Group Title: Department of Computer and Information Science and Engineering Technical Reports
Title: Simulation based planning in support of multi-agent scenarios
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Title: Simulation based planning in support of multi-agent scenarios
Series Title: Department of Computer and Information Science and Engineering Technical Reports
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Language: English
Creator: Lee, Jin Joo
Fishwick, Paul A.
Affiliation: University of Florida
University of Florida
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Place of Publication: Gainesville, Fla.
Copyright Date: 1997
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Simulation Based Planning in Support of Multi-Agent Scenarios

Jin Joo Lee and Paul A. Fi-lii, 1:
Computer & Information Science and Engineering Department
University of Florida
Abstract
Whenever a simulation involves multiple interacting intelligent objects, called agents,
there is the issue of how to code the decision making procedures that drive the agents.
I I usual method of encoding decision-making procedures has been to use operator
or rule-based models, representing the decision making intelligence of the coordinator
(i.e., commander on a battlefield). If the purpose of the simulation is to precisely
emulate a particular coordinator's intelligence, then such rule-based models may often
be most appropriate. However, the goal is often to win the engagement or have the
agents perform a task to the satisfaction of an optimal condition. In these cases, we
have created a methodology, Simulation-Based Planning, that embeds one simulation
inside another. I hl embedded simulation simulates the actions of agents and inten-
tions of coordinators before committing to a plan. Plan alternatives are generated
based on discrete paths through spatial regions of a domain, while specific optimal
plans are generated through the use of experimental design and simulation. We have
found that, through simulation-based i'l..iji ji-. near-optimal plans can be constructed
by using simulation, in addition to using simulation once a plan has been adopted.
In the case of semi-automated force (SAFOR) development, this involves embedding
the simulation-based planner inside the computer generated force simulation. I I
results point to extensions for SBP beyond the military domain.


1 Introduction

Planning and decision making are key aspects of human intelligence and therefore automated
planning methods have become important in modeling intelligent behavior within Artificial
Intelligence and Simulation. In a multi-agent system, one needs to simulate the individual
agents, but also the coordination of the agents and methods employed for achieving their
goals through interaction, cooperation and adversity. Our approach is not to create cognitive
models for individual agents, and then to apply simulation, but instead to create models for
multi-agent systems that are tightly constrained by their environments. Example constraints
include 1) geometric paths that are to be followed, 2) a task or mission to be accomplished,
and 3) a strict set of operating conditions for all agents. With these constraints, it is feasible
and logical to apply quantitative simulation techniques to support decision making involving
multiple agents. A classic case where multiple agents are modeled without using cognitive
models can be found in the simulation area for emergency planning and queuing. In many
environments, agents are constrained to act in ways that can be captured with quantitative
models calibrated with statistical measures. With less constrained scenarios where decision
making is made locally and dynamically among a small number of agents, one would need to
augment SBP with cognitive agent models; however, our research focuses on the constrained
scenario theme. In executing these scenarios, we create a simulation-based decision model
which can be said to reside in a decision-making object or agent.









Through time, planning domains have evolved from the typical "toy-world" domains
such as the blocks world to i, ,i-world" domains such as mission planning in the military.
Ti, earlier classical planning methods have often been shown to be inappropriate for these
real-world planning problems which can contain uncertainties and real-time constraints in
decision making. A major problem with these uncertain domains is that it is hard to predict
the outcome of events. A significant amount of work has been done in the area of planning
under uncertainty-generating universal plans [26], conditional plans [32] to using probabilistic
networks and decision theories [21, 18].
We have developed SBP as a method incorporating simulation models into the planning
process. By building simulation models for individual agents and simulating them to gather
the combined effects at the required level of detail, we are able to plan for more complex,
adversarial environments more readily and effectively. In addition, SBP's ability to reason at
a level of finer granularity can bridge the gap between the two planning areas: 1) the classical
AI planning domain which represents the coarser level of planning, dealing mainly with
symbolic and abstract actions; and 2) the intelligent control planning domain representing
the lowest level of planning, dealing with actual optimal execution of the given plan.
In the simulation literature, -iiil.,ii i .1" is defined as i !, discipline of designing a model
of an actual or theoretical physical system, executing the model on a digital computer, and
analyzing the execution ii lIip" by Fi-li"i' 1: [10, page 1]. In the planning literature, Dean
and Wellman [7] state that the idea of using a model to formulate sequences of actions is
central to planning and, given a sequence of actions, a robot can use the model to simulate
the future as it would occur if the actions were carried out. Tlil- once simulation models
are built for individual entities of the world, simulation can be used as a tool to provide the
planning system with information useful for evaluating its hypothesis.
Using the system theoretic approach, recent work by Dean et al. [6] focuses on a method
based on the theory of .iil,, 1.v decision processes for efficient planning in stochastic domains.
This approach is closely related to our work in that the world is modeled as a set of states
and actions having a transition model that maps state and action pairs into discrete proba-
bility distributions over the set of states. However, it differs considerably in several aspects.
First, probability is handled analytically which means the outcome is probabilistic but de-
terministic. In SBP, it is nondeterministic since data is either sampled from a distribution
or produced by a more detailed simulation model. Second, the value or reward of each state
has to be predetermined with a probability. With SBP, the value of the entire path is calcu-
lated at the end of each simulation based on an objective function. Another way to describe
this difference is in terms of the objective function: our method uses a dynamic evaluation
function based on simulation data while the other uses a static evaluation function based on
probability and static values. Another difference is the type of domain it can handle. As
Dean et al. [6] state, the method is reasonable only in a benign environment while SBP can
fairly complex environments involving adversarial agents. In Wellman [30, 31], the problem
of route planning is treated as an extension of the well known shortest-path problem. He
points out that for most AI route planning domains, the cost of a route is the sum of the
cost of its segments and the cost of each edge in a route are assumed to be known with
certainty. Standard search algorithms such as best-first and A are based on these assump-
tions, and therefore optimality is no longer guaranteed when the route costs are probabilistic
and dependent. Wellman proposes a generalized dynamic-programming approach based on









