a new algorithm to solve apparently unsolvable ...

A NEW ALGORITHM TO SOLVE APPARENTLY UNSOLVABLE PROBLEMS (with nuclear examples)

Dr. Bhaskar Mukherjee Australian Nuclear Association

ANA Public Lecture 15 August 2002, Lucas Heights, Sydney

Voyage of Mr. Charles Darwin aboard HMS Beagle During 1831-36 Charles Darwin, a 21y old English naturalist embarked on a round-the-globe expedition aboard the research vessel HMS Beagle Darwin circumnavigated the GLOBE twice and visited many remote places (Katoomba, Bl. Mtn !!) of the world Darwin studied plants and animals everywhere he went, kept a meticulous log, collected fossils and rock samples for further analysis

Darwin’s Findings and the Birth of Theory of Evolution Upon his return to England and after 23 years of profound scientific investigation in AD 1859 Sir Charles Darwin published the Origin of Species

The Theory of Evolution was born • All biological organisms have their origin in other pre-existing forms • The organisms evolve through natural selection and adaptation processes to survive in the hostile environment • The organisms produce a large number of offspring, only the fittest individuals survive • The surviving organisms reproduce and evolve and pass on their characteristics to succeeding generations • “Struggle for existence” results in the “Survival of the fittest”.

Application of Evolution Paradigm in Physics & Engineering

A powerful tool to solve complex “multi dimensional” optimisation problems

Example # 1

Example # 2

Example # 3

Example # 4

Example # 5

Example # 6

The Principle of Genetic Algorithm Genetic Algorithm emulates the Theory of Evolution. 1. Random creation of a set of prospective solutions (in the form of binary strings). 2. Deviation of each solution from its true value is tested. 3. The top 5% of the best solutions are selected. 4. The selected solutions are copied and the rest is rejected. 5. Pairs of solution are selected, parts of the strings exchanged and the solution set is replaced by the new solutions. 6. Deviation of each solution from its true value is tested. 7. Steps 2-6 are continued until the “Best Solution” is found.

The Recipe for a PERFECT Family Pastry

1) Add right quantity of cake-mix with flour 2) Add right quantity of egg yolk 3) Add right measure of water to make dough

The baking process is successful when all the following conditions: 1) and 2) and 3) and 4) and 5) and 6) and 7) and 8) and 9) and 10) are met and make “every” family member SATISFIED

4) Add right amount of chocolate powder 5) Divide the dough in equal portions 6) Bake at right oven temperature 7) Bake for right duration 8) Decorate the pastry nicely 9) Keep the cost low 10) Keep quality high

GLOBAL OPTIMISATION of a function of 10 Independent Variables

Neutron Spectra Unfolding Technique Using a Genetic Algorithm A Neutron Spectrum is represented by the Fredholm’s Integral Equation of 1st kind (Eqn 1) :

Where, Ci = Count Rate of the ith BS , (E) = N-Fluence, Ri(E) = BS Resp. Matrix There is NO Unique Solution of Eqn 1

but There is ONLY ONE Neutron Spectrum

Fredholm’s Equation in Matrix Form (Eqn 2)

Normalisation Factor (Eqn 3)

The Fluence Vector was optimised by varying the N-Factor using a Genetic Algorithm Manipulation a (80x10) and three (0x10) Matrices is a daunting task. The GA (BONDI-97) made it in just 600 seconds by using the “Family Pastry Recipe” Paradigm

Applications of Bonner Sphere Neutron Spectrometer TRIUMF 1989 Type: Active BSS Unfolding Code: LOUHI 78 Application: Validation of Shielding Materials for the TR13 Self-Shielded Medical Cyclotron

NASA 1993 Type: Passive BSS Unfolding Code: SAND 2 Application: Assessment of Cosmic Ray induced Neutron Dose in Space Shuttle Columbia

Passive Bonner Spheres using TLD for Aerospace Dosimetry Atominstitut, Vienna Technical University

Set of Passive Bonner Spheres TLD Reader developed at ATI Vienna TLD Capsule A Genetic Algorithm based TL Glow Curve Analysis Program (TGAGA-01) has been developed

Proton Beam-Spill Simulation Experiment at 500 MeV H- Cyclotron operated by TRIUMF (UBC, Canada)

Beam-line Maintenance Cave Neutron Source: A 500 MeV Proton beam hits a Steel VAT-valve Neutron Spectrum was simulated with the FLUKA Monte Carlo Code The real Neutron spectrum was unfolded with a Bonner Sphere Spectrometer and the BONDI-97 Genetic Algorithm Code

Detail View of the Main Experimental Hall of the TRIUMF Cyclotron Vault

Pb-Beam Dump (A Spallation Neutron Source)

Meson Hall

Main Beam-line (Heavily Shielded)

Neutron Spectrum Measurement during a Simulated Beam Spill Concrete Slab Shielding

Bonner Sphere Spectrometer

A 500 MeV Proton beam hits the VAT-Valve Monte Carlo Simulation of the Neutron Field

(thematic mapping of neutron DE rate)

Results and Data Analysis Unfolded Neutron Spectrum near the Concrete Slab Shielding

Important Neutron Field parameters derived from the Unfolded Spectrum Dose Equivalent Derived from Neutron Spectrum

Dose Equivalent Recorded by REM Counter

Neutron Spectrum gives a more realistic value of Dose Equivalent

SUMMARY AND CONCLUSION Genetic Algorithm (GA) is based on “Evolution Strategy” (survival of the fittest) prevalent in the nature GA is inherently a “parallel processing technique” suitable to solve complex non-linear problems and ideal for searching for a “global optima” in a “multidimensional solution space” GA is a “robust mathematical tool” and requires a minimum computing power GA has been used to solve “neutron spectra unfolding problem” of various High Energy Particle Accelerators, relevant to radiological safety assessment GA is highly flexible, it allows to include different types of detectors (i.e. 3He, 6LiI, foil-activation, proton recoil, TLD) as a single, “vastly diversified” and “powerful” spectra unfolding device.

SUMMARY AND CONCLUSION (cont.) Some major applications of GA in Applied Nuclear Science are: Cost-Benefit Analysis of Nuclear Installations and ALARA Analysis Unfolding of Cosmic Ray Neutron Spectra at High Altitude and Interplanetary Space (with Professor N Vana, ATI Vienna) Deconvolution of TLD Glow Curves irradiated with Neutrons and Heavy Ions Optimisation of Radiological Shielding for Medical Cyclotrons Job Scheduling for Air Crew and Flight Attendants to Minimize the Cosmic Ray Exposure (with Mr R Alsop, ANA) Optimisation of the Brachytherapy Dose Planning for Prostate Cancer Patients (with Dr P Cross, St Vincent’s Hospital)

The Genetic Algorithm had emerged from Darwinian Evolution  Paradigm. It can solve  Most Complex Problems of Modern Physics  and Engineering with Elegance and Ease.