Handling Large Datasets in Parallel Metaheuristics:A Spares Management and Optimization Case Study

Chee Shin Yeo

Institute of High Performance ComputingSingapore

yeocs@ihpc.a-star.edu.sg

Elaine Wong Kay Li

EADS Innovation WorksSingapore

elaine.wong.kl@eads.net

Yong Siang Foo

Institute of High Performance ComputingSingapore

fooys@ihpc.a-star.edu.sg

Abstract—Parallel metaheuristics based on Multiple Inde-pendent Runs (MIR) and cooperative search algorithms arewidely used to solve difficult optimization problems in diversedomains. A key step in assessing and improving the speedof global convergence of parallel metaheuristics is tracingsolutions explored by the MIR-based algorithm. However,this generates large amounts of data, thus posing executionproblems. This problem can be resolved by using a flowcontrol workflow to govern the execution of the MIR-basedparallel metaheuristics. Using a Spares Management andOptimization case study for the logistics industry, this paperanalyzes the performance of the flow control workflow withdifferent problem sizes. We show that by appropriately settingworkflow parameters, namely: (1) stop criterion to limit theamount of data cached and exchanged, and (2) clustering policyto distribute/aggregate parallel processes to compute nodesselectively, the performance of the algorithm can be improved.

I. INTRODUCTION

The use of metaheuristics to solve problems in a wide

range of domains has been exceedingly popular. Meta-

heuristics unlike exact methods and heuristics exhibit two

distinctive features. Firstly, random modifications (either

from a population of possible solutions or around the

neighbourhood of current solutions) are involved in deriving

the approximated optimal solution. Secondly, heuristics are

applied specifically on the solution space based on a belief

of the topology of the space, as opposed to applying domain-

specific heuristics. Because of the domain independence,

metahueristics have been successfully applied to solve many

different types of difficult optimization problems. These

works have been described and compared in [1], [2], [3],

[4], [5], laying ground for more advanced applications and

performance improvements.

A significant development is the parallelization of meta-

heuristics. Parallelization approaches have been broadly

classified according to the nature of (i.e. same or differ-

ent) initial solutions and parallel search strategies [6], [7].

Although different initial solutions add complexity to the

algorithm, the latter has been motivated by performance im-

provements. For example, initiating searches from different

points avoid being trapped in local optimal solutions [8],

and decomposing the data into smaller sets can improve

the speed of convergence (assuming that decomposition

is possible in the first place). The use of different initial

solutions, search strategies, and random modifications give

rise to potentially very different intermediate solutions. For

this reason, cooperative methods, where parallel searches ex-

change intermediate results, have been applied with notable

success.

Another exciting development is hybridizing metaheuris-

tics. Hybridization is a combination of (typically two) meta-

heuristics to leverage on their respective strengths [9], [10].

A popular hybrid is applying tabu search [11], for example

with simulated annealing [12], or ant colony searches [13].

The tabu search method avoids repeated searches by keeping

track of past searches, which we term solution trace. The use

of solution traces is not unique to the tabu search method,

traces are also commonly used to assess the convergence

of problems visually. For problems involving large datasets,

generating solution trace poses execution problems. For one,

the memory required to support such effort is very large, and

often insufficient. Furthermore, the communication between

parallel processes deployed on different compute nodes

is very high leading to network bottlenecks. As a result,

problems involving large datasets either require very long

execution times or are limited in terms of the extent of

performance analysis supported.

To our knowledge, the efficient handling of large datasets

generated by and shared between metaheuristics to improve

execution timing has not been studied. To address this

problem, we propose using a flow control workflow to

govern the execution of the metaheuristics without needing

to change the metaheuristics themselves. We incorporate two

workflow settings: (1) stop criterion to control the exchange

of intermediate results, and (2) clustering policy to control

the assignment of jobs onto compute nodes.

To assess the performance of the flow control workflow,

the Spares Management and Optimization (SMO) case study

is used. The SMO problem is a stochastic, integer program-

ming problem, which is a class of difficult optimization

problem. Since the pioneering work [14], [15], there has

been extensive work to include additional conditions and

2011 Workshops of International Conference on Advanced Information Networking and Applications

978-0-7695-4338-3/11 $26.00 © 2011 IEEE

DOI 10.1109/WAINA.2011.112

261

constraints into the model, such as emergency supplies [16],

service level agreements [17], [18], and pooling [19], [20].

