Combinatorial Optimization Network Reliability and Security: Using Genetic Algorithms and AI Methods

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Combinatorial Optimization Network Reliability and Security:

Using Genetic Algorithms and AI Methods

Dissertation Idea Paper

Doctor of Professional Studies in Computing


Pace University

School of Computer Science & Information Systems


Henry Wong


This paper discusses using GA (genetic algorithms) and simulation approach to develop
empirical results for combinatorial networks to identify network node survivability and
total network reliability.


We live in a

society surrounded by networks

social networks, telecommunication
networks, computer networks, highway networks, electric power grids, terrorist networks,
and etc. Networks can take different structures and do evolve into new structures. Given
a budge
t, where the funds should be allocated to optimize the reliability of dismantling
the network? For static networks, the solutions can be found using a mathematical
model. For large scale networks, sub
networks within a larger network, combinatorial
orks, and evolving networks, finding a solution using a mathematical model can be
inefficient or impossible. This research focuses on developing a computer simulation
model using genetic algorithms and AI methods to efficiently search the solution space t
optimally secure or dismantle a network or networks of networks.

Our economy is heavily dependent on our infrastructure

airports, trade ports, trains,
highways and telecommunication system. What happens to our economy when one of
these infrastructure
s suffers a terrorist attack, similar to the 9/11 event? To prevent such
an attack, we have to efficiently identify the survivability of each network node and total
reliability of a network when impacted by crippled nodes. We need to efficiently allocate

resources to secure nodes which can indirectly impact the total reliability of the network.

In the inverse, we can efficiently dismantle a terrorist cell, identifying the impact of the
cell’s reliability and node (terrorist) survivability.


The research plan is to search the solution space and develop empirical results for
different structures of networks and/or networks of networks. The research method
consists of


Graph Model
: the network is depicted using a graph model with nodes a
nd edges.

Let G = (V,E) with node set V and edges set E


Mathematical Model

Overall reliability can be determined by the size of connected components
which survive.

Probability of survivability for each node [3]


: The GA (genetic algorithms) creates an
d evolves an encoded population of
potential solutions so as to facilitate the creation of new feasible members
(solutions) by mating and mutating.

The algorithm will be implemented in a high level programming language such as Java or
C++. The algorith
m will search through the solution space to generate experimental and
empirical results for different graph structures and/or graphs of graphs (network with in a


Star graphs

Wheel graphs

Fan graphs

Cycle graphs

Path graphs

Complete grap

Complete Bipartite


Further research includes:

How we can efficiently restructure a network after it is crippled or partially

For social networks, such as ants and terrorists, how will it reorganize itself [2]?


A s
reorganizing simulation method can be develop to generate these
empirical results

How far does a network need to be dismantled, making it impossible to reorganize


My thanks to Professor Michael Gargano and Professor Fred Gros
sman for advisement and coaching.


[1] Jonathan Farley,
Breaking Al Qaeda Cells: A Mathematical Analysis of
Counterterrorism Operations (A Guide for Risk Assessment and Decision Making).

Taylor & Francis, Volume 26, Number 6 Novemember
mber 2003

[2]Gargano. M.L and Edelson W, M.,
Minimal Edge
Ordered Spanning Trees Solved By
Genetic Algorithms With Feasible Search Space
, Congressus Numerantium 135, 1998,
pp. 37


Jennifer J. Xu*, Hsinchun Chen,
Fighting organized crimes: using short
algorithms to identify associations in criminal networks
, Decision Support Systems 38
(20040), ELSEVIER, pp 473

[4] Goldberg, David E.,
Genetic Algorithms in Search, Optimization and Machine
, Addison
Wesley, Reading, 1989

Vito Lat
ora a,*, Massimo Marchiori,
How the science of complex networks can help
developing strategies against terrorism
, Chaos Soliton & Fractals 20 (2004)69