ,r ≤ Qm,r , ∀m ∈M,∀r ∈ R

Transient Resources

Transient resources (T R) are consumed twice during the livemigration: at the initial and final hosts (e.g. RAM, Disk):∑

v∈V|M0(v)=m∨M(v)=m

dv ,r ≤ Qm,r , ∀m ∈M, ∀r ∈ T R



Constraints (1)

Capacity

Ensures that the capacity of the machine m ∈M satisfies therequirements of the VMs it hosts:∑

v∈V | M(v)=m

dv ,r ≤ Qm,r , ∀m ∈M,∀r ∈ R

Transient Resources

Transient resources (T R) are consumed twice during the livemigration: at the initial and final hosts (e.g. RAM, Disk):∑


dv ,r ≤ Qm,r , ∀m ∈M, ∀r ∈ T R



Constraints (2)

Anti-cohabitation

VMs are organised by services s ∈ S with anti-cohabitationconstraints (i.e., VMS cannot share the same host) for somereliability, security and performance reasons:

∀vi , vj ∈ V , i 6= j ,∀s ∈ S, (vi , vj) ∈ s2 ⇒ M(vi) 6= M(vj)

Dependency

Services can also depend on each other and in this case VMsof these services need to be close to each other (e.g., toincrease the performance of the system). We introduce herethe concept of neighbourhood N(m) of a machine m.

∀si , sj ∈ S, si ↪→ sj =⇒ ∀va ∈ si , ∃vb ∈ sj | N(M(va)) = N(M(vb))



Constraints (2)

Anti-cohabitation

VMs are organised by services s ∈ S with anti-cohabitationconstraints (i.e., VMS cannot share the same host) for somereliability, security and performance reasons:

∀vi , vj ∈ V , i 6= j ,∀s ∈ S, (vi , vj) ∈ s2 ⇒ M(vi) 6= M(vj)

Dependency

Services can also depend on each other and in this case VMsof these services need to be close to each other (e.g., toincrease the performance of the system). We introduce herethe concept of neighbourhood N(m) of a machine m.

∀si , sj ∈ S, si ↪→ sj =⇒ ∀va ∈ si , ∃vb ∈ sj | N(M(va)) = N(M(vb))



Constraints (3)

Spread

Some services require their VMs to be spread over differentlocations l ∈ L. This allows increasing the resilience in case offailure of a data centre: the bigger the spread number, thesafer the service:∑

l∈L min (1, |{v | v ∈ s ∧ M(v) ∈ l}|) ≥ spreadNumbers , ∀ s ∈ S



Objectives

(1) The cost of migrating v from M0(v) to M(v) is:

relocation = µ1(p,Mo(p)) + µ2(p,Mo(p),M(p)) + µ3(p,M(p))

(2) m ∈M is reliable if it is not loaded more than a reliabilityvalue ρ(m, r) for each resource r ∈ R:

reliability(m) =∑r∈R

max

0 ,∑


dp,r − ρ(m, r)

(3) The electricity cost of m ∈M in l ∈ L depends on αm, βm(electricity consumption constants) and γl (electricity cost in l):

electricity(m) = γl ×

(αm ×

∑p∈P|M(p)=m

dp,CPU + βm

)if m is running

0 otherwise








5 Conclusion



State-of-the-art

We compare our evaluation three different types of algorithms:

First-Fit family

First Fit (FF), Random Fit (RF) and First Fit DescentBin-Balancing (BB).

Metaheuristics

GRASP, NSGA (NSGA-II) and PLS.

Random reassignment (R)

To feel the hardness of the instances.



Testbed

We evaluate our method using 14 instances of the ROADEFChallenge 2012 (grouped in three classes a 1 “easy”, a 2“medium” and b “hard”).

Class of instances Ressources Machines Services Processesa 1 2 - 4 4 - 100 79 - 981 100 - 1000a 2 3 - 12 50 - 100 129 - 1000 1000b 6 - 12 100 - 500 1732 - 15025 5000-20000

We add variables related to electricity consumption (generaterandomly the tangent α and the idle consumption β) for eachmachine. In addition, a price is also given (randomly) to everylocation.



Evaluation: # Solutions

Figure: # non-dominated solutions found by each algorithm.