Due to the nature of service levels (measured across all

parts) and pooling (applicable across all airports), it is not

possible to decompose data for SMO problems without

making scenario-specific assumptions. In this work, we

consider two SMO problem sizes involving 59 inventory

stocking locations with 10 and 60 parts, equating to 590

and 3540 decision variables respectively. We implement the

flow control workflow for parallel metaheuristics based on

Multiple Independent Runs (MIR) [21] executing parallel

search strategies and the cooperative exchange of results at

predefined intervals.

The rest of the paper is organized as follows: Section II

discusses related work. Section III explains the proposed

flow control workflow and its settings in terms of stop

criterion and clustering policy, Section IV describes the

implementation of SMO as a case study to apply the

flow control workflow for parallel metaheuristics, Section V

presents and analyzes the results from the SMO case study,

and Section VI concludes and describes future work.

II. RELATED WORK

To our knowledge, there is no previous work that proposes

using a flow control workflow to efficiently handle the

large datasets generated by and shared between parallel

metaheuristics in order to satisfy the memory constraint

and improve execution timing. A number of frameworks

have been proposed for executing parallel evolutionary algo-

rithms, such as DREAM [22] and Distributed BEAGLE [23].

DREAM only implements the cooperative island model us-

ing threads and sockets, while Distributed BEAGLE enables

the MasterSlave parallel evaluation of the population model

and the synchronous migration-based island model. There

are other more advanced frameworks that can execute not

only parallel evolutionary algorithms, but also parallel local

searches. For instance, MALLBA [24] and ParadisEO [25]

supports different hybridization mechanisms in addition to

the two previous models.

III. FLOW CONTROL WORKFLOW FOR PARALLEL

METAHEURISTICS

Figure 1 shows how a metaheuristic algorithm can be

implemented as a flow control workflow. Instead of pro-

cessing the entire sequence of computations at once in the

metaheuristic algorithm, an alternative strategy is to break

down the computations into chunks (which we term states)

and describe the computations as a workflow comprising

multiple 𝑛 states. The output solution 𝑂𝑘−1 of each state

𝑆𝑘−1 is used as the initial solution for the next state 𝑆𝑘.

The optimal solution is the output 𝑂𝑛 of the last state 𝑆𝑛.

To speed up the search, the metaheuristic algorithm

can be parallelized, deploying Multiple Independent Runs

(MIR) [21] in each state to generate different randomized

S1 S2 S3 Sk SnO1 O2 OnO3 Ok-1 Ok On-1

DistributeInitial Solution

MIRka

MIRkb AggregateResults

MIRkx

Figure 1. Implementing a metaheuristic algorithm as a flow controlworkflow comprising 𝑛 states with Multiple Independent Runs (MIR) ineach state

results simultaneously. With a single processor, MIR can

only be executed as multiple threads. With multiple pro-

cessors, MIR can be executed as multiple jobs with each

of them running independently on a single processor. In

both cases, data is generated by MIR and communicated

during distribution/aggregation. The initial solution of a state

is first distributed as inputs to each of its MIR before their

execution. The output solution of the state is then aggregated

after the completion of all its MIR. Hence, the cooperative

search process is established by the parallel MIR of search

strategies through the exchange of intermediate results at

predefined intervals between states.

A. Stop Criterion

As the stop criterion to limit the optimization process

within each MIR, we define a fixed number of iterations

based on the number of solutions visited by the metaheuristic

algorithm. Since a smaller number of iterations generates a

smaller amount of data, the stop criterion is able to control

the exchange of intermediate results by limiting the amount

of data cached and exchanged. However, the stop criterion

also determines the precision of the optimization in terms of

the quality of the solutions reached. Therefore, it is essential

to ensure that a smaller number of iterations for the stop

criterion does not cause extremely poor solution quality even

though it is able to reduce the amount of data. This issue

is resolved by increasing the number of states in the flow

control workflow. For the same stop criterion, a flow control

workflow comprising a larger number of states will achieve

a higher precision of the overall optimization with better

solution quality as compared to a workflow comprising a

smaller number of states.

