ALLOCATING EDUCATIONAL RESOURCES THROUGH

HAPPINESS MAXIMIZATION AND TRADITIONAL

CSP APPROACH

Juan I. Cano

1,2

, Luis S´anchez

, David Camacho

, Estrella Pulido

and Eloy Anguiano

1,2

Computer Science Department

Centro de Referencia Linux UAM–IBM

Universidad Aut´onoma de Madrid, C/ Francisco Tom´as y Valiente, n

11, 28049, Madrid, Spain

Keywords:

Constraint-Satisfaction Problems, Simulation, Model-based agent optimization, Educational Resource Allo-

cation, Multiagent Resource Allocation.

Abstract:

An instance of an Educational Resources Allocation (ERA) problem is the distribution of a set of students

in different laboratories. This can be a complex and dynamic problem if non-quantitative considerations (i.e.

how close the ﬁnal allocation is to the student preferences or desires) are involved in the decision process. Tra-

ditionally, different approaches based on Constraint-Satisfaction techniques and Multi-agent negotiation have

been applied to the general problem of Resource Allocation. This paper shows how a Multi-agent approach

can be used to model and simulate the assignment of sets of students to several predeﬁned laboratories, by

using their preferences to guide the allocation process. This approach aims at ﬁnding new solutions that try

to satisfy individual student needs with no knowledge about the general allocation problem. The paper shows

some experimental results and a comparison, between a CSP-based solution modeled in CHOCO, a CSP

Java-based library, and a Multi-agent model implemented using MASON, a multi-agent simulation platform.

1 INTRODUCTION

Efﬁcient resource assignment, or resource allocation

(Choueiry, 1994), is a complex problem (usually NP-

hard) that has been studied in several research ar-

eas, such as Constraint-Satisfaction Problems (Modi

et al., 2001; Tsang, 1993), Artiﬁcial Intelligence and

Multi-Agent Systems (Chevaleyre et al., 2006; Das-

gupta and Hoeing, 2007; Winstanley, 1993). Impor-

tant application areas such as Industrial procurement,

Satellites, Manufacturing Systems, Grid computing,

Manpower planning/scheduling, or Educational man-

agement, have applied different Resource Allocation

techniques to solve their particular problems (Das-

gupta and Hoeing, 2007).

The main goal in a resource allocation process

is to ﬁnd either a feasible allocation, that is, some

kind of assignment over the resources elements con-

sidered; or an optimal allocation. In the latter case,

it is necessary to deﬁne some kind of metric to know

when the optimum is reached, for example an alloca-

tion of resources that maximizes the average utility of

several agents.

The concept of resource can vary over previous re-

search areas. In this work, a resource is deﬁned as a

set of non–sharable indivisible items that can be dis-

tributed amongst several agents. Therefore, a particu-

lar distribution of resources amongst agents is called

an allocation. For instance, in our case study we have

a set of laboratories that need to be assigned to a set

of student teams (made up of 1, 2 or more students).

Students could prefer different timetables to others,

and they can express their desires, or preferences, as

a restriction. An assignment, or simply an allocation,

is a distribution of the set of resources (laboratories)

amongst the agents (student teams).

The focus of this paper is to design a system based

on the real dynamics of student scheduling, that is

how students apply for laboratory slots and how they

interact (negotiate) with each other. This is done by

measuring the student happiness, which is modelled

as how far is the assignment from his preference,

and maximizing this value. The distribution of stu-

dents among groups is also taken into account, us-

ing this factor as a measure of how loaded is the re-

source. This model is compared with a traditional

CSP (monolithic) approach where each agent prefer-

ence is deﬁned as a new constraint. The MAS ap-

proach shows how easy it is to model the agent prefer-

ences (in form of preferred groups and non-assignable

113

Cano J., Sánchez L., Camacho D., Pulido E. and Anguiano E. (2009).

ALLOCATING EDUCATIONAL RESOURCES THROUGH HAPPINESS MAXIMIZATION AND TRADITIONAL CSP APPROACH.