Say something about PLS/NSGA/GRASP



Evaluation: Hypervolume

R RF FF BB GRASP NSGA PLSa 1 1 2.36 2.70 2.71 2.72 2.73 2.71 2.40a 1 2 7.49 7.49 7.49 7.49 7.49 7.49 7.49a 1 3 4.17 4.17 4.17 4.17 4.17 4.17 4.17a 1 4 9.72 9.72 9.72 9.72 9.72 9.72 9.72a 1 5 2.42 2.49 2.52 2.45 2.62 2.57 2.52a 2 1 4.57 4.89 5.00 4.57 5.50 5.46 4.61a 2 2 1.33 1.33 1.33 1.33 1.33 1.33 1.33a 2 3 2.02 2.02 2.02 2.02 2.02 2.02 2.04a 2 4 6.42 6.42 6.42 6.42 6.42 6.42 6.42a 2 5 9.91 9.91 9.91 9.91 9.91 9.91 9.91b 1 8.20 8.20 8.20 8.20 8.20 8.20 8.24b 2 1.43 1.43 1.43 1.43 1.43 1.43 1.43b 3 6.25 6.25 6.25 6.25 6.25 6.25 6.27

Table: Hypervolume × 10y achieved by each algorithm.








5 Conclusion



GRASP

Description

The constructive phase of GRASP is based on the sorting ofthe VMs according to their dependancy and requirements, andtheir assignment to a random util machine.

Problem

The function of GRASP (the original version), allows thereassignment of all processes without limitation. This hasseveral chain reactions:

No reassignments limitation induces more transientresource consumption.

Means more risk of constraint violation.

Implies less feasible solutions found.



Modification of GRASP

Proposed solution

A limitation of one percent reassignment is taken in order toavoid the consumption of a lot of resources. This number(1%) has to be computed in a cleverer way (using bounds).



Hypervolume & Solutions

oldGRASP newGRASPa 1 1 2.70 (16) 3.6 (42)a 1 2 7.49 (1) 8.47 (26)a 1 3 4.17 (1) 4.27 (19)a 1 4 9.72 (1) 11.1 (40)a 1 5 2.62 (29) 2.74 (49)a 2 1 5.5 (108) 5.43 (57)a 2 2 1.33 (1) 1.55 (22)a 2 3 2.02 (1) 2.36 (30)a 2 4 6.42 (1) 7.62 (28)a 2 5 9.91 (1) 10.3 (28)b 1 8.2 (1) 8.34 (27)b 2 1.43 (1) 1.48 (23)b 3 6.25 (1) 6 (20)








5 Conclusion



GeNePi

A three steps method

Find some quick solutions, good or not, as seeds (kind ofgreedy search).

Find a lot of good solutions on all directions in order tocover a lot of space (genetic algorithm).

Refine around the found solutions to increase the numberof solutions (local search).

Implementation

We developed a hybrid-metaheuristic based on the successionof (i) the adapted GRASP, (ii) NSGA-II and (iii) PLS.



Impact on GeNePi

Instances OldGRASP-based NewGRASP-baseda 1 1 3.77(234) 3.95(193)a 1 2 9.51(93) 9.14(133)a 1 3 4.28(165) 4.32(62)a 1 4 1.21(182) 1.22(187)a 1 5 3.09(263) 2.78(66)a 2 1 5.61(206) 5.68(227)a 2 2 1.45(126) 1.76(171)a 2 3 2.02(2) 2.67(250)a 2 4 6.43(3) 8.63(374)a 2 5 1.01(14) 1.10(245)b 1 8.34(39) 8.49(207)b 2 1.43(2) 1.53(300)b 3 6.27(25) 6.30(162)b 4 3.68(32) 3.70(118)

Table: hypervolumex (#non-dominated solutions ) for by GeNePi.



Conclusion

Reassigning processes to servers automatically is complex,large scale for most of the real instances and needs toconsider different objectives.

We defined the multi-objective machine reassignmentproblem and analysed the performance of differentalgorithms in terms of hypervolume and number ofnon-dominated solutions.

We propose an adaptation of GRASP for this problemand shows that it suits well the problem.

Integrated to GeNePi, it is very promising.



Thank you for your attention!Any questions?

Acknowledgement: This work was supported, in part, by ScienceFoundation Ireland grant 10/CE/I1855 to Lero - the Irish SoftwareEngineering Research Centre (www.lero.ie).



Towards a Multi-Objective Capital Allocation within Data Centres

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