B. Clustering Policy

Figure 2 shows three different clustering policies for a

flow control workflow comprising 3 states with 2 MIR.

Depending on the type of clustering policy (Workflow, State,

or Job), the total execution time of a job includes the time

to complete the job itself (as the entire workflow, a state,

or a MIR respectively), the time to distribute the jobs to

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TaTd

S3

MIR3aMIR3b

S2S1

MIR1aMIR1b

MIR2aMIR2b

S3

MIR3aMIR3b

S2S1

MIR1aMIR1b

MIR2aMIR2b

P2P1

Time

entire workflowP2P1

Time

P2P1

Time

S3

MIR3aMIR3b

S2S1

MIR1aMIR1b

MIR2aMIR2b

Processor

Processor

Processor

Job Clustering Policy: Executes each MIR in a state as a single job

State Clustering Policy: Executes each state of the entire workflow as a single job

Workflow Clustering Policy: Executes the entire workflow as a single job

Td TaS1 Td TaS2 Td TaS3

TaTa

MIR1aMIR1b

TdTd

TaTa

MIR2aMIR2b

TdTd

TaTa

MIR3aMIR3b

TdTd

Figure 2. Clustering policy at the level of Workflow, State, or Job

the processors (𝑇𝑑), and the time to aggregate results from

them (𝑇𝑎). The first policy called Workflow executes the

entire workflow (with many states) as a single job on a

single processor. The second policy called State executes

each state of the entire workflow as a single job on a single

processor. The third policy called Job executes each MIR

of a state as a single job on a single processor. In this

way, the Job clustering policy is able to execute the parallel

metaheuristic with the smallest problem size on a single

processor, followed by State with a larger problem size and

Workflow with the largest problem size.

IV. CASE STUDY: IMPLEMENTATION OF SMO

As a case study for handling large datasets in parallel

metaheuristics, we have implemented the middleware to

manage the parallel processing of SMO problems over a

cluster of desktops. Designed based on a Service-Oriented

Architecture (SOA) [26], the entire system consists of three

tiers: (1) Application, (2) Middleware, and (3) Resource.

The Application tier contains an analysis service for

users to perform high-level business analysis of optimization

problems. The Middleware tier consists of three services: (1)

Optimization Service which configures domain-specific op-

timization requirements, (2) Workflow Management (WM)

Service which monitors the execution progress of the flow

control workflow, and (3) Job Management (JM) Service

which is a wrapper to Torque Resource Manager [27] and

interacts via the RESTful web service [28]. We use an

Optimization Service for SMO as a case study. Our generic

system architecture can support many types of Optimization

Service specific to different optimization problems. The

Resource tier comprises a compute cluster with a head node

and multiple compute nodes to execute the optimization

problems. The cluster uses Linux NFS [29] for shared stor-

age and Torque Resource Manager for executing jobs across

multiple nodes. Torque provides control over distributed

compute nodes and batch jobs, thus enabling more efficient

resource management of the cluster.

The complete end-to-end system flow is incorporated

between Analysis Service and JM Service via Web API.

The system flow begins with Analysis Service initiating an

optimization request and ends with it receiving the results of

the optimization. Optimization Service creates the flow con-

trol workflow for the optimization problem to be executed.

When the flow control workflow is started, WM Service

submits workflow tasks to JM Service based on the selected

clustering policy (Workflow, State, or Job). It also uploads

the optimization program (e.g. SMO program in Java) and

initial solution data (e.g. SMO data in XML) to JM Service.

JM Service acts as an interface for the user to execute jobs

to the cluster. It provides a job submission interface that

supports all the three different types of clustering policy. It

also provides a job cancellation interface so that submitted

jobs can be cancelled if they have not started or completed.

The Torque Executor at each compute node sends the latest

status updates of job execution to JM Service, which in turn

notifies WM Service of any workflow task completion. In

particular, for Job clustering policy, JM Service will wait

for all the jobs constituting the MIR of a state to complete

before notifying WM Service.