stochastic dominance which solves these problems. However, again this approach does not
consider problems where the state transition itself is nondeterministic. Recently, there have
been some efforts to develop a combined planner [14, 3, 13]. Ti, major difficulty in trying
to build a combined planner is integrating the different methods of the two areas of planning
and control. For instance, a typical deliberative planner may use some type of first-order
predicate logic to model knowledge and reasoning, whereas a reactive planner or controller
may use methods from control theory such as differential equations. '.! ill in dealingg [8, 9]
allows the integration of these different techniques as submodels.
With combined planning and control, we now want to integrate the different modeling
types that exist in AI and simulation. T11i, has been previous work done in the integra-
tion of AI and Simulation [19, 20]. However, combining different modeling paradigms and
techniques is often a difficult task. Because of the ability to combine different modeling
paradigms at multiple levels, we consider the object-oriented approach of multimodeling to
be a natural approach to solving the problem.
In planning, there are several different types of uncertainty [23] and in our particular
domain, there are two major types. Tli, first type is uncertainty in the knowledge of the
environment such as the location or existence of the enemy. Uncertainty due to noise of the
sensors or other systems also belong in this category. Tli, second type is due to the fact
that some domains are inherently random. Even when the available knowledge is complete
and certain, stochastic properties exist. For example, it is never possible to perfectly predict
the reaction of another agent in response to a given stimuli. Although we may be able
to make a good guess, we can never be completely certain and thus, a form of randomness
exists. Another good example is uncertainty due to the randomness of the outcome of events.
Predicting the outcome of such events as engagement between two entities in the battlefield
is difficult due to its random nature.

1.1 Object-Oriented Multimodeling Methodology
T11, object oriented approach to simulation is discussed in different literature camps. Within
computer simulation, the system entity structure (Mi) [33] (an extension of DEVS [22])
defines a way of organizing models within an inheritance hierarchy. In SES, models are
refined into individual blocks that contain external and internal transition functions. Within
the object oriented design literature [24, 2], the effort is very similar in that object oriented
simulation is accomplished by building 1) a class model and 2) dynamic models for each
object containing state information. Harel form of -1.11, (!.iii!- so that the dynamics may
be seen in the form of finite state machines.
.ldels that are composed of other models, in a network or graph, are called multimod-
els [8, 9, 10, 11]. '.1 i ii ndels allow the modeling of large scale systems at varying levels of
abstraction. Tli combine the expressive power of several well known modeling types such
as FSAs, Petri nets, block models, differential equations, and queuing models. By using well
known models and the principle of orthogonality, we avoid creating a new modeling system
with a unique syntax. In the original multimodeling concept, when the model is being ex-
ecuted at the highest level of abstraction, the lowest level (representing the most refined
parts of the model) is also being executed. Each high level state duration is calculated by
executing the refined levels that have a finer granularity.









To optimize execution time of these models, we are making an extension to the multi-
modeling concept. By using concepts and methods from ;., i .-.- i i .f we plan to build levels
of i -:-regated models so that when time is a limiting factor, we can choose to execute at
higher levels of abstraction [17].


2 Contribution to Knowledge

Tli, primary contribution of our research is the introduction of the SBP methodology for
decision making. SBP extends and improves the planning horizon in three aspects. First,
it handles probabilistic uncertainty through detailed and replicated simulation of models
rather than solving them analytically using probability theory or using simple '. i, 1I Carlo
sampling. Second, simulation models can naturally extend the level of reasoning to a finer
level of granularity, often involving continuous state space. Tli t- SBP is able to produce
plans that are closer to the detailed level of execution and thereby often discovering subtleties
(which would have been missed by a higher-level planner) that may lead to failure of a
plan. Finally, multi-agent adversarial planning is easily achieved through object-oriented
multimodel simulation where each agent or adversary is individually modeled and simulated
in response to each plan.
Simulation can be a time consuming solution method especially when there are many al-
ternatives to consider or when many replications are necessary in order to gather the effects
of uncertain factors. However, we show that simulation time can be reduced, allowing time
constraints to be met, through the use of experimental design methods and multimodeling
methods. Domain-specific heuristics can also be useful in pruning out alternatives. Experi-
mental design is a well established method in simulation which allows the optimization of the
experimental process so that as much information as possible is obtained at the least cost.
Tliiit- simulation experiments can be designed so that the plans are evaluated in the time
available with a certain confidence level. Another way to control the simulation time (i.e.,
planning time) is to decide at which level of abstraction the model will be simulated. Ti,
newly extended multimodeling will allow the simulation models to be defined at different
levels of abstraction so that any one of the levels can be chosen for execution. A high-level
simulation can be done by sampling from a distribution, employing a closed-form analytic
technique. A complex low-level simulation can be done by simulating the state change in
greater detail at each time step with the use of differential equations or continuous-state
control block models. In the next section, we provide a general framework for developing an
experimental design block called the Executive model that will accomplish such a task.


3 Simulation-Based Planning

SBP refers to the use of computer simulation to aid in the decision making process. In the
way that game trees are employed for determining the best course of action in board games
(using a game tree), SBP uses the same basic iterative approach with the following items:
1) a model of an action is executed to determine the efficiency of an input or control decision,
and 2) different models are employed at different abstraction levels depending on the amount









of time remaining for the planner to produce decisions. In the first item, board game trees
implement a static position evaluation function, whereas, in SBP, a model is executed to
determine the effects of making a move. In the second item, SBP can run more detailed
models of a physical phenomenon when there is sufficient planning time or fast computation
or parallel methods are instrumented.
Tli, military has been using simulation-based planning for many decades in the form of
constructive model simulation. A constructive model is one based on equations of attrition
and, possibly, square or hexagon-tiled maps using discrete jumps in both space and time. To
decide whether to accept a course of action, one can use a constructive model (a .,ini )
to evaluate the alternatives. Related work by Czigler et al. [4] demonstrates the usefulness
of simulation as a decision tool. Our extension in SBP is one where we permit many levels of
abstraction for a model, not just the ; r--.i-egate abstraction level characterized by Lanchester
equations and combat result tables. Tli, idea is to allow the planner the flexibility to balance
the need between the required level of detail and the amount of time given to make a decision.
This is similar to Dean and Boddy's anytime algorithm [5]. Tli, notion that simulation can
be used for decision making is covered in several disciplines, such as for discrete event based
models [29].
We do not claim that SBP is the method to use in all types of planning problems. For
planning problems whose problem domain is well known, the outcome of each action certain
and their interaction simple, SBP will not be able to exhibit its advantages. And for most
cases, SBP should be used in conjunction with some type of higher level reasoning system
so that the initial set of candidate plans are produced by this higher level system. Til ii for
evaluating which is the near-optimal plan and for refining the plan to the execution level to
ensure near-optimal results, SBP should be employed.

3.1 The SBP framework

We present the SBP framework in terms of three components: the simulation component,
the experimental design component and the output analysis component.
Ti, model in Figure 1 is the top level general framework for simulation-based route
planning systems. We discuss each of the three components and the individual blocks that
belong to each component.

