In a nuclear reactor there are fuel rods of different ages. At the end o=
f each fuel cycle, the oldest rods are moved to a spent fuel pool and are r=
eplaced by fresh rods. At this point, it is possible to make reallocate rod=
s in the core leading to a combinatorial problem. This problem may be model=
ed as a Mixed Integer Nonlinear Problem (MINLP). The model includes depende=
nt variables that describe physical properties such as neutron flux, burn-u=
p, and yield. The neutron transport equations are converted to a set of alg=
ebraic equations using Green's functional theory, giving rise to a stationa=
ry description of the neutron flux in the core. The fuel burn-up is a=
pproximated by discretizing the differential equation.

More physically accurate models are solved with Meta-heuristics search m=
ethods. There for each given reloading pattern the neutron flux etc. are ca=
lculated by the numerical solution of the relevant differential equation.

There is a symmetric problem to optimize the unloading process of fuel r=
ods. The operations to determine are the placements of rods in the spent fu=
el pool and to optimize the manipulations of rods in the pool by automated =
handling systems.

**References**:

[1 ] T. O. Sauar. Application of Linear Programming to In-Core F=
uel Management Optimization in Light Water Reactors. Nuclear Science and En=
gineering (1971), Volume 46, Number 2. Pages 274-283.

[ 2] E. de Klerk, C. Roos, T=
. Terlaky, T. Illes, A.J. de Jong, J. Valkoc, J.E. Hoogenboom. Optimization=
of nuclear reactor reloading patterns. Annals of Operations Research Janua=
ry 1997, Volume 69, Issue 0, pp 65-84

[ 3] A.J. Quist. Application=
of Mathematical Optimization Techniques to Nuclear Reload Pattern Design. =
Ph.D. Thesis, T. U. Delft 2001.

[ 4] Opti=
misation de la gestion du combustible dans les reacteurs CANDU refroidis a =
l'eau legere. These de doctorat Ecole Polytechnique de Montreal (200=
6).

[5] E. Rachelson. The Optimal Swapping Problem=
during Nuclear Refueling Operations. ROADEF 2014, February 2014. Bordeaux =
(France).

#### Software:

XIMAGE - Interactive Loading Pattern Design (Studsvik)

**Contributors**:

Prof. Christoph Helmberg, TU Chemnitz

Prof. Etienne de Klerk, Tilburg University

Dr Thomas Triboulet, EDF

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