In Proceedings of the 4th International Conference on Software and Data Technologies, pages 113-119

DOI: 10.5220/0002259601130119

 SciTePress

groups) and to look for a solution that tries to maxi-

mize their desires.

The paper is structured as follows: Section 2 de-

scribes the educational resources assignment prob-

lem and how it can be modelled as a constraint-based

problem and a MAS negotiation problem; Sections 3

and 4 describes the CSP library (CHOCO) and the

MAS platform (MASON) considered, and how the

model has been implemented in both frameworks.

Section 5 shows the data sets used in the experiments,

and the experimental results obtained. Finally, Sec-

tion 6 describes some conclusions and future lines of

work.

2 ALLOCATION OF

EDUCATIONAL RESOURCES

The problem of allocating educational resources can

be brieﬂy described as the process assigning resources

to actors in a solution, or solutions, which optimize

(or simply looks for a feasible solution) the avail-

able resources amongst those actors. For example,

and as a case study, we could consider the problem

of distributing students among different laboratories.

In this case, the amount of computers, or other ma-

terial, available in every laboratory sets the number

of student teams allowed per laboratory. The differ-

ence between these resources (laboratory slots) lies on

the number of places available and the slot timetable.

Educational resources are grouped into resource sets

and each student team must select their preferred lab-

oratory slot among those available in a resource set,

or even to indicate what slots are incompatible with

their needs. Preference will be represented by three

different values: “Preferred” (P), “Indifferent” (I) and

“Forbidden” (F). These values are not ﬁxed and can

be adapted to other needs. In addition to student re-

strictions, it could be necessary to use other assign-

ment policies (i.e. ﬁrst group to make a request has

the highest priority) to look for new alternatives. Fig-

ure 1 shows a schematic representation of this situa-

tion, where a student team has deﬁned its preferences

among three different lab slots corresponding to the

resource set RS1. ER1.1 is Preferred over ER1.2

that is Indifferent for this student team. As

the student team has indicated that ER1.3 should be

avoided in the allocation process, this group is stored

as Forbidden. This ﬁgure also represents the cur-

rent allocation state for each lab slot in the resource

set RS1.

As illustrated in Figure 2, the previous example

can be extended to a more realistic and, therefore,

complex situation, where two different types of con-

Figure 1: Current assignment for the resource set RS1

that contains three Educational Resources (ER1.1, ER1.2,

ER1.3). The agent provides a set of restrictions, or con-

straints, to describe its preferences (Preferred-P, Indifferent-

I, Forbidden-F).

straints can be established. Horizontal constraints ap-

pear between educational resources belonging to the

same educational set (solutions with lab slots with

overlapping timetables are not allowed). Vertical con-

straints relate educational resources in different ed-

ucational sets (this is a quite usual situation in en-

gineering where a student can register for courses

from different degree years). Why is it necessary

to distinguish between horizontal and vertical con-

straints? The educational institution is usually re-

sponsible of guaranteeing the satisfaction of horizon-

tal constraints. This is not the case with vertical con-

straints whose satisfaction is usually taken as a prob-

lem that must be solved by the student.

As Figure 2 shows the current needs of Student-

Agent, could be described as a set of constraint vec-

tors that need to be allocated. The ﬁnal solution pro-

posed by the algorithm will generate the “happiness”,

or how close the ﬁnal allocation is to the StudentA-

gent preferences.

Constraint vector: (hRS1 : {P, I};RS2 :

{P, I, F};RS3 : {F,P, F}i, hRS4 : {F, P};RS5 :

{P, I, F, I, F,I}i )

3 CONSTRAINT

SATISFACTION-BASED MODEL

Constraint Satisfaction and Constraint Programming

(Tsang, 1993) can be described as the process (in-

cluding techniques, methodologies and algorithms) of

ﬁnding a solution to a set of constraints that impose

conditions that a set of variables must satisfy. A so-

lution is, therefore, a set of value assignments to vari-

ables that satisﬁes all constraints. A Constraint Satis-

faction Problem (CSP) uses constraints to enumerate

the possible values a set of variables may take. This

kind or problems can be formally described by using a

triple hX, D,Ci, where X represents a set of variables,

D is a set of domains that are related to variables (the

domain of a variable contains all the values the vari-

ICSOFT 2009 - 4th International Conference on Software and Data Technologies

114

Figure 2: Horizontal and vertical constraints.