3.2 Simulation block : Trial

To use simulation in planning, we first need to identify the set of controllable and uncon-
trollable variables. Speeds, routes, actions of objects are controllable, whereas any kind of
uncertainty such as uncertainty of weather conditions and outcome of combat are uncon-
trollable. Tli, controllable variables or factors are sometimes called as parameters in the
simulation literature [25]. Tli, main objective of plan simulation is to gather the effects of
the uncontrollable through repeated sampling (replication) while varying the parameters to
find a near-optimal combination of controllable values in spite of the uncertainty. We say
near-optimal because we can never guarantee the optimality of a plan given the uncertainties
of actual plan execution. In addition to parameters, there are noise factors and artificial
factors. Noise factors include sources of variation within the real-world system as well as































Figure 1: Generic Top Level Architecture of a Route Planner


exogenous factors such as customer and supplier characteristics. Artificial factors are sim-
ulation specific variables such as the initial state of the system, termination conditions and
random number streams. Due to the nature of our problem, artificial factors such as initial
state of the environment and termination conditions of plans are assumed to be given by the
user. Other issues of artificial factors are discussed mostly in Section 3.3. Here we present
some definitions that will help us formally describe the simulation algorithm we have created.
Unlike most plan evaluation schemes where the predicted state transition occurs by ana-
lytic (therefore, deterministic) and probabilistic functions, SBP nondeterministically chooses
the ini likely to lII1Il,, 1" transition given the situation by either sampling the probabil-
ity or by executing a detailed model of the transition itself. Tlii- both an advantage and
possibly a drawback, SBP may come to evaluate transitions which do not have the highest
probability of occurring.
We now define the following:

Let W = WI, TV2, ..., Wk be the set of all objects in the environment. And let Q(t)
qi(t) x q2(t) x * x qk(t) be the world state at time t where qi(t) is the state of object
Wi at time t. a finite set of world states. Also, we define Ai(t) as the set of actions
Wji can take at time t. And zero or more actions may be chosen from this set to be
simulated at time t.

Let R be a set of routes that need to be simulated and chosen from. Tli, total number
of routes is N and Rj denotes the jth route where 1 < j < N.

Stationary Object refers to an object that remains physically in the same location
throughout the simulation and objects that do not have the ability to physically change









location. Ground radars, missile sites and buildings are some examples. A stationary
object may no longer exist when it is destroyed during the simulation. Let O be the
set of all stationary objects where I O = I-.

Moving Object refers to an object that has the ability to physically move and change
its location during simulation (e.g. planes, AWACS and missiles). Let D be the set of
all moving objects where I D I= L.

Planner Object refers to the object which is the planning entity itself. We denote it
by OP and it belongs to the set D if it is a moving object and to set O if it is not.

Let 0 be the set of uncertain stationary objects. Let D be the set of uncertain moving
objects. T!, 11, these objects can have one or more of the following uncertainties:

initial location (if associate total probability is less than 1 then the object's exis-
tence is also uncertain)
type (e.g. type of plane, type of missile)
configuration (e.g. power, speed, etc)
decision logic of the object

Tli, i, the simulation algorithm follows:

1. Initialize environment:
For every replication P, (1 < p < n) setup all objects in 0 and D by sampling from
their respective distributions using the random seed produced by the replicator.

2. For each route Rj,

WHILE ( (not success) or (not failure) )
Obtain current state Q(t)
FOR each object Wi in W
Determine actions for Wi from the set Ai(t)
Update state qi(t) to qi(t+l)
by 1) detailed simulation of chosen actions from Ai(t)
or
2) sampling distribution
Update world state Q(t+l)
t =t + 1

TIl, simulation strategy is usually a mix of time slicing and event scheduling. Time slicing is
used to routinely check each object for its responses to any change in the world state. Event
scheduling is needed to allow objects to schedule any delayed response or action that is to
occur in some future time which may not necessarily coincide with a particular time slice.
Tli, simulation proceeds until the termination criteria-such as goal success or failure-is
met. Tli, necessary output data of the simulation is now sent to the Evaluator block.









3.3 Experimental Design block : Executive

In simulation, experimental design is a method of choosing which configurations (i.e., pa-
rameter values) to simulate so that the desired information can be acquired with the least
amount of simulating [15]. In experimental design terminology, the input parameters and
structural assumptions composing a model are called factors and the output performance
measures are called responses. Tli, number of runs depends on three factors: the total
number of factors, the number of factor levels and the number of replications (repetitions).
One way to reduce these numbers is by using heuristics. Drawing nomographs of all of
the three factors to determine the dominant elements and to evaluate design tradeoffs is
another method [27]. Fractional factorial design is also applicable [27, 15]. Ti, variables
are screened, based only on a fractional number of runs of the total combinations, for their
effect on the response variable. An issue exists, however, as to whether we can use them
effectively inside the planner as part of the system, since these methods are designed to be
used by humans.
For domains where the response variable is continuous, response surface methods can
be used. However, for route planning problems that involves discontinuous surfaces where
factors such as alternative routes and alternative strategies exist, the standard simulation
methods can not be applied.
In general, the total number of computer runs, S, required for a replicated, symmetrical
experiment [27] is
S= p(ql)(q2)... (k) (1)
where
p = number of replications
qi = number of levels of ith factor, i = 1, 2,..., k
k = number of factors in the experiment.

For a typical route traversal simulation we can express the computational complexity of
a single run for route Rj, in the worst case, as follows (given that we are using time slicing),

(Rj) = 0 ((NuTso + L) dst (2)
Adist
where:
distRj = the total length of route Rj
Adist = the size of time slice At Speed(t)
Nunmso = the number of stationary objects previously calculated
L = the total number of moving objects in the simulation.
Tlhi- the total time complexity of the experimental part of the SBP algorithm will be,
in the worst case,

N
O (ES (Rj) (3)

In summary, we can save time in two ways: one by reducing S or by reducing O(Rj) while
still obtaining meaningful results. We first present various heuristics in reducing S:









Reducing the number of factors:
For our problem domain, routes, behaviors and the planner's speed are some candidate
factors. By setting any one of these factors to be a constant, we are effectively reducing
the number of factors. Because, setting a factor to be a constant implies that qi = 1.

Reducing the levels of ith factor:
Reducing the number of levels of the ith factor from A to B reduces S by a factor of
A B. For instance, using some heuristics, we can prune away unpromising routes
before they are simulated and thus resulting in the reduction of the number of levels
of the route factor.

