The concept of constraint propagation was discussed. Performance increases are possible with careful application of these constraint mechanisms. The degree of performance increase is related to the interdependence of the different activities resource usage. Although this method of applying constraints to activities and resources is often beneficial, it is obvious that this is no panacea cure for the computational woes that are experienced by dynamic resource allocation and scheduling problems. A combined effort for execution optimization in all areas of the system during development and the selection of the appropriate development environment is still the best method of producing an efficient system

Rogers, John S.

English

NASA Technical Reports Server

 90-27278
Resource Allocation Using Constraint Propagation
John S. Rogers
Artificial Intelligence Lab
Johnson Research Center
The University of Alabama in Huntsville
Introduc_iQn
Scheduling and resource allocation considerations are fast
becoming one of the major areas of research today. Although these
are not new problems, technological advances continue to open new
and ever increasing areas where having the right resources at the
right place at the right time is crucial. As we enter into the
space age and as the costs involved in doing specific research and
development tasks increase the fundamental equation is truly, Time
is Money.
The methods and techniques applied in this area are often as
much an art form as a truly mathematical form. This is not to say
that the foundations of each of these methods are not
mathematically sound, but rather the how, when and why used in
applying the mathematical principals can produce rather unique and
sometimes more acceptable results. More specifically, there are
certain parameters that are common to most resource allocation
problems. How a particular application manipulates and utilizes
these parameters often determines the degree of performance of a
resource allocation system. A technique that can be applied to
one of these parameters is presented here.
In many resource allocation and scheduling problems one of
the major difficulties facing the investigator is determining how
to apply different constraint equations. Numerous research
efforts have been done in this'area in an attempt to increase the
investigator's control and ability in applying constraints. There
are many widely varying techniques that are available and
frequently used to solve this problem. Usually specific
characteristics of the particular domain involved and the types of
constraint equations that must be applied are the deciding factors
in the selection of the appropriate technique. This is usually
adequate for the current application; however, this solution
usually does result in a generalized mechanism that can be applied
to differing domains with only minor modifications.
In most cases a traditional approach of evaluating the
constraining parameters for each one of the activities that is
being scheduled at the time it is scheduled is sufficient. This
is reasonable when the constraining relations for the activities
are functions which depend upon resources solely. However, when
an interdependency exists between the activities or if the domain
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is not constant new problems may arise. A method that addresses
this in resource allocation problems is the method of constraint
propagation. In the following sections of this paper the concepts
involved in applying this technique are presented.
Dynamic Allocation ScenariQs
One area of interest today which can pose some unique and
sometimes tedious constraint evaluation problems is that of
dynamic domains. In this arena the domains are either constantly
changing or possibly modifiable at discrete points of time within
the analysis process. This scenario creates a true illustration
of reality since all to often activities may require the
consumption of a variable amount of a resource. Then as the
activity is performed a more refined estimate of future available
quantities of the resource is determined. This causes the domain
to be dynamically modified. Due to the newly refined domain, a
new allocation may need to be performed over the modified range to
best utilize the remaining resources.
In approaching this task one might consider some type of
readily available dynamic programming technique that would
iteratively reformulate the resource allocation scheme based on
the current domain state. Usually this is a plausible approach;
however, in many instances this can cause severe time delays in
the allocation softwares ability to traverse the domains time
range. This only tends to magnify the often already excessive
computational time required to perform the allocation process.
Figure 1 Dynamic Changing Over Time
What is needed is an alternative approach that can
incorporate the effects domain changes can have on an existing
allocation. In such an approach hopefully only those particular
activities that are effected will be engaged and therefore reduce
2O
any unnecessary constraint calculations.
Constraint Propagation.
One such technique is
What is Constraint Propagation?
Constraint Propagation is the technique of having localized
mechanisms that control the behavior of individual activities as
changes in the domain occur. This is more than just a
constraining equation that is applied at a local level. It
requires activation control to be maintained at a local level
while domain changes happen globally. If only those activities
that are directly affected by the domain change are activated then
a direct reduction in the number of constraint equation
