AN ASSESSMENT OF HEURISTICS FOR FAST SCHEDULING OF

GRID JOBS

Florian M¨oser, Wolfgang S¨uß, Wilfried Jakob, Alexander Quinte and Karl-Uwe Stucky

Institute for Applied Computer Science, Karlsruhe Institute of Technology, P.O. Box 3640, D-76021, Karlsruhe, Germany

Keywords:

Scheduling, Benchmarks, Heuristics, Computational grid, Restricted resources.

Abstract:

Due to the dynamic nature of the grid and the frequent arrival of new jobs, rescheduling of already planned

and new jobs is a permanent process that is in need of good and fast planning algorithms. This paper extends

previous work and deals with newly implemented heuristics for our Global Optimizing Resource Broker and

Allocator GORBA. Of a range of possibly usable heuristics, the most promising ones have been chosen for

implementation and evaluation. They serve for the following two purposes: Firstly, the heuristics are used to

quickly generate feasible schedules. Secondly, these schedules go into the start population of a subsequent run

of our Evolutionary Algorithm incorporated in GORBA for improvement. The effect of the selected heuristics

is compared to our best simple one used in the ﬁrst version of GORBA. The investigation is based on two

synthetically generated benchmarks representing a load of 300 grid jobs each.

A formal deﬁnition of the scheduling problem is given together with an assessment of its complexity. The

results of the evaluation underline the described intricacy of the problem, because none of the heuristics

performs better than our simple one, although they work well on other presumably easier problems.

1 INTRODUCTION

Planning of jobs and resources of a computational

grid is a complex optimization task, if the interests

of both resource providers and users are taken into

account and the resources are modeled with the nec-

essary detail. This will be described in the second

section, where a formal deﬁnition of the problem will

be given as well. In this paper we report about an

investigation of four heuristics which have been se-

lected out of seven well-known ones. They are com-

pared to the best simple method used in our Global

Optimizing Resource Broker and Allocator GORBA

(S¨uß et al., 2007; Jakob et al., 2008; Jakob et al.,

2009). GORBA pursues a two-step planning and op-

timization strategy: after a fast heuristic construc-

tion of feasible, but suboptimal schedules, the latter

are improved by our Evolutionary Algorithm (EA)

GLEAM (Global Learning Evolutionary Algorithm

and Method) (Blume, 1991; Blume and Jakob, 2009).

The motivation was to ﬁnd better heuristics so that

either the subsequent EA run gets a better start pop-

ulation or becomes superﬂuous. GLEAM is an EA

of its own, which includes elements from traditional

Evolution Strategies and real-coded Genetic Algo-

rithms. Here it is used to determine the processing

sequence of the grid jobs and to choose a resource se-

lection strategy out of three possible ones. The latter

are described in section 3.2.2. Usage of a heuristic

resource allocation has proven to yield good results

faster than a gene model, where both resources and

grid job sequence are determined by evolution (Jakob

et al., 2008).

In section 3 the choice of the heuristics is ex-

plained and the heuristics are described in more de-

tail. Section 4 reports about the results and the bench-

marks used. The work is summarized and an outlook

is presented in section 5.

As we concentrate on the investigation of four

different scheduling heuristics here, the benchmarks,

GORBA, and GLEAM are described only very brieﬂy

due to the lack of space. The interested reader is re-

ferred to (S¨uß et al., 2007) for a detailed description

and explanation of the benchmark construction and to

(Jakob et al., 2008; Jakob et al., 2009) for GORBA,

where a survey of related work is also given, espe-

cially of EA-based scheduling in the grid domain. An

up-to-date description of GLEAM can be found in

(Blume and Jakob, 2002) and in (Blume and Jakob,

2009), where the algorithm is described in detail and

various real-world applications are introduced.

184

Möeser F., Süß W., Jakob W., Quinte A. and Stucky K. (2010).

AN ASSESSMENT OF HEURISTICS FOR FAST SCHEDULING OF GRID JOBS.