able can take), and C is a set of constraints that repre-

sents some kind of restriction imposed to the possible

values assignments. A constraint is composed of a

sequence of variables (or scope), and a set of values

satisfying the constraint. It is possible to deﬁne a wide

range of constraints, unaries (“x

< 2.5”), binaries

that involve exactly two variables (i.e. “x

− 3 × 2 =

0”), or n-aries (“x

− 3x

+ 4x

> 0”). Variables can

be assigned values from different domains such as

Boolean, Integer, Real. A constraint is used to de-

ﬁne some kind of property that the solution must sat-

isfy. Constraints are usually embedded within a pro-

gramming language (i.e. g-Prolog, Sictus-Prolog) or

provided via separate software libraries (i.e. Choco,

ILOG CP, JOPt, Koalog, etc...). The Choco Solver is

a Java library for CSP designed to easily model CSP-

based problems. It allows considering different kinds

of variables, domains and constraint types, and pro-

vides several implementations of well known algo-

rithms for constraint propagation and heuristic-based

search (i.e. Arc Consistency algorithms). The library

provides a complete API which helps users to model,

implement, and test a CSP-based algorithm (Team,

2008).

Using the formalism and basics of CSP design, the

problem described in Section 2, has been translated

into the following CSP-based model:

• Resource Set and Educational Resources. The re-

sources that ﬁnally are assigned (labs slots) deﬁne

the possible values of the variables. As an exam-

ple, in Figure 1, the RS1 generates three different

domains (one for each ER), the number of slots

available are used to set the domain cardinality.

• Student teams. Student team preferences are used

to create both, the variable set that needs to be as-

signed, and a set of constraints that must be satis-

ﬁed. In Figure 1, the StudentAgent is represented

by variable “x

” and the restriction x1 6= ER1.3

represents that ER1.3 is a forbidden value for this

team. Each student team has as many variables as

ER to be allocated, and each RS generates a new

set of constraints. Every variable can take a value,

which represents a lab slot in a particular RS-ER

that must satisfy the team constraints. Associ-

ated to each team a new variable is deﬁned, the

Optimization Variable (OV

), which takes a differ-

ent value depending on the relation ¡team prefer-

ence, lab slot- ER assigned¿. Therefore, OV

= 5

if lab slot assigned was a “P” (Preferred) value

for the student team, OV

= 3 if lab slot is “I” and

= 0 if lab slot is “F”. When two different RSs

related to the same course are considered, the pre-

viously described values are increased in 2 units

(so that Horizontal constraints will have a higher

value, than Vertical constraints). These variables

(OV

) are used to ﬁnd a solution, maximizing their

global values (see equation 2).

• Two incompatibles ER (i.e. with the same

timetable belonging to different RS) imposes a

new restriction that makes that only one of them

can be assigned to a student team.

H =

∑

i=1

H(a

) (1)

H(a

) =

∑

j=1

(RS

(i)) (2)

The CSP algorithm maximizes the global value

of OV

(RS

(i)) for all the student teams considered,

since it looks for the maximum value of H as shown in

Equation 1, where k is the number of Students teams

to be allocated. Equation 2 shows how to calculate the

H value, where n represents the number or Resource

Sets to be allocated.

Negotiation is not possible if the previous restric-

tions are used because the CSP approach is mono-

ALLOCATING EDUCATIONAL RESOURCES THROUGH HAPPINESS MAXIMIZATION AND TRADITIONAL

CSP APPROACH

115

lithic. A heuristic has been designed for those cases

where there are a high number of very restrictive stu-

dent teams to be allocated. If a solution is not feasible,

this new heuristic incrementally selects those student

teams with higher restrictions, and their Forbidden lab

slots become Indifferent so their restrictions are not

considered (those restrictions that do not affect hor-

izontal constraints). Once a solution is found, these

modiﬁcations appear as “suggestions” for a feasible

allocation.