Reducing the number of replications:
Ti, number of replications depends on many factors. .i,1-t of all, it depends on the
type of output analysis method used (i.e. what is the analysis criteria for obtaining
the correct selection of the best alternative?). Some different output analysis methods
we have employed are discussed in Section 3.4.
Another way to reduce the number of replications is heuristic sampling or controlled
sampling of the uncertainties. This way, we can converge on the answer faster than
sampling purely by random. Tli, number of replications will partly depend on the
randomness of the data. Tli, wider the range of varied answers, the lower the confi-
dence level and, therefore, will require additional number of replications. Although in
some cases where the input variables create an unstable environment, the additional
number of replications will not make much difference in reducing the interval width.
In effect, the number of uncertain objects in an alternative greatly affects the number
of replications needed to reach an acceptable level of accuracy.

.i, \ we discuss some ways to reduce ((Rj), the total simulation time spent during the
evaluation process. In time critical situations, the quality of the desired information may be
sacrificed to meet a given time constraint.

Increasing the size of the time slice At (assuming the simulation is based on time
slicing). Speed up will result at the expense of accuracy since the longer the time slice,
the faster the simulation.

Reducing number of stationary (Num,,o) to be simulated for route Rj. Although the
actual number of objects involved in the planning problem can not be controlled, we
attempt to reduce this set to a minimal size while still obtaining meaningful data.
Acquiring this minimum set of objects to be simulated is done using the following
structures:

Dynamic PlanSim Window
Static PlanSim Window
SD(,t1)

Dynamic PlanSim Window is a rectangular area that includes all stationary objects
that may be affected by or effect the moving object. Every moving object has a






















Figure 2: Dynamic PlanSim Window


Dynamic Plansim Window and for every moving object DI, we will denote its Dynamic
PlanSim window as DIVt. It is expected that area covered by DWVi will change over
time. Stated more formally, let Di(x, y, t) denote the fact that Di's location is x,y at
time t. Let i )Range be the maximum detection range (or range of interaction) of
all stationary and moving objects. Ti, 11i the DWVI is defined by the rectangular area
whose left top point is (x .\axDRange a, y + .~axDRange + a) and right bottom
point is (x + t\axDRange + a, y .~axDRange a). Figure 2 shows an example
window with four radar sites Rl, R2, R3 and R4. Tir, 1, DWI will contain Rl, R2 and
R3 but not R4 since the center location of R4 is not inside the window. As shown,
DWIV can include stationary objects such as R2 which will not actually be affected
by Di since it is out of R2's range. This occurs when the distance between Di and
the center of a stationary object O is greater than the radius of O. By checking the
distance between Di and all stationary objects, we can build a more accurate set of
DWi. However, this should only be done if the number of stationary objects are very
large and the efficiency gained exceeds the overhead of performing this additional test.
Static PlanSim Window is a rectangular area that remains unchanged throughout
one simulation run when the planning problem does not involve alternative routes and
if alternate routes are involved, a window is created for each route Rj which we will
denote as SPWRj. SPWIj includes the route and all stationary objects that may
affect the planner object.
We first compute the bounding box of route Rj by finding the minimum and maximum
coordinates of the route. Til Ii we extend the boundaries of this box by enlarging it by
\[axDRange calculated above. Fini illy, the set SPWV is created for each route Rj
by finding all stationary objects that belong inside this box. Figure 3 shows a typical
Static PlanSim Window.
SD(1,t) is the set of stationary objects such that for a single simulation run, SD(y,t) C
{O U 0} and is within the PlanSim window of a moving object DI at time t. T11,
degree that the performance improves by updating the PlanSim Window and the set
SDI for every 8t will vary depending on the total number of stationary objects.































Figure 3: Static PlanSim Window for Path i

:l:niler of moving objects that need to be simulated is the entire set D whose size is
L.

If there is no previous simulation history to base it on, we must obtain the total
number of stationary objects from the Static PlanSim Window for Rj as described in
Section 3.2. If some simulation history is available, then we can calculate the total
number of stationary objects to be:
L TT
Numn, = U U SD(,t) (4)
/=1 t=0
where t denotes the simulation time, 0 denotes the beginning time, and TT denotes
the end time of the simulation.

Although it is not explicitly shown in Figure 2, the level of detail of the simulation
object models considerably affects the overall simulation time. Simulation of objects
at the lowest level of detail will obviously require the most amount of time. We can
save time by using ;r.--.-egated or abstract models where possible. For example, for the
combat simulation of two airplanes, we can either simulate them at the lowest level
of detail such as simulating each event of gun fire, missile fire and so on or we can
simulate the combat result by simply sampling from a distribution. This probability
distribution can be constructed based on expert knowledge or can be uniform (random)
if no such knowledge is available.

By distinguishing routes based on their distance, we can build experimental strategies based
on this information. Depending on the particular problem domain, the effect of the route










CPU Time vs Route Length


200

180

160
E
I--
S140-

120

100

80-
500 1000 1500 2000 2500 3000 3500 4000 4500
Route Length

Figure 4: Plot of average cpu time vs route length


distance on the simulation time varies (i.e., the relation may not be strictly linear as shown
in Figure 4). and thus, the Executive must make a decision as to where the time must be
saved, either in S or O(j)s, depending on which is dominant.
We now present an approach which can produce simulation results within a given time
constraint. Tli1 approach is best explained in two phases. In the first phase, we perform a
set of n replications. It is hard to tell what is a good value for n but 20 is a commonly used
number in simulation [15]. While the n replications are being performed, the CPU times of
each replication for each route Rj are recorded1.
In the second phase, we make a decision as to which output analysis approach (strategy
of performing replications and choosing the appropriate stopping conditions) to use based
on the expected simulation time and the current remaining time. Before we describe the
algorithm, we define some variables:

mCPU(j) denotes the mean CPU time over n replications for route Rj. Instead of
the mean, other measures such as maximum CPU time of Rj can be used if you wish
to take a conservative approach. We can also gather some sample data and draw a
relation between the route length and the mean cpu time needed to simulate the route.
Figure 4 displays such a graph which was obtained from the simulation trials in [16].
Here, we observe that the mean cpu time grows more slowly than the route length.
This data is likely to be different for different application areas based on factors such
as the domain, the type of models and the number of objects.

T is the given time constraint.

Time_Left is the remaining time to perform the simulations.

'An issue exists whether CPU time is a good measure since it can vary depending on the load of the
computer or the network.









* Time_Used is the time used in the first phase.


Tot_:'..', I i lii;, refers to the total simulation time (real time) necessary in order
to produce results under the "Selecting best of k systems(alternatives)" (SelectBestk)
algorithm.

Time_:-'-, 1 iPer_Rep is the time needed to perform one round of replication of all
the alternatives.

1. iii: N is the minimum number of replications among all alternative, as calculated
by the How_-. iiiy_ -., ,re() function.