V. EXPERIMENTAL RESULTS

We evaluate the performance of the flow control workflow

by using SMO as a case study to understand the effect

of stop criterion and clustering policy on handling large

datasets in MIR-based parallel metaheuristics. Table I lists

the SMO, flow control workflow, and environment configu-

rations for our experimental setup. We use the stop criterion

of 44000 iterations and Workflow clustering policy as the

base case for the comparison of results.

The complexity of SMO problems mainly depends on

two factors: (1) the number of parts, and (2) the number of

inventory stocking locations. We consider two SMO problem

sizes involving 59 inventory stocking locations with 10

and 60 parts, equating to 590 and 3540 decision variables

respectively. We also consider 7 cases of service levels. A

service level specifies two details: (1) the time deadline in

which the requested spare parts have to been delivered to the

required locations, and (2) the number of airport locations

that needs to be delivered to. For example, “24 hrs KUL

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Table IEXPERIMENTAL SETUP

Settings Parameter ValueSMO Decision 1) 590 (10 Parts × 59 Locations)

Variables 2) 3540 (60 Parts × 59 Locations)Service 1) 1 hr KULLevels 2) 1 hr KUL BKK

3) 4 hrs KUL BKK4) 24 hrs KUL BKK5) 1 hr KUL BKK CGK HKG SIN6) 4 hrs KUL BKK CGK HKG SIN7) 24 hrs KUL BKK CGK HKG SIN

Flow MIR 1) 2Control 2) 4Workflow Iterations for 1) 44000

Stop Criterion 2) 116000Clustering 1) WorkflowPolicies 2) State

3) JobExecution Systems 1) IBM (IBM ThinkStation D20Environment multi-core workstation with

32GB of memory and16 Intel Xeon E5520 2.26GHzprocessors)

2) DELL (Cluster of Dell OptiPlex360 desktops with each node having4GB of memory and2 Intel Duo E8400 3.0GHzprocessors)

BKK CGK HKG SIN” means that the spare parts have to be

delivered within 24 hours to all 5 airport locations of Kuala

Lumpur, Bangkok, Jakarta, Hong Kong, and Singapore.

We consider two execution environments: (1) IBM

(2.26GHz, 32GB) which is less memory-constrained, and (2)

DELL (3.0GHz, 4GB) which is more memory-constrained.

We use three metrics to measure the performance: (1) solu-

tion quality, (2) memory utilization, and (3) execution time.

We calculate average values of these three metrics based on

the 7 service levels since their results are about the same

and thus deriving average values for them are sufficient. To

facilitate easier comparison across these various metrics, the

average values are then normalized to standardized values

between 0 and 1.

A. Effect of Stop Criterion

We first examine the effect of stop criterion on the flow

control workflow to limit the amount of data cached and

exchanged by executing not more than 44000 and 116000

iterations on the IBM multi-core workstation with 2.26GHz

of processor speed and 32GB of memory.

The memory utilization increases with more MIR and

decision variables (Figure 3(a)) as they generate a larger

amount of data that has to be stored in the memory. This

increasing memory utilization in turn requires increasing

execution time (Figure 3(b)). Hence, memory availability

is a critical factor to enable the faster execution of parallel

metaheuristics based on MIR and cooperative search algo-

rithms, in particular with more MIR and decision variables.

0

0.2

0.4

0.6

0.8

1

3540Var4MIR

3540Var2MIR

590Var4MIR

590Var2MIR

Norm

aliz

ed A

vg. M

em

ory

Utiliz

ation

Number of Decision Variables and MIR

44kIter 116kIter

(a) Stop Criterion: Memory Utilization

0

0.2

0.4

0.6

0.8

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3540Var4MIR

3540Var2MIR

590Var4MIR

590Var2MIR

Norm

aliz

ed A

vg. E

xecution T

ime

Number of Decision Variables and MIR

44kIter 116kIter

(b) Stop Criterion: Execution Time

Figure 3. Effect of stop criterion on IBM (2.26GHz, 32GB)

However, the stop criterion is able to limit the exchange

of data with a smaller number of iterations to reduce the

execution time of the entire workflow. Figure 3(a) shows

the memory utilization of 44000 iterations only increases

by 10% as compared to 116000 iterations which increases

by 93%. Likewise, Figure 3(b) shows the execution time of

44000 iterations only increases by 6% instead of 91% for

116000 iterations.