In Proceedings of the 5th International Conference on Software and Data Technologies, pages 184-191

DOI: 10.5220/0002919201840191

 SciTePress

2 PROBLEM DEFINITION

The users of a grid describe their application jobs,

consisting of one or more elementary grid jobs, by

workﬂows, each of which may be regarded a directed

acyclic graph deﬁning precedence rules between the

grid jobs. The users state which resources like soft-

ware, data storage, or computing power are needed

to fulﬁll their grid jobs. Resources may depend on

other ones. A software tool, for instance, may require

a certain operating system and appropriate computer

hardware to run on. This leads to the concept of co-

allocation of resources. Furthermore, users specify

due dates and cost budgets and may express a pref-

erence for cheap or fast execution. The execution

times of the grid jobs, which are necessary for plan-

ning, are either estimations or values based on experi-

ence. Resources are offered at variable costs depend-

ing on e.g. day time or day of the week and their

usage may be restricted to certain times according to

the policy of their owners. In addition, heterogeneous

resources usually differ in performance as well as in

cost-performance ratios.

To meet the different needs of resource users and

providers, the following four objectives are consid-

ered: completion time and costs of each application

job, measured and averaged as fulﬁllment of user-

given limits, and to meet the demands of resource

providers, the total makespan of all application jobs

and the ratio of resource utilization. Some of these

criteria, like costs and time, are obviously conﬂicting.

As grid jobs are assumed to require computing

time in the magnitude of several minutes at the mini-

mum, a certain but limited time frame for planning is

available. A time limit of three minutes was regarded

reasonable for planning. Changing an existing plan is

the usual situation, because e.g. new application jobs

or resources enter the system more or less frequently.

All grid jobs that will be started within this time slot

according to the old schedule are regarded ﬁxed jobs

and will not be subject of (re)scheduling (Jakob et al.,

2009).

A notation common to the scheduling literature

(Brucker, 2004; Brucker, 2006) is used to facilitate

comparisons with other scheduling problems. Given

are a set M of resources, a set J of application jobs,

and a set O of grid jobs. The n grid jobs of appli-

cation job J

are denoted O

,...,O

. The following

functions are given:

• a precedence function p : O × O → { TRUE,

FALSE} for the grid jobs

• an assignment function µ : O → P (P (M)) from

grid jobs to resource sets. P (M) is the power set

of M. µ

is the set of all possible combinations

of resources from M, which together are able to

perform the grid job O

• a function t : O× P (M) → R, which describes the

time needed to process each grid job O

on a re-

source set R

∈ µ

• a cost function, c : R × P (M) → R, which de-

scribes the cost per time unit of the given resource

set for each time z ∈ R

Optimization is done by choosing suitable start times

s(O

) ∈ R and resource allocations R

∈ µ

. A valid

solution must meet the following two restrictions:

1. All grid jobs are planned and resources are allo-

cated exclusively:

∀ O

: ∃ s(O

) ∈ R,R

∈ µ

: ∀M

∈ R

is in[s(O

);s(O

) +t(O

)] exclusively

allocated by O

2. Precedence relations are adhered to:

∀ i, j 6= k : p(O

) ⇒

s(O

) ≥ s(O

) + t(O

)

A violation of the two following soft constraints is

treated by penalty functions such that the amount of

time and cost overruns is considered as well as the

number of application jobs affected.

1. All application jobs J

have a cost limit c

, which

must be observed:

∀ i : c

≥

∑

j=1

s(O

) + t(O

)

s(O

)

c(z,R

) dz

2. All application jobs J

have due dates d

, which

must be adhered to:

∀ i : d

≥ s(O

) + t(O

)

where O

is the last grid job of J

The ﬁtness calculation is based on the above-

mentioned four objectives and an auxiliary objective

described in (Jakob et al., 2008). Lower and upper

estimations of costs and processing times are calcu-

lated in the ﬁrst planning stage of GORBA described

in section 3. Except for the utilization rate the relative

value rv

of each criterion i is calculated based on its

actual value v

i,act

relative to these limits:

i,act

− v

i,min

i,max

− v

i,min

This makes the single values rv

independent of

the task on hand and results in a percentage-like

range. These values are weighted and summed up

AN ASSESSMENT OF HEURISTICS FOR FAST SCHEDULING OF GRID JOBS

185

which yields the raw ﬁtness, again in a percentage-

like range. Due to the nature of the problem, values

of 100% or close to 100% are unlikely for nontrivial

cases. Values greater than 50% can usually be consid-

ered good results. To avoid unwanted compensation

effects, the criteria are sorted separately or in groups

according to priorities. The criteria of the highest pri-

ority always contribute to the sum, whereas the oth-

ers are added, if all criteria of the next higher priority

fulﬁll a given threshold value. Weights and priorities

are based on experience and aimed at reaching a fair

compromise between users and resource providers. If

the two soft constraints are violated, the raw ﬁtness is

lowered to the end ﬁtness by a multiplication by the

corresponding penalty function, each of which deliv-

ers a factor between 0 and 1. Otherwise, end and raw

ﬁtness are identical.

Generalizing, this task contains a special case of

the job shop scheduling problem. The extensions

are co-allocation of heterogeneous and alternative re-

sources of different performances and time-dependent

availability and costs, earliest start times and due

dates, parallel execution of grid jobs, and multiple ob-

jectives. As our task includes the job shop problem,

it is NP-complete. For this reason and because of the

three minutes runtime limit, only approximated solu-

tions can be expected.

A comparable problem could not be found in liter-

ature, see e.g. (Brucker, 2004; Brucker, 2006) whith a

comprehensive presentation of scheduling problems.

This corresponds to the results of the literature review

found in (Set¨amaa-K¨arkk¨ainen et al., 2006). There, it

is concluded that only few publications deal with mul-

tiple objectives in scheduling and, if so, they mostly

deal with single machine problems.

3 HEURISTICS

In order to ﬁnd better heuristics than the currently

used ones, a literature study was performed (M¨oser,

2009). In this study a number of heuristics were con-

sidered and some of them were selected for further

investigation.

3.1 Considered Heuristics

There are currently four heuristics available in

GORBA. These are three simple heuristics (S¨uß et al.,

2007) and an adaptation of the Gifﬂer Thompson Al-

gorithm (GTA) (Gifﬂer and Thompson, 1960; Neu-

mann and Morlock, 2002). To our surprise, the

adapted version of the GTA neither yielded better re-

sults than our best simple heuristic method, nor were

the results appropriate seeds for the subsequent EA

run (Jakob et al., 2008; Sonnleithner, 2008). The best

simple heuristic is the Shortest Due Date Heuristic

(SDD) described in section 3.2.2. As the two others

yield only poor results as well, other heuristics were

searched for in a subsequent investigation (M¨oser,

2009). They were evaluated in order to select some

of them for implementation and further investigation.

The methods were assessed according to statements

from literature. The criteria were problem coverage,

reliability, adaptability with respect to the problem on

hand, speed, quality of results, and possible value for

GLEAM. The considered heuristics are appropriate

variants of the following ones, of which the ﬁrst four

met the criteria for further investigation:

• List Scheduling

• Shifting Bottleneck

• Taboo Search

• GRASP

• Branch & Bound

• Lagrange Relaxation and Neural Networks

• Simulated Annealing

3.2 Investigated Heuristics

The implemented versions of the heuristics List

Scheduling, Shifting Bottleneck, Taboo Search and

GRASP (Greedy Randomized Adaptive Search Pro-

cedure) will be introduced brieﬂy hereinafter. They

all assign resources to grid jobs and use selection

strategies for scheduling, which are presented ﬁrst.

Also, a short description is given for the SDD which

presently is the best performing heuristic in GORBA

and hence serves as a reference for assessing the four

new scheduling heuristics.

3.2.1 Selection Strategies

Several selection strategies which can be divided into

grid job selection strategies (JSS) and resource selec-

tion strategies (RSS) are used. If it is not clear which

grid job should be scheduled next, one of these JSS

is applied, if not stated otherwise. The implemented

strategies select a grid job according to the following

rules:

• ShortestJob: grid job with the shortest duration

• LongestJob: grid job with the longest duration

• MostSuccessors: grid job with the greatest num-

bers of successors

• EarliestStart: grid job with the earliest possible

start time

ICSOFT 2010 - 5th International Conference on Software and Data Technologies

186

• LeastRemainingTime: grid job where the differ-

ence between the maximal end time of the corre-

sponding application job and the earliest possible

start time of that grid job is minimal

Selecting a resource for a grid job works similarly.