How_-.l',iy_ -.i ,re(j) using the equations 5 and 6 in the SelectBestk algorithm, the
exact number of replications necessary to reach a decision (select the best alternative
among k alternatives) for alternative j is computed and returned.

Ti, basic idea of the algorithm is to perform the needed number of replications for
each route as determined by the How_-.l, iiiy_. i, re() function given that the remaining time
is sufficient for the completion of this method. If the TimeLeft is not sufficient, then
we perform as many replications as possible given the time allowed. As the replications are
performed iteratively, we also try to eliminate any alternatives that appear to be significantly
worse than other alternatives. With the latter approach, the idea is to incrementally converge
on the answer while trying to meet the time constraints.

Tot_Ileeded_Time = 0
Time_IIeeded_Per_Rep = 0
TimeLeft = T TimeUsed
Min_RN = RN(1);
Ilaum_Routes = N;
FOR each Route j (1 <= j <= N)
RN(j) = How_many_more(j)
Time_Ileeded(j) = RN(j) mCPU(j)
Tot_IIeeded_Time = Tot_IIeeded_Time + Time_IIeeded(j)
Time_IIeeded_Per_Rep = Time_IIeeded_Per_Rep + mCPU(j)
IF ( RN(j) < Min_RN )
Min_RN = RN(j)
IF ( Tot_IIeeded_Time > T )
WHILE ( Time_IIeeded_Per_Rep < Time_Left )
FOR ( Remaining Alternatives )
Perform replication
Decrement Time_Left
Eliminate any significantly worse alternatives
Update the Remaining Alternatives set
Update Time_IIeeded_Per_Rep
with the new set of remaining alternatives
ELSE
SelectBestk()









Ti, general algorithm for function SelectBestk( is explained in more detail in the next
section.


3.4 Output Analysis blocks : Replicator, Evaluator, Analyzer

Specifying the right types of statistical analyses is just as important as performing the right
types of simulation runs. With simulation, several different interpretations can be obtained
from the same output data. This is the main concern of output analysis and is a distinct
feature resulting from using simulation. Different analysis methods apply depending on
whether a simulation is terminating or steady state. Because plans have a definite start and
an end time, ours are terminating simulations. Suppose we are simulating k alternatives
(or routes in our case). We describe in the following our current strategy for obtaining the
appropriate outputs and their analyses.

3.4.1 Replicator

Replication provides the easiest form of output analysis. Because our domain is stochastic,
we must perform n runs replicationss) for each alternative i, each jth replication generating
a sample value for an output variable Xj. Different random number streams are to be used
for each run so that the results are independent across runs. For a sufficiently large n, due
to the central limit theorem [15], the random variable A will be approximately normally
distributed. This assumption allows the use of confidence intervals which is later calculated
in the Evaluator block.
Another issue is using common random numbers (CRN) to provide a controlled environ-
ment for comparison among alternatives. This is to eliminate any i i.,ii;!l i11! differ-
I !,, -" that can exist between different simulations. CRN is a standard variance reduction
technique in simulation and we use it here across different alternative route plans within the
same replication so that we may converge on the final answer faster.
Thi Replicator block controls the replication environment by controlling the random
number streams for each replication. Depending on how the Trial block proceeds with the
simulation, the designer may choose to vary the random number streams either in between
each execution of the Trial block or within a single execution of the Trial block. In the air
force route planning system in [16], for example, a single execution (or replication) of the
Trial block consists of simulating all alternatives using a common random number seed. Ti,
next time the Trial block is invoked, the Replicator will provide a different random number
seed so that a different environment will be created in the next replication.

3.4.2 Evaluator

In its simplest form, the Evaluator serves as the accumulator of any relevant simulation
data that is produced from the Trial Block. If the objective function within the Trial block
produces a set of scores for each alternative, a straightforward way is to total the scores
produced from the replications for each alternatives. Other relevant data such as elapsed
CPU time for simulation of each alternative may also be accumulated so that the Executive
block may later analyze and predict future time usage.









3.4.3 Analyzer


Based on statistical criteria (e.g., highest mean, smallest variance), we can consider several
alternate plans and choose the I, -t" plan for execution. Criteria other than statistical in
nature can also be imposed, that are based on heuristics or expert knowledge.
This block is primarily responsible for analyzing data that was accumulated in the Eval-
uator. Different analysis methods may be used here based on the user's requirements. T1l,
mean, the standard deviation, the variance and confidence intervals are some measures that
we can acquire. For most of our applications, the mean of the replication results serve as
the basic ', 1, point in our response surface or graph, representing the goodness of a plan.
Variance can be a measure of predictability or stability when the variance is small. Confi-
dence intervals are useful because given a sample output distribution and a confidence level
x, it gives you the interval in which you can say with x % confidence that the real mean lies
within the interval.
Using the confidence-interval approach, there are mainly two ways to compare among
k alternatives that are discussed in the literature [15]. IWe discuss the two methods here
and later compare their differences in terms its efficiency and accuracy through a sample
implementation in [16]. Since we are trying to select the best out of k alternatives,
we must detect and quantify any significant pairwise differences in their means.
This approach, although quite accurate in terms of the results, can include unnecessary
number of replications due to the fact that a constant number of replications is performed
uniformly across the current set of alternatives.
T!, second approach, which we call the i ni -in 1 i 11 i, approach (also called the "Select-
ing the Best of k S i -" approach) selects one of the k systems or alternatives as being the
best one while controlling the probability that the selected system really is the best one [15].
Tit, statistical procedure for this approach, involves two-stage sampling from each of the
k alternatives. In the first-stage sampling, we make no > 2 replications of each of the k
alternatives and acquire the first-stage means and variances using the standard method. For
i = 1, 2, ..., k, let the mean for system i be Xr (no) and the variance for system i, Sj(no).
Ti1, it we compute the total sample size Ni needed for system i as

Ni max no h S (no) (5)
N = no + (d*)2 (5
where hi (which depends on k, P*, and no) is a constant that is obtained from a table. T1lI
table in [15] provides values of hi for P* = 0.90 and 0.95 for no = 20 and 40. 'i, \xI we
make Ni no more replications of each system i and obtain the second-stage sample means
as


A(2)ji ) = fno+1 X' (6)
Ni no

Since each system i may involve different number of replications, we must weigh the
means from each stage accordingly. We define the weights for the first stage










T no N (N no) (d* )2)
i 1= 1+ 1 1- (7)
N, no hS (no)
and for the second stage i2 1 il, for i 1,2, ..., k. Finiill, we obtain the weighted
sample means

(N) = W X1 (no) + Wi2 (2)N no) (8)
and select the system with the largest Xi(N,).