B. Effect of Clustering Policy

We now analyze the effect of clustering policy (described

in Section III-B) on the flow control to understand how

the performance of MIR-based parallel metaheuristics is

improved by controlling the assignment of parallel jobs

onto compute nodes. We run this experiment using 44000

iterations in the more memory-constrained DELL cluster so

as to more effectively highlight the significance of memory

constraint.

Figure 4(a) shows the Job clustering policy maintains the

264

0

0.2

0.4

0.6

0.8

1

3540Var4MIR

3540Var2MIR

590Var4MIR

590Var2MIR

Norm

aliz

ed A

vg. M

em

ory

Utiliz

ation

Number of Decision Variables and MIR

Workflow State Job

(a) Clustering Policy: Memory Utilization

0

0.2

0.4

0.6

0.8

1

3540Var4MIR

3540Var2MIR

590Var4MIR

590Var2MIR

Norm

aliz

ed A

vg. E

xecution T

ime

Number of Decision Variables and MIR

Workflow State Job

(b) Clustering Policy: Execution Time

Figure 4. Effect of clustering policy on DELL (3.0GHz, 4GB)

lowest memory usage even as the problem size increases

with more MIR and decision variables. The Job clustering

policy only incurs 6% more (from 590 variables with 2 MIR

to 3540 variables with 4 MIR), whereas Workflow and State

incur 65% and 66% more respectively. Hence, instead of

using the Workflow clustering policy to execute the entire

workflow as it is in a more memory-constrained execution

environment, the Job clustering policy is a better alternative

than State to improve the performance of MIR-based parallel

metaheuristics. This shows that the Job clustering policy

is able to effectively reduce the memory utilization by

executing MIR on multiple processors simultaneously as

compared to both Workflow and State which only execute

MIR in parallel on a single processor.

However, Figure 4(b) shows the Job clustering policy

requires more execution time than Workflow (except for 590

variables with 4 MIR) as the problem size increases. This

is because the time taken to distribute and aggregate data

across multiple processors negates the time improvements

achieved from the lower memory utilization. This highlights

the trade-off between memory utilization (space constraint)

and execution time (time constraint), in which the impact

is greater for larger datasets due to the bigger problem size

making it inefficient for data to be distributed.

VI. CONCLUSION

This paper investigates whether large datasets generated

by and shared between parallel metaheuristics can be ef-

ficiently handled by using flow control workflow for ex-

ecution. Through the actual implementation of a Spares

Management and Optimization (SMO) case study for the

logistics industry, we are able to understand the performance

impact of setting two configuration parameters appropri-

ately: (a) stop criterion to control the exchange of data, and

(b) clustering policy to control the execution process onto

compute nodes.

Experimental results show that memory availability is

a key factor for improving the performance of parallel

metaheuristics involving Multiple Independent Runs (MIR)

and cooperative search algorithms. Using a smaller number

of iterations for the stop criterion of a metaheuristic reduces

the amount of memory utilized and the execution time. The

memory utilization can also be reduced by using Job cluster-

ing policy in two situations, in particular with more MIR: (1)

a more memory-constrained execution environment, such as

a cluster of desktops, and (2) a larger number of iterations is

required for the stop criterion of the metaheuristic. However,

the improvement in execution time is dependent on the

problem size. For bigger problem sizes (with larger datasets),

the time taken to distribute and aggregate data in the cluster

negates the time improvements achieved from lower mem-

ory utilization. In such cases, Workflow clustering policy

achieves lower execution time than Job clustering policy by

executing the entire workflow without any communication

overheads between parallel MIR of each state deployed on

different compute nodes.

Our future work will focus on more intelligent optimiza-

tion of parallel metaheuristics, such as self-configuring the

stop criterion depending on the progress of the optimization.

We will also conduct the performance analysis of paral-

lel metaheuristics in a multi-user execution environment,

whereby resource contention can be an issue. For instance,

using the Job clustering policy, the execution of the flow

control workflow belonging to one user may be delayed due

to waiting for the jobs of other users to be completed first.

Hence, an effective scheduling mechanism is essential to

resolve this issue.

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