Finally, the value of OV

variables can be used to

see how close the solution found is to the student pref-

erences. The higher the value, the ‘happier’ the stu-

dents will be with the given assignment. The global

value of gives us an idea about the ‘global happiness’

of OV the solution found.

4 THE AGENT-BASED MODEL

The main characteristics of ERA problem described

in Section 2 make Multi-agent technologies a natu-

ral framework to test and prove these kinds of algo-

rithms. For this reason there exist several multi-agent

frameworks, such as NetLogo, Swarm, Repast or Ma-

son (Railsback et al., 2006), designed to facilitate the

speciﬁcation of collective behaviors (represented as

agents) that can be simulated into a simulation toolkit.

Among existing MAS-based simulation toolkits, the

Mason library was selected.

Mason is a discrete-event multi-agent simulation

library core in Java, designed as a foundation for

large custom-purpose Java simulations. This toolkit

provides some graphical facilities, and other utilities

to easily modify the simulation domain (Luke et al.,

2004). A basic model in Mason requires the deﬁ-

nition of two main elements; the environment and a

set of agents with a deﬁned behavior. For this rea-

son, we have modeled an environment containing the

Resource Set (RS) from which the agents can con-

sume the available lab slots (ER). On the other hand,

the student teams are modeled as Mason-based agents

that evolve in each simulation step looking for a so-

lution. One of these agents executes three different

actions in each step. First, it updates its utility func-

tion, called “happiness”, then it looks for a new “lo-

cation” that improves its happiness, and ﬁnally it tries

to “go” there (the agent tries to obtain the selected

ER). The maximization process can be described as

follows:

1. The happiness function is a tradeoff between the

particular happiness of the student team, and the

current distribution of the available ER. This func-

tion (see equation 3) rewards an egalitarian distri-

bution of student teams among RS and ER, and

tries to satisfy the agent allocation preferences.

H(a

) =

∑

j=1

( f

(RS

(i)) + f

(q′, RS

(i)))

(3)

H(a

) represents the average happiness of agent-

i and is calculated by using f

(RS

(i)) the total

number (n) of Resource Sets to be allocated, and

the sum (for each ER) of how close the current al-

location is to the agent preferences. This is cal-

culated by using to transform the agent prefer-

ence into an integer value (currently the values

hP = 5;I = 3;F = 0i are used), and the level of oc-

cupancy (q′) of the ER (this is evaluated through

function f

(q′, RS

(i))). This latter function has

been introduced to quantify the occupation of the

ER. The social reason is related to the problem

that appears when a student team prefers attending

a not overloaded lab group (they will receive more

attention from educators). On the other hand, ed-

ucators would prefer an egalitarian distribution of

students (and therefore an egalitarian distribution

of the teaching work). The f

function measures

how close the ER occupation is to an egalitarian

distribution.

2. Therefore, each agent in the system tries to max-

imize its own happiness function, so it will try to

look for an ER (i.e. lab slot) that maximizes its

preferences although a global egalitarian distribu-

tion is indirectly used by the agent. In the ﬁrst

simulation step any agent (randomly selected) can

select only one ER from its Resource Set, to avoid

initial and premature resource occupancy.

3. Once no slots are available in a particular ER,

a negotiation procedure is executed by the agent

which is interested in:

(a) The bidder agent (a

) sends a message to all the

current agents (a

) assigned to the desired ER.

(b) .The a

agent proposes to exchange one of its

own ER (currently allocated) for this one. The

list of available ERs is evaluated by each agent

). Each a

answers to a

with their pre-

ferred ER from the exchange list (or sends a

void value if it is not interested in any). If the

bidder agent (a

) is not interested in the pro-

posal from a

, it removes the ER from the ex-

change list and sends it back. This process con-

tinues until an exchange is made, or no agent is

available for negotiation (no one is interested to

give up this ER).