4 Nondeterministic Adversarial Route Planning Ex-
ample

4.1 Air Force Mission Planning
Air Force :i--i,.ii Planning is a good candidate for SBP since it is adversarial and also
nondeterministic. As the example shows, large part of the mission is dependent on which
particular route or air corridor you will fly through and it basically becomes a route planning
problem with many uncertainties on the way. Of course, some higher-level expert system
can be used and should be used as a meta reasoning system on top of the SBP planner to
provide guidelines as to-given the current situation-what general heuristics we are to use in
generating alternative air corridors for simulation.

4.2 Demonstration Mission
Our demonstration air mission is interdiction. Interdiction mission is a typical air mission
where the purpose is to destroy, delay, or disrupt existing enemy surface forces while they are
far enough from friendly surface forces that detailed coordination of aerospace and surface
activities is not needed. Ti, objective of interdiction entails the execution of carefully
conceived, comprehensive plan designed to isolate an area and to stop all support from
reaching the area of conflict.
TIi, 1, fi;.e, the task of the attack aircraft can be defined as I11 iing the target swiftly
and accurately with whatever munitions are carried, and return to base -,l!I [28]. To
achieve this task, the enemy defense must be penetrated. However, difficulties arise be-
cause methods of penetration can vary according to the strength and sophistication of the
enemy's detection, reporting, command and control network, and how much intelligence is
available about its capabilities. A balance between fuel and munitions in determining the
load to be carried is also important in mission planning. Considering these uncertainties and
constraints, selecting the best route is a very difficult task.


5 An Air Interdiction Scenario

As one of the applications of the SBP, we have chosen a typical air interdiction scenario, and
developed its Simulation Based Planner (C++) and GUI (Tk/Tcl) under our :i, il i indeling









Object-Oriented Simulation Environment ('.1 OOSE). In order to show the usefulness of the
SBP approach, consider an air interdiction scenario in Figure 5. This figure defines a scenario
wit h dynamically moving objects. Ti, mission of the blue force aircraft is to destroy a red
force munitions factory. T!i, ,_ are three Radars (Ri, R2, R3) and two Surface-to-Air 'i. --i!,
(SA'-.i) sites(S1, S2), each with different effective detection ranges. Two red force aircraft
(Al, A2) are located in air defense zones Zone2 and Zone3 respectively, while one red force
aircraft (A3) is located outside of the air defense zones. At a first glance, the problem of
guiding the blue force around the radar, SA'. I and air defense zone coverages, and toward the
factory seems like a simple problem in computational geometry. In fact, this is the manner
in which most route planning is done. A typical rule might be formed "To locate a path,
avoid radar and SA -. fields, and avoid fighting against enemy fighters." However such a rule
based reasoning becomes more onerous when uncertainty and dynamics are present.
To see what kind of uncertainty and dynamics are involved, consider the following avail-
able information at some point during the mission.

Uncertain location and range : Radar R1 and R2 have been identified as permanent
fixtures, but an intelligence report -i-il.-. -. that R3 may have mobility. All the ranges
(target, missile, arm range) of SA -. site Sl is well known, but only the arm range of
S2 is known and it has been reported to have a better guidance system including swift
mobility making its location uncertain.

Uncertain enemy mission : red force aircraft Al and A2 are known to be on a Combat
Air Patrol (CAP) mission, since they are always detected around zone2 and zone3.
But A3's mission type is unknown.

For each simulation trial, the uncertainty of S2 is handled by first sampling a random
location for S2 within the boundaries of the circle drawn around S2 in Figure 5. Taking this
location as the center point of the SA .I site, a boundary circle is drawn representing the
arm range of the SA':. 1 site. Til, uncertainty of the radar R3 is handled in a similar manner.
Tli, location is first determined by sampling the point within the uncertainty circle drawn
by the user. Using the sampled point as the center point of the radar, a boundary circle is
drawn representing the detection range.
For the objects in our air force mission planning domain, we can categorize the uncertainty
into several types:

1. uncertainty of existence: the object may or may not even exist.

2. uncertainty of location: an area of uncertainty of the object's location is available but
it is not certain of the exact location of the object.

3. uncertainty of range: the exact detection range or firing range is not known.

4. uncertainty of mission: the exact mission type of an object is unknown.

5. uncertainty of fire power: the destruction capability of the object is uncertain.

For our current prototype, we have concentrated mainly on location and range uncertainties.
















































Figure 5: A Typical Air Interdiction Scenario









6 Results


Figure 6 shows two possible routes (Route3, Route4). Ti, goal of blue force aircraft is to
destroy the red force munitions factory while satisfying three constraints: time or fuel level,
safety, and destruction of the target. Given the possible routes, the role of the simulation-
based planner is to choose the best route minimizing time and fuel consumption, and maxi-
mizing safety and target destruction. In Figure 6, RouteS was chosen to avoid direct attack
from Al, but for a short time period it will be detected by R1. RouteS also takes the blue
aircraft into the track range of Sl, but not into its arm or missile range. Being detected in
the track range of Sl is not very dangerous since only tracking functions may be performed
by S1
Overall, we expect the success rate of route 3 to depend largely on the result of the
samplings for uncertainty factors: specifically, the location and guidance capability of SA .I
S2 and the mission type of A3. If the powerful guided system of SA '.1 is sampled close to
this route, or A3 has an intercept capability, then the chance of success will be very small.
Otherwise, the chance of mission success will be very good. T111 nondeterministic and
stochastic characteristics are resolved by multiple simulations using different samplings of
the uncertainty factors. :'i \;1 Route4 was carefully chosen to minimize the amount of time
that a blue force aircraft falls within the detection ranges of R2 and R3 as in Figure 6.
Tit, result of the SBP shows almost the same mean score for Route3 and Route4 (RouteS :
110.36, Route4 : 103.08) with RouteS being slightly better2. Intuitively, Route 4 seems like a
better route since it only involves radar sites whereas Route 3 has a SA 1 site S2, although
its location may be uncertain. With simulation-based planning, however, we discover that
Route 3 is a slightly better. But depending on our objective, we may select Route4 as the best
overall route based on its narrower confidence interval (Route4 : 1.3, Route : 6.0). I'. \;i in
order to reduce the total number of replications in the simulation, we compare two different
methods of output analysis. T111 two methods are discussed in detail in [16]. Ti, first
one, which we refer to as the in, ;i.. method, attempts to quantify significant pairwise
differences among the k means within a given confidence interval a. We call it 71, i.,i "
because of the fact that the algorithm iterates-performing for every iteration, a set number
of b replications and analyzing data to see if there are any significant differences. Whenever
a route is found who is significantly worse than all the other routes, it is eliminated. T11i
iteration continues until only two routes remain and a difference exists between the two of
them. Note that since we have 4 routes in our experiment, each confidence level for the
pairwise differences must be made at 1 a/6 3. Ti, second method, which we refer to
as the ii,'i-i, i.i. method(referred to as "Selecting best of k ;- -i, in- in Section 3.4),
is a method that avoids making unnecessary number of replications to resolve what may
be an unimportant difference. When two alternatives are actually very close together, in
terms of their goodness, we might not care if we erroneously choose one system(the one
that may be slightly worse) over another(the one that is slightly better). TliiL- given a
"correct -I !1, 1 .1" probability P* and the "iili, 7i1, i amount d*, the method calculates
how many more replications are necessary in order to make a selection-a selection where
2The goal is to maximize the mean score for determining the better plan.
i;. 1. r to Section 3.4 for detailed explanation