The implemented strategies select a resource accord-

ing to the following rules:

• Cheapest: fastest one of all cheapest resources

• Fastest: cheapest one of all fastest resources

• Pref: “Cheapest” or “Fastest”, depending on the

user’s preference stored in the application job

• EarliestStart: earliest available resource

• MostRemaining: minimally used resource

3.2.2 Shortest Due Date Heuristic

This heuristic ﬁrst creates a grid job sequence by or-

dering the grid jobs of all application jobs by their

due dates, beginning with the application job to be

ﬁnished ﬁrst. The resulting job sequence is processed

by one of three resource allocation strategies (RAS).

The different RAS assign resources to grid jobs ac-

cording to the following rules:

• RAS-1: fastest one of the earliest available re-

sources

• RAS-2: cheapest one of the earliest available re-

sources

• RAS-3: RAS-1 or RAS-2, depending on time/cost

preference of the application job

SDD yields three solutions each of which goes into

the initial population of the subsequent GLEAM run.

The best, of course, is regarded as the preliminary re-

sult which should be improved by GLEAM or with

which the new heuristics are compared.

3.2.3 List Scheduling

List Scheduling (LS) is a simple heuristic that creates

a schedule by ﬁrst putting all grid jobs into a list as

described below and afterwards assigning resources

to the grid jobs. It is an adaptation of the ideas out-

lined in (Schuster, 2003). The RSS used is a strategy

parameter of this procedure. List Scheduling is deter-

ministic and consists of the following steps:

1. Creation of the list

First, all grid jobs are put into a list by using a

path-based approach. From all application jobs,

all possible paths are built from the ﬁrst to the last

grid jobs. As a result, grid jobs are contained in

various paths, if the application job has parallel

branches. Then, all paths are processed iteratively

and for each path the ﬁrst grid job is removed (it

is also removed from all other paths containing

that grid job). The removed grid job is added to

the list. This is done until all paths are empty.

The list now contains the resulting grid job se-

quence. This method maintains the precedence

rules of grid jobs.

2. Scheduling of the list

Finally, the resulting schedule is built by choosing

a resource and a time slot for every grid job using

the given RSS.

3.2.4 Shifting Bottleneck

Variants of Shifting Bottleneck (SB) for job shop

scheduling are described for example in (Adams et al.,

1988), in (Dauz`ere-P´er`es and Lasserre, 1993), and

for parallel resources in (Chen et al., 2006). Unfor-

tunately, none of them deals with inhomogeneous re-

sources, which is why another approach must be used.

The implemented version builds resource groups with

associated grid jobs and schedules the grid jobs using

the resources of the respective group only. The result-

ing schedules are ordered by a bottleneck criterion as

described below. Using the results of these schedules,

the ﬁnal schedule is created and returned. An RSS is

used as a strategy parameter. SB is deterministic and

comprises the following steps:

1. Creation of resource groups

Each grid job has one ore more usable resources.

For each grid job a resource group consisting of

these resources is built. If a group that is going

to be created contains exactly the resources of an

already existing one, a reference to that group will

be established instead of creating a new one. If a

resource group is built, which contains only some

resources overlapping with resources from other

resource groups, the overlapping resource will be

removed from the group with more resources or,

if two groups have the same number of resources,

from the newer one. In case a resource group is

emptied, it is removed and the corresponding grid

jobs are associated with the remaining group. Af-

ter this step, each resource group contains at least

one resource and at least one associated grid job.