4. Finally, to avoid a cyclic negotiation process from

an agent that tries to access a particular ER, a

discouraging factor is used. Equation 4 shows

ICSOFT 2009 - 4th International Conference on Software and Data Technologies

116

how when an agent repeatedly tries to get an ER

that it is already full and there is no negotia-

tion possible (we are considering s negotiation cy-

cles; t ∈ [0··· s]), the initial ER preference value

(RS

(i)) ≡ f

(0)

(RS

(i))) is decreased by a con-

stant factor (currently 0.75).

(t)

(RS

(i)) = 0.75

t−1

× f

(0)

(RS

(i)) (4)

With this structure, the system is completely au-

tonomous and there is no need for a coordinator or

central structure (no auctioneer is used). Agents se-

lect ERs by themselves and try to maximize their pref-

erences while keeping a balanced distribution of re-

sources. If a group is completely full, and an agent is

interested in it, a negotiation process with other agents

is started in order to ﬁnd an agreement. Any agent

that tries to access into an ER insistently decreases

the happiness that could gain by obtaining that ER

(so that it is better for an agent to shift its preferences

from preferred groups that are overloaded, to others

with an initial lower interest). By using this approach,

the system converges to a solution that is measurable

not only by the preference satisfaction, but also by the

social welfare and distribution of the resources.

5 EXPERIMENTAL RESULTS

This section describes how the experimental datasets

have been generated to compare both algorithms, and

the experimental results obtained.

5.1 Data Sets

Several data sets, with incremental constraint-based

complexity, have been considered. They have been

generated by using real statistical information from

the Technical School at Universidad Autnoma de

Madrid (UAM). For each course, the number of labo-

ratories available, students registered for each course,

capacity of labs, and time tables, has been consid-

ered. These data have been used to generate a prob-

ability distribution of students/course and the num-

ber/capacity of labs that students need to attend.

A four year degree has been considered (it corre-

sponds to the current Bachelor in Computer Science

at UAM). Table 1 shows the student enrollment distri-

butions by course (only those courses with laborato-

ries are considered), the number of courses for which

students have enrolled and the distribution of students

with this number of courses.

A row in Table 1, for example the second one,

shows that 2

year students can register for up to 2

Table 1: Distribution of labs by course.

Year No. courses Distribution (%)

2 100

2 - 3 - 4 20 - 50 -30

4 - 5 - 6 15 - 70 -15

ﬁrst-year courses, up to 3 second-year courses, and up

to 4 third year courses. The distribution shows that it

is more common to register for courses of the year for

which you have enrolled.

Based on the previous information, six data sets of

1000 student teams were generated. The synthetic re-

strictions for each team were also randomly generated

by using some historic data related to previous years.

Table 2 summarizes the basic features for each data

set, where Ds0 considers only one Preferred group per

ER and StudentAgent (i.e. SA

= hhP, I, Ii, hP, I, Iii),

whereas Ds5 considers that 30% of ERs are marked

as Preferred and the rest (70%) are Forbidden, for ex-

ample: hhP, F, Fi, hP, F, Fi, hP, F, Fii makes a 30–70

distribution. The number of Forbidden and Preferred

constraints has been adjusted along different datasets

to cover different complexity situations.

Table 2: Student datasets.

Data Set % Preferred (P) % Forbidden (F)

Test 100% 0%

Ds0 1P/(ER,agent) 0%

Ds1 30% 0%

Ds2 1P/(ER,agent) 20%

Ds3 30% 50%

Ds4 1P/(ER,agent) 70%

Ds5 30% 70%

5.2 Results

The previously described datasets were generated as

data ﬁles of student preferences

, and translated, by

following the CSP and MAS models described in sec-

tions 3 and 4, into an adequate representation. Tables

3 and 4 show the results obtained for both algorithms.

Since the happiness functions were obtained by using

different preference values, they are not comparable

across systems but they givea good estimation of their

performance with different restrictions.

As it could be expected, the CSP model provides

good results when there is a feasible solution, this

usually happens when the student teams are not very

Data sets available at: aran-

txa.ii.uam.es/˜dcamacho/mason/mara.htm

ALLOCATING EDUCATIONAL RESOURCES THROUGH HAPPINESS MAXIMIZATION AND TRADITIONAL

CSP APPROACH

117

Table 3: CSP experimental results for datasets considered.

