טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKaminer Boaz
SubjectA Methodology for Estimating and Optimizing Non-
Independent Layered Defense Effectiveness
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Yoseph Ben-Asher
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

In the published literature dealing with layered defense, it is usually assumed that the layers of defense are independent of each other. Unfortunately real life experience reveals that layered defense does not conform to this assumption. A methodology for modeling the dependencies between defense systems engagements of a single attacker or a salvo of attackers is developed through a model named the "decay function model". The "decay function" model is proposed to estimate the conditional probabilities of engagements based on their dependencies on all prior engagements of the same salvo attack. Modeling the influences necessitate the augmentation of the weapon allocation problem with the additional solution dimensions of location and time. Opportunely these additional dimensions enable the removal of the homogeneous effectiveness assumption.

The Non-Independent Layered Defense Problem (NILDP) is formulated as a Mixed-Integer Non-Linear Programming problem maximizing the layered defense effectiveness subject to linear constraints on the continuous decision variables and binary (allocation) decision variables. The complex nature of calculating the success and failure probabilities, considering the dependencies between interceptors, called for the development of a unique algorithm for computing the objective functions.

Complexity analysis and comparison survey of methods were conducted for the optimization of the objective functions. The Cross-Entropy method attributed to Rubinshtein R. Y. is selected as the most powerful of all heuristics tested against the problem, solving the Mixed-Integer-Non-Linear-Programming in a single simulation run.

Results comparison between existing independent layered defense papers and the NILDP outcomes achieved, prove that the independency assumption fails to accurately predict non-independent layered defense performance. Several results are presented of multi-objective optimization conducted for the ever existing performance duality of effectiveness and cost / efficiency. Several heuristic tools implementable by developers and operators of layered defense are presented, e.g. demonstration of centralized defense planning for non-independent defense systems dominance.

In order to implement the "Influence Decay Function" model, a continuous study resulting in reliable models of the interactions between defense systems is essential. Widening the study on systems influences and interactions consequences will surely allow a more reliable development and deployment of layered defense architectures.