2. Scheduling of resource groups

In the next step the grid jobs of each resource

group are scheduled using the resources of the

respective resource group only. The scheduling

order of grid jobs is given by the order in which

they were added to the group and the resource for

a grid job is chosen by the given RSS. When all

grid jobs of a resource group have been processed,

they have a temporary start time which will be

AN ASSESSMENT OF HEURISTICS FOR FAST SCHEDULING OF GRID JOBS

187

used later as an order criterion. The total lateness

(or earliness) of each resource group is calculated

and the groups are ordered from biggest lateness

to biggest earliness.

3. Creating the ﬁnal schedule

Finally, all grid jobs are scheduled again, this

time using all available resources. The order of

scheduling the grid jobs is given ﬁrstly by the or-

der of resource groupsand secondly by the tempo-

rary start times of their grid jobs, beginning from

the earliest start time. This means that all grid jobs

belongingto the ﬁrst resource group are scheduled

before those of the second resource group and so

on. Thus, bigger bottlenecks have more “schedul-

ing freedom”, whereas smaller bottlenecks have

less freedom due to already allocated resources

and time slots. Precedence rules are adhered to.

The given RSS is used to select one resource for

each grid job.

3.2.5 Taboo Search

Taboo Search (TS) is a heuristic with random ele-

ments. It creates a schedule in x steps, where x is

the number of grid jobs to be scheduled. There is a

JSS and an RSS for each step. These chains of strate-

gies are used as the representation of a solution. This

approach yields a feasible schedule for each solution

and was originally presented by (Baykaso˘glu et al.,

2002). Another approach is to use the grid job se-

quence as the representation, as done in GLEAM. To

change a solution, the JSS and/or RSS are exchanged

as described below. Various solutions are declared

“taboo” during the process, as common with TS. They

may be used further in special cases only. They are

stored in a taboo list which is a First-In-First-Out list

of a speciﬁc size. Taboo search performs a number

of iterations, creating solutions in each iteration. The

currently best solution is always saved. The following

steps are conducted in the heuristic:

1. Setup

In this step, the taboo list size tl

size

, the number of

solutions per iteration tl

, the minimal number of

changes of JSS jc

min

and RSS rc

min

after each it-

eration and the likelihood l of accepting a change

are set. An initial solution is created by choos-

ing a random JSS and RSS from the pool for each

step. The schedule for this solution is computed

and evaluated.

2. Updating solutions

Starting from the initial solution, a number of it-

erations is performed. In each iteration tl

so-

lutions are created by exchanging strategy rules

from the initial solution with randomly chosen

ones from a pool. The number of changes depends

on jc

min

and rc

min

respectively. The parameters

min

, rc

min

, and l are adapted during the process

such that the chance of a change is increased with

the number of unsuccessful iterations (i.e. an it-

eration that did not improve the currently best so-

lution). If there is a successful iteration, the three

parameters will be reset to their original values.

In each iteration the schedules for the solutions

are created by choosing one of the grid jobs that

have no unscheduled predecessor by the current

JSS and by selecting a resource for the chosen grid

job by the current RSS. The resulting schedule is

evaluated using the criteria of cost and makespan

only. A solution is better than another one, if its

schedule is better than that of the other. The so-

lutions that are worse than the initial one are put

into the taboo list. The Pareto optimal solutions

from that list are aspirants. The best non-taboo

solution is chosen as the new initial one. If no

non-taboo solution exists, the best aspirant is cho-

sen instead. If the new initial solution is better

than the currently best one, the latter is updated.

If a given number of iterations or a given amount

of time has passed, the schedule of the currently

best solution is returned as the ﬁnal result.

3.2.6 GRASP

The main idea of GRASP presented in (Pitsoulis and

Resende, 2001) has been adapted to the task on hand.

The adapted implementation makes use of the same

solution representation as taboo search. To create a

schedule for a solution, x steps are needed, where x is

the total number of grid jobs. Although the represen-

tation is the same, the resulting schedule is different,

because the methods of solution creation and schedul-

ing used in GRASP are different. An RCL (restricted

candidates list) is used to select grid jobs to be sched-

uled. GRASP is a multi-start heuristic, which means

that there are multiple independent iterations. In each

iteration one solution is produced. The currently best

solution is always saved. GRASP is stochastic and

consists of the following steps:

1. Setup

In this step the maximal size max and the tuning

parameter α for the RCL are set. A high value

of α means more random behavior, whereas a low

value means more greediness.