Data Mean Happiness Mean Distribution P’s I’s F’s

Set Happiness Deviation Distribution Deviation (%) (%) (%)

Test 9.85 0.07 81.5 0,66 100 0 0

Ds0 9.69 0.15 81.3 21.8 86.9 13.1 0

Ds1 9.78 0.1 81.2 15,2 94.2 5.8 0

Ds2 9.32 0.25 81 17.7 89.8 1.07 9.19

Ds3 7.82 1.09 80.6 17.9 61.3 15.6 23.1

Ds4 7.03 1.12 80.8 15.8 66 8.2 25.8

Ds5 6.02 1.59 80.9 19.5 71.9 0 28.1

Table 4: MAS experimental results for datasets considered.

Data Mean Happiness Mean Distribution P’s I’s F’s

Set Happiness Deviation Distribution Deviation (%) (%) (%)

Test 9.85 0.07 81.5 0,66 100 0 0

Ds0 9.29 0.29 81.3 4.21 85.3 14.7 0

Ds1 9.74 0.14 81.4 0.64 94 6 0

Ds2 9.4 0.24 81.1 4.36 86.9 12.75 0.35

Ds3 9.72 0.19 81 0.89 95.53 2.42 2,05

Ds4 9.09 0.43 81 5.92 86 11.1 2.9

Ds5 9.67 0.29 80.9 0.91 95.8 0 4.2

restrictive (Test, DS0 and DS1). However, when the

number of restrictions is increased (forbidden ERs),

we use a heuristic that penalize those teams with a

higher number of restrictions, allowing to allocate

teams to initially forbidden groups (these restrictions

are relaxed; some ERs are translated from F to I). This

allows ﬁnding a partial solution but not the optimum.

As Table 3 shows, initial datasets can be allocated

using only preferred and indifferent groups, however

once the dataset includes a 20% of Forbidden ERs, the

algorithm needs to allocate about the 9% in forbidden

groups. This problem increases linearly with the in-

crement of F groups (e.g. using a 70% of Forbidden

ERs the solution allocates up to 28% of the teams to

Forbidden ERs), therefore the global happiness of the

solution decreases.

The results obtained for the MAS model are

shown in Table 4. This method is able, by using the

negotiation-based approach, to maintain the global

happiness of the solutions found. Although “hap-

piness” values cannot be directly compared between

CSP and MAS solutions (because their equations are

different), the percentage of allocated Forbidden can

be compared. In the worst situation (DS5) only the

4% of the students needs to be assigned to a Forbid-

den ER, and the 95% of student teams are satisfactory

allocated. Finally, the low variation of the happiness

among the different datasets can be remarked com-

pared to the variation of this value for the CSP solu-

tions. This is due to the facility (given by the Multi-

agent approach) to change preference values, or to ex-

change the current ER allocation with other agent in

the system.

6 CONCLUSIONS AND FUTURE

WORK

The experimental results obtained with our algorithm

within the simulating platform MASON, and its com-

parison with a traditional CSP approach, show that

the negotiation-based simulation algorithm allows us

to dynamically ﬁnd new solutions that maximize non-

quantitative parameters, such as student happiness,

i.e. how close the proposed solution is to the needs

of speciﬁc students. These results show how a multi-

agent (lightweight and collective) model can be used

to optimize the allocation of a set of educational re-

sources based on a set of distributed (negotiable) re-

strictions that represent the student team preferences.

In the near future some properties of our approach

will be modiﬁed and tested, modifying the happiness

function considered and incorporating other actors,

such as the interests of educators in the allocation

of the educational resources. On the other hand, the

model proposed for ERA problemscould easily be ex-

tended to consider a broker, or auctioneer agent, that

could be designed to compare with other MAS classi-

cal algorithms (i.e. trading systems).

ICSOFT 2009 - 4th International Conference on Software and Data Technologies

118

ACKNOWLEDGEMENTS

This work has been supported by research projects

TIN2007-65989 and TIN2007-64718. We also thank

IBM for its support to the Linux Reference Center.

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