I _AIR FORCE MISSION PLANNING
Out Load File save AS Qiurent Fe :Sce namlo4 :x-z Y:200 V



"- . .. . i -...,,
7 1



,,



.A",,%



r' ~ ,- i .. I I -. I ..
-- .. ....I r.



Am 9


_ Help Window I I


Figure 6: A Typical Air Interdiction Scenario


with the probability at least P*, the expected score of the selected alternative will be no
smaller than by a margin of d*. In the following experiment, we have chosen P* = 0.95 and
d* = 13. A smaller d* will produce more accurate results but with many more replications.
In addition to the two routes that appear in Figure 6, we add two more routes to test how
much the number of replications reduce and also if the identical selection is made. Tli, routes
are shown in Figure 7 and are renumbered. Route 2 and Route 0 represent two alternatives
that are very close together and is likely to require many number of replications to quantify a
significant difference between them. As expected, Routes 0 and 2 do exhibit similar responses
as shown in the following plots. Figures 8 and 9 are results with just 3 routes: 0, 1 and 2.
Figure 8 shows the mean score change of the routes using the simple iterative method. After
the first 20 replications, the planner decides that route 1 can be eliminated since its scores
are in general significantly lower than the other two routes. It then performs 120 replications
for both routes 0 and 2 before it decides that there is significant pairwise difference in their
means to make a selection. Using this method, we perform in total 120 + 120 + 20 = 260
replications. With the non-iterative method, although the method decides that 10 more
(130) replications are needed to make a decision on route 2, less number of replications are
made in terms of the total number-130 + 54 + 20 = 204. Note the weighted means calculated
by the non-iterative method which is used in making the final decision as to which of the
two remaining routes is the best one. In this particular scenario, both the iterative and the
non-iterative methods select route 0 as the best alternative. Now, we add a 4th route, Route
3 which is the shortest but perhaps the most dangerous route. Figures 10 and 11 show the
mean score changes for these 4 routes. Route 1 and 3 are eliminated after 20 replications since


.,.,i~~---;- ---~:i:~:; ---~, -;- ;:~:i~:~i:~~:.~:~~-:i: ......


ic~.


Wii
















































j Help Window



Figure 7: Inserting two new routes


Mean Score Change(iterative)


120-


0 20 40 60 80
Number of Replications Rt0 -, Rtl --, Rt2


100 120


Figure 8: Plot of mean score changes of 3 routes using iterative method


VI I
I /










Mean Score Change(non-iterative)


110 .
1 10" .," " + weightedd mean

w100
ID
90 I,I

80 1


0 20 40 60 80 100 120 140
Number of Replications RtO -, Rtl -, Rt2

Figure 9: Plot of mean score changes of 3 routes using non-iterative method


the average scores are significantly lower than routes 0 and 2. With another route added,
the mean score change plots are somewhat different than in the case where there were only
3 routes. And this difference pushes the iterative method to continue replicating 60 more
times (180 in total) for each of the two routes before it makes a decision. Consequently,
it chooses route 0 as the better route-a different selection than when only 120 replications
were performed. In the non-iterative method, it makes only 69 replications for route 0 and
21 replications for route 2 before it makes a selection. It chooses route 2 to be the best route
in this particular case. As discussed in [16], this can occur because the non-iterative method
only ensures that it makes a correct selection within a given probability P*. And since
the indifference amount d* was chosen to be 13, it basically decides that route 0 and 2 are
indifferent and many more replications is really not necessary. Overall, the iterative method
performed 400 replications whereas the non-iterative method only did 130 replications. To
find out whether the mean scores of the two routes 0 and 2 reach some kind of steady state
or just continue to oscillate, we performed 500 replications. Figure 12 shows this result. As
we can see in the graph, the two routes do reach a steady state and route 0 does seem to
have a higher average than route 2.


7 Conclusions

We have presented the method of simulation-based planning as a new approach to route plan-
ning under uncertain and complex environments. In particular, for the area of multi-agent
planning, SBP can break down the complexity of reasoning by distributing the reasoning
tasks to individual objects using the object-oriented multimodel simulation. Our claim is not
that SBP should completely replace all other forms of planning, but that this approach be
used in conjunction with already existing, higher level planning approaches. This way, given
a set of alternatives to consider, SBP is able to extend the evaluation horizon in mainly three

















Mean Score Change iterativee)
140

120 -

10 0

80


Figure 10:





















8

o


w
a)



8


-60,
0 20 40 60 80 100 120 140 160 180
Number of Replications Rt0 -, Rtl --, Rt2 Rt3 -


Plot of mean score changes of 4 routes using iterative method


Mean Score Change (non-iterative)


0 10 20 30 40 50 60 70 80 90
Number of Replications RtO -, Rtl --, Rt2 Rt3 -


Figure 11: Plot of mean score changes of 4 routes using non-iterative method


+ weighted mean(.
+ weighted mean((



4










Mean Score Change (Iterative)


uc 60
0
I 40-
LU
C 20-

0-

-20

-40

-60
0 100 200 300 400 500 600
Number of Replications RtO -, Rtl --, Rt2 Rt3 -

Figure 12: Plot of mean score changes of 4 routes for 500 replications


aspects: probabilistic uncertainty is handled through replicated simulation of models rather
than solving them analytically using probability theory; the level of reasoning is extended
to a finer level of granularity, producing plans that are closer to the level of execution while
discovering subtleties that may be missed by a higher level planner.
SBP goes about its business in a way that is considerably different to the cognitive model
method that attempts to model each individual agent in terms of a knowledge-base and
reasoning engine. In the cognitive approach, the idea is that by modeling each agent, the
end result will be significantly different than if one were to model the more quantitative,
behavioral constraints thrust upon the agent by the overall mission and objective. If agents
conform to a tight regimen of rules and procedures, it is unlikely that individual cognitive
models will affect the outcome of the global simulation, or that the decision-making will
be affected. Tli, behaviors of humans in tightly constrained environments or in emergency
conditions has successfully been modeled without employing cognitive modeling. With this
in mind, SBP performs adequately and we expect that an increasing number of decision-
making and planning tasks will be driven by the kind of quantitative simulations that are
discussed. To be flexible and realistic, we acknowledge that the hypothesis of the ',. ff.. !,.'
cognitive model in a crowd/multi-agent scenario may not always hold true. We are unsure
how effective SBP would be in scenarios which are not as tightly controlled and orchestrated
as command and control in the military. For these reasons, it is prudent to view SBP as one
method of handling decision making for multiple agents. Possibly, a hybrid SBP/cognitive
modeling approach may yield the best decision-making results.
TIi 1, are several advantages to using Simulation to predict the results of plan execution.
We list them here in addition to the ones that have been stated in Section 2.