2. GRASP iterations

A number of GRASP iterations are performed.

After a given number of iterations or a given

amount of time has passed, the schedule of the

currently best solution is returned. Each iteration

ICSOFT 2010 - 5th International Conference on Software and Data Technologies

188

works as follows: A solution is created by choos-

ing x JSS and RSS at random from the pool of

selection strategies. Afterwards, a schedule is cre-

ated from that solution. At all times, a list of grid

jobs without predecessors exists. Let that list be

1st

. In each step, the RCL consists of the ﬁrst

max grid jobs from L

1st

. The RCL is ordered by

the criterion reﬂected by the current JSS. One of

the ﬁrst α% of the grid jobs in the RCL is selected

randomly and removed from L

1st

. All successors

of that grid job are added to L

1st

, if they do not

have any other predecessors that are still in that

list. The removed grid job is assigned a resource

using the current RSS. When L

1st

is empty, the

schedule was created and is evaluated. The cur-

rently best solution will be updated, if it is unde-

ﬁned or if the newly created one is better.

4 EXPERIMENTAL RESULTS

In order to compare the new heuristics with our SDD,

different benchmark tests have been performed. The

setup and the results of these benchmarks are pre-

sented below.

4.1 Benchmarks

The benchmarks used are created synthetically which

allows for controllable diversity, as opposed to most

benchmarks originating from real-world applications,

see also (S¨uß et al., 2007).

The characteristics of total number of application

jobs N, total number of grid jobs n, variation of grid

job number n

var

, average number of resources per

grid job R

avg

, variation of resource number R

var

, and

average degree of dependencies d ∈ [0.0, 1.0] are used

to categorize a benchmark scenario. There are N ap-

plication jobs to be scheduled in the scenario. Each

application job consists of an average of N/n grid

jobs. This number may vary by an amount of n

var

percent, but the total number of grid jobs is ﬁxed.

Each grid job has an average of R

avg

usable resources.

This number may vary by an amount of R

var

. The de-

gree of dependenciesd indicates the parallelism of the

workﬂow or how much the grid jobs depend on each

other. For d = 0.0 all grid jobs are parallel and for

d = 1.0 there is no parallelism at all. Table 1 shows

the parameters used to create the benchmarks sl300

and ll300. The ﬁrst letter denotes the freedom of re-

source selection, the second one the average degree of

dependencies. Both can either be s (small) or l(large).

A large degree of dependencies was chosen, because

Table 1: Parameters used for creating the benchmark sce-

narios.

PARAMETER sl300 ll300

Total no. of application jobs N 60 60

Total no. of grid jobs n 300 300

Variation of grid job no. n

var

0.3 0.3

Avg. res. no. per grid job R

avg

3 8

Variation of resource number R

var

1 2

Avg. degree of dependencies d 0.9 0.9

such benchmarks were the hardest ones in previous

investigations (Jakob et al., 2008; Jakob et al., 2009).

As in earlier experiments, time and cost budgets

were set such that our simple SDD heuristic could not

solve them. The following criteria were applied for

assessing the heuristics:

• Does the heuristic yield a schedule that adheres to

the budgets?

• How do the ﬁtness values compare to the each

other?

• Do the results improve the subsequent GLEAM

run?

4.2 Results of Heuristic Planning

The results of the heuristic planning step can be seen

in Figure 1 (raw ﬁtness) and Figure 2 (end ﬁtness).

Neither old nor the new heuristics yielded schedules

that adhered to all budgets for the given scenarios.