evaluations can be achieved. Theoretically this evaluation
reduction would result in the time required in the reallocation
being reduced. Quite possibly each modification made by the
adjustment of the allocated items across the time range could
cause a subsequent alteration in the consumption of additional
resources. More than likely this would initiate a series of
downstream allocation modifications which could in effect initiate
even more downstream allocation modifications and so on. The
procession of changes effected on the downstream allocation of
events can be considered analogous to a propagating wave across
the domains remaining range. Thus arises the term Constraint
Propagation.
Obviously the effectiveness of this methodology is closely
tied to the amount of interdependence that exists between the
different activities regarding the type and quantity of usage of
the various resources. It may be logical to assume that as the
commonalties regarding resource requirements between the different
activities increases then the level of increased performance in
this method decreases. However, logically one would assume that
any reduction in the application of constraint equations should
produce some amount of time savings. This implies that the
overall performance increase seen by the system should always be
non-negative.
How do you design a Constraint Propagation System?
Specific considerations must be made in designing a resource
allocation software system that applies the technique of
constraint propagation. First, there is the need for local
control of processes. This tends to exhibit a requirement for
code encapsulation at the activity level while maintaining global
access to domain information. Although there are possibly a
variety of approaches to achieve this, the best approach is
through the implementation of Object Oriented Programming
Techniques (OOP) . With this approach the individual activities
and resources can be constructed as objects. An activity object
locally contains all the information describing not only resource
consumption requirements and constraints, but also information
which controls what activation triggers exist that would cause a
9,1
re-evaluation of this activity in the allocation process. All the
information would exist as specific slot values located within the
object itself. Likewise a resource object could contain the
resources current state, usage history, any global limitations,
and other pertinent resource specific information.
Figure 2 Object Data Structure
Many of the desired characteristics of a Constraint
Propagation system are similar to those found in Frame Based
Reasoning (FBR) systems. In an FBR system components can be
designed that describe the control structure of the frame. These
so called "daemons" are activated and controlled by the
environment in which the frame resides. For example, an "if-
decreased" daemon could possibly cause the initiation of the
control code when a quantity of a specific resource is reduced for
the time frame containing the specific performance of the
activity. The range of functionality of these daemons is limited
only be the developers ability to tailor the environments object
manipulation characteristics.
There are several programming environments (C++, ADA, LISP,
etc.) that boast an object data structure. For ease of
manipulation and flexibility of control LISP is probably the most
conducive of these environments in which to develop a Constraint
Propagation system. This is due to the extensive functionality
associated with the Lisp object as compared with other programming
environments. These structures support the full range of message
passing capabilities and can have external functional bodies
called "Methods" which can be applied to each object. Simply put,
a "Method" is a segment of computer code that acts similarly to a
function that can be applied to a specific class of objects. It
is through the use of these "Methods" that the behavior of each of
22
the daemon slots within the object is defined and controlled. By
the use of this varied level of control constraint propagation
techniques become feasible.
In this brief presentation the concept of constraint
propagation has been discussed. Certainly, performance increases
are possible with careful application of these constraint
mechanisms. The degree of performance increase is related to the
interdependence of the different activities resource usage.
Although this method of applying constraints to activities and
resources is often beneficial, it is obvious that this is no
panacea cure for the computational woes that are experienced by
dynamic resource allocation and scheduling problems. A combined
effort for execution optimization in all areas of the system
during development and the selection of the appropriate
development environment is still the best method of producing an
efficient system.
2S
°.
°
°
.
Howard, Geoffry S., "Object Oriented Programming Explained,"
Journal of Systems Management, July 1986 pp. 13-18.
Cox, Bred J., Object Oriented PrQgr_mming, Reading,
Massachusettes: Addison Wesley Publishing Company, 1986.
Rich, Elaine, Ar%ifigial In%_lligenc_, McGraw Hill, New York,
1983.
Ozden, Mufit, "A Dynamic Planning Technique for Continuous
Activities Under Multiple Resource Constraints," Management
Science, Vol. 33, No. I0, October, 1987 pp.1333 -1346.
Dreyfus, S. E. and A. M. Law, Th_ Ar% and TheQry ©f Dynami_
programming, Academic Press, New York, 1977.
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Resource allocation using constraint propagation

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