1. Simulation provides a uniform method without resorting to adhoc solutions In simu-
lation, each object in the environment is simulated in a uniform and consistent manner









by using models that represent both the physical and behavioral properties. Tli,-
simulating a plan is a natural consequence of simulating each of the entities by itself
without having to worry about the global state change as a result of each entities ac-
tion. Using object-oriented programming methods, each object is simulated using its
own internal dynamic model [12].

2. Because there is no single central reasoning node for the simulation but many individual
simulation models for different objects, we believe scalability will be a natural conse-
quence in the sense that model complexity does not affect the validity of the model.
Also, this distributed manner of reasoning creates a good environment for multi-agent
planning. Extensibility is another advantage that object-oriented simulation provides.
For example, the effects of adding a new type of object tends to be easier using the
object-oriented approach, and will allow the behavior models of existing objects to
be more easily extended. Ti, aspects of how this occurs in w;----i, .~ll.il, relations is
discussed in [12].

3. Similar to how simulation is used for visualization, simulation can be easily used to
perform visual playback of how a plan was simulated to explain the planner's decision.
This can be very useful for the military, in particular, since much of the military
training is done through 1t i action I ii. "-which is reviewing and analyzing the
actions that were performed during battle.

4. Once a plan is chosen for execution, the simulation data that was generated during the
planning process can be used to match with the current real world state. This can be
compared to a common technique used in adaptive control theory where a reference
model is compared with the actual performance data in order to tune the controller to
a desired state [1].

5. Once the simulation results have been produced, the data can be analyzed and inter-
preted in several ways to choose the I, -i" plan. For instance, we can choose the plan
which has not only a good average score but also the minimum variance to ensure that
it is the safest plan possible. We may also decide to choose a plan that has the most
number of highest scores even though the confidence interval width may be large in
order to select a plan that has the best potential in spite of risks involved. We can even
decide to choose a plan at random (given that the scores are above some threshold)
which will produce nondeterministic planning. This is particularly useful for mission
planning-opposing forces should not be able to predict your plan.

A common drawback of simulation is that it can be quite time consuming. Before the
advent of fast low-cost personal computers, few researchers would consider simulation of a
fairly extensive experimental design to be a possible candidate for real-time mission plan-
ning. However, as the speed of low-cost computers increases, the simulation-based planning
technique is becoming more and more attractive. In order to build SBP planners that can
satisfy time constraints, we have presented various ways of reducing the simulation time in
terms of output analysis, experimental design and multimodeling. We have also presented a
heuristic algorithm that records the average cpu time of each route simulation, uses the data









to predict time usage and then designs the experiment accordingly to produce the result
within the time constraint.
We have also identified some problem areas where SBP will be most useful. It is expected
that for areas where there is little uncertainty involved or the level of reasoning required is
only at a higher level-not involving execution of physical movement such as robots actually
moving to a location x,y-SBP is not likely to do any better than methods that do not employ
simulation. '. AIly factors affect the success of an SBP planner and we briefly mention some
of them here. As with any simulation, SBP will be only as good as the models that we
build to represent the world that we are planning in. In most cases, building valid models is
not a straightforward task. Validating that models indeed accurately represent the world is
an issue that we have not addressed in this thesis. Building good evaluation functions that
correctly represents the need of the user is also an important aspect and is still somewhat of
a trial and error process. All these and many other factors must be carefully researched and
some guidelines must be developed in order to ensure that a user will build a useful planning
system.


8 Future Work

We must address the issue of the validation of simulation models-making sure that the
models we build appropriately represents the actual object's behavior. A common approach
is using sensitivity analysis or an inspection by an expert. An interesting area related to
this issue is validating and checking consistencies of a higher rule-based systems. Using the
predicted outcome of an existing higher rule-based systems and the prediction of an SBP
system (perhaps at a lower level of detail), we can compare the two predictions. Based on
the comparison, we can validate one system against another and find any inconsistencies,
subtleties that may have been missed by the higher level system. Taking it another step
further, we may modify and improve the higher level system using the information obtained
from the comparisons. Currently, research is underway in our simulation group that focuses
on studying effective consistency measures which will rectify differences in rules produced
empirically (through knowledge acquisition) and rules generated automatically from multiple
low-level simulations.
.ire detailed, sophisticated models should be built to obtain better results in terms of
answer quality and also test the degree of cpu time consumption in respect to the model's
complexity. An immediate future work would be to extend the implementation of the Air
Force models to include all the levels of abstraction. Larger number of objects should also
be simulated to further study the scalability and the rate change of time consumption.
Extending the multimodeling paradigm to enable model execution at any level of abstrac-
tion is also currently underway and SBP can greatly benefit from the success of this work
since it will allow reduction of model execution time. Possibilities exist for future work in
finding other ways of meeting real-time constraints: a hybrid approach of using quantitative
and qualitative (fuzzy) simulation, developing additional heuristics to aid in optimizing the
simulation process are some ideas that we plan to research in the future.
Finally, to further extend the study of the SBP methodology, additional experiments in
other application areas should be performed. Also, building and comparing two planning









systems, one built using the SBP approach and one built using another planning approach,
should prove to be useful in further improving the SBP approach.


9 Acknowledgments

We would like to thank the following funding sources that have contributed towards our study
of modeling and implementation of a multimodeling simulation environment for analysis and
planning: (1) Rome Laboratory, Griffiss Air Force Base,' York under contract F30602-
95-C-0267 and grant F30602-95-1-0031; (2) Department of the Interior under grant 14-45-
0009-1544-154 and the (3) :'.-, it i in1 Science Foundation Engineering Research Center (ERC)
in Particle Science and Technology at the University of Florida (with Industrial Partners of
the ERC) under grant EEC-94-02989.


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