This is also evident from the ﬁtness values. Only SB

achieved a better raw ﬁtness than SDD, and only in

one of the two scenarios. However, the results of LS

and GRASP were also acceptable. TS did not perform

well, which had not been expected, because it had

performed much better for smaller scenarios. After

applying the penalty function, all of the new heuris-

tics dropped to a ﬁtness of below 1%, whereas SDD

maintained a ﬁtness of roughly 10%. The reason why

TS yields such bad results may be the representation

and the method for creating new children from a solu-

tion. A great part of it is changing selection rules ran-

domly, which favors smaller scenarios. In scenarios

with many grid jobs it is more likely that the exchange

of a certain percentage of rules will result in a child

that is inferior to the parent. Moreover, TS internally

works with a simpler evaluation as described before

and the comparison of the results is based on the more

comprehensive GLEAM evaluation. GRASP experi-

ences similar problems. However, it does not depend

on a single initial solution, but rather creates random-

ized ones in each iteration. This is beneﬁcial, because

new solutions do not inherit bad parts from a parent.

AN ASSESSMENT OF HEURISTICS FOR FAST SCHEDULING OF GRID JOBS

189

SDD

GRASP

fitness in %

sl300

ll300

Figure 1: Raw ﬁtness after the heuristic planning step.

The 95% conﬁdence intervals are shown for the stochastic

heuristics.

4.3 Results of GLEAM Runs

As GLEAM works stochastically, 100 runs were done

for each setting. The start populations are either plain

randomly seeded or a mixture of random seeds and

results from each heuristic. Start populations us-

ing heuristic outcomes must be completed by ran-

domly generated (poor) solutions, because there are

not enough results and, more important, there must

be a great variety to start with for the evolutionary

search. More or less homogeneous (start) populations

are the death of evolution. The comparisons are based

on the success rate and the averaged ﬁtness in con-

junction with 95% conﬁdence intervals. The success

rate of GLEAM optimization is measured by the per-

centage of penalty-free runs. A penalty-free run is a

run, where all application jobs have been scheduled

to meet their budget constraints.

SDD

GRASP

fitness in %

sl300

ll300

Figure 2: End ﬁtness after the heuristic planning step.

Population sizes from 120 to 300 have been tried

out, because the population size yielding the best

quality may differ for each scenario and heuristic used

for seeding.

The results are shown in Figure 3. If the initial

population was created with SDD, GLEAM achieved

a success rate of about 50% in either scenario within

the given time frame of three minutes. With both

the new heuristics and random initialization, GLEAM

only achieved a success rate between 0% and 2%.

Consequently, there was no improvement. A success-

ful run can be spoiled by exceeding cost or time lim-

its. For scenario ll300, the reason of unsuccessful runs

mainly was a violation of the time limit for all tested

heuristics. Only up to 10% of the runs were spoiled

by exceeding cost limits. For scenario sl300, the num-

ber of cost and time limit violations was about equal.

Even though violations could not always be removed

completely, the schedules produced by the heuristic

planning step were improved by GLEAM in all cases

by reducing the amount of violations and improving

raw ﬁtness.

SDD

GRASP

RAND

success rate in %

sl300

ll300

Figure 3: Success rate of the GLEAM optimization.

5 CONCLUSIONS

Although SDD is a very simple heuristic, it yields the

best results of all heuristics tested for the given bench-

marks. This conﬁrms previous investigations, where

similar results were found. The fact that SDD beats all

heuristics tested so far underlines its ability to solve

the given problem well. Although it is not perfect, the

results are by far the best ones obtained during all our

investigations.

It must also be noted that the current version of

GLEAM performs better with a good heuristic seed-

ing of the initial population than with pure random

initialization. Obviously, the raw ﬁtness from heuris-

tic planning is not at all related to the success of

GLEAM, the end ﬁtness turns out to be the decisive

factor. For scenarios of the given size (amount of jobs

and resources) it is essential for the initial population

to be as penalty-free as possible, which currently is

ICSOFT 2010 - 5th International Conference on Software and Data Technologies

190

achieved best by SDD. GLEAM cannot compensate

ﬂaws in the initial population within the runtime of

three minutes only.

The unexpected poor results of the new heuris-

tics are a motivation for us to change our focus to the

identiﬁcation of suited local searchers that can assist

GLEAM. They are intended to improve the offspring

of a mating of the Evolutionary Algorithm. This con-

cept of hybridization was applied successfully to op-

timization tasks from the continuous parameter do-

main, as reported by (Jakob, 2006).

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