Computational Intelligence - August 2012 - 60

Given that exact optimization techniques are ill-suited
for addressing such large multi-objective problems,
CI methods ... may help to address these challenges.
a nd Billyard [58], and Mazurek and
Wesolkowski [22] developed the Stochastic Fleet Estimation (SaFE) model
that relaxes the closure time constraints
of all tasks, and aggregates multiple scenarios. The relaxation of closure time
constraints removes the scheduling
aspect of the simulation; therefore, only
the number of occurrences and duration
of each type of task is generated for a
given scenario using a Monte Carlo
method. In this way, several scenarios can
be quickly generated, and the average
[22] and variance [13] of the platformspecific task durations can be computed.
The fleets generated using SaFE can be
considered lower bounds on the number
of platforms required to accomplish the
average scenario requirements given that
the tasks are all done one after another
without any delays in between taskings
(which happen frequently in simulations). In addition, many of the features
of a simulation such as time constraints
on tasks [71] and risk assessment [13]
have been adapted within objective
functions applied to SaFE. Work has
been done on using SaFE in a multiobjective optimization framework to
compute fleets that minimize cost, task
durations, risk of failure to meet requirements, and flexibility [13], [22], [71], [72].
Much of the improvement in the
area of combining simulations and optimization will come about with better
computational power. Significant challenges remain in decreasing the computational complexity of hybrid methods
in order to make them viable alternatives at both the strategic and operational levels. A promising avenue for
research would be the use of cloud or
parallel computing [73].
VI. Challenges

The military fleet mix problem presents
many challenges that Computational
Intelligence methods may be well suited
to address.

The challenges relating to simulating
combat scenarios are due to: (a) the large
degree of uncertainty given incomplete
knowledge of enemy forces, (b) simulating the actions of each combatant, (c)
blue and red team tactics, and (d) determining probabilities of loss of vehicles
due to enemy (or friendly) fire, necessitating the development of models for
unit loss during combat [74]. The challenge for those researching improved
simulations will be in learning how to
better translate the learned qualitative
assessments of subject matter experts and
decision makers into quantifiable repeatable computer experiments, a challenge
that fuzzy logic along with improved
agent-based models may help to address.
Given that military fleet mix problems are multi-objective in nature, the
challenge in many of those problems is
to identify the objectives to optimize.
Many military fleet mix studies have
used a weighted sum of multiple objectives in order to obtain an optimal solution using exact optimization methods.
The challenge would be to re-cast many
of those studies into multi-objective
ones carefully choosing or re-defining
objectives. CI based multi-objective
optimization methods would be very
good tools to compute non-dominated
solutions, thus providing decision makers with more options from which they
can assess the trade-offs among the
many previously merged objectives.
Furthermore, the challenge then would
be to decide which solutions would be
of interest to decision makers. Bonissione et al. outline many useful methods as
well as future research directions [75].
One of the challenges in computing
an optimal fleet mix is asking the question of what optimal means to a decision
maker. For example, a fleet mix taken
from the non-dominated solution set may
be optimal with respect to some performance and cost measures; however, adding other objectives such as those based

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2012

on notions of risk, and domestic economic benefit can dramatically change
the make-up of a fleet. Input from decision makers and subject matter experts on
these objectives and how different vehicles relate to them is subjective, therefore
fuzzy logic may be useful in addressing
this challenge. Another related challenge
is establishing the task requirements
(especially the frequency of occurrence).
Modeling those requirements using fuzzy
logic may help in this context.
Furthermore, several challenges remain relating to the translation of military capability requirements into a fleet
mix due to the complexity of military
operations and the uncertainty in future
events. One such challenge is simulating
highly detailed fleet operations in stochastic scenarios over multiple years
using optimization based scheduling
and routing methods. Another challenge
is incorporating these simulations into
an optimization framework to search for
fleets that are optimal with respect to
multiple fleet characteristics such as cost,
risk, robustness, and flexibility. The
problem is further complicated when
expanded to compute fleet mix plans
over multiple decades that are nondominated with respect to multiple
objectives such as cost and risk. Given
that exact optimization techniques are
ill-suited for addressing such large
multi-objective problems, CI methods
based on Genetic Algorithms, Particle
Swarm Optimization, and Approximate
Dynamic Programming may help to
address these challenges.
References
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www.defensenews.com/story.php?i=4644394
[2] U.S. Air Force. (2011, Feb.). U.S. Air Force fiscal year
2012 budget estimates: Aircraft procurement. [Online].
Available: http://www.saffm.hq.af.mil/shared/media/
document/AFD-110211-038.pdf
[3] Department of Defense Fiscal Year (FY) 2012 Budget Estimates, Justification Book Vol. I, Aircraft Procurement, Air
Force-3010, Feb. 2011.
[4] R. C. Owen, "The airlift system: A primer," Airpower
J., vol. VIV, no. 3, 1995.
[5] R. Richbourg and W. K. Olson, "A hybrid expert system
that combines technologies to address the problem of military terrain analysis," Expert Syst. Apps., vol. 11, no. 2, 1996.
[6] T. M. Williams, R. P. Gittins, and D. M. Burke, "Replenishment at sea," J. Oper. Res. Soc., vol. 40, no. 10, 1989.
[7] G. G. Brown, C. E. Goodman, and R. K. Wood, "Annual scheduling of Atlantic f leet naval combatants," Oper.
Res., vol. 38, no. 2, 1990.

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