This paper addresses the problem of distributing uniformly the energy flux intercepted by a thermoplastic sheet surface during the infrared radiation. To do so, we discretized this problem and then formulated it as an integer linear programming problem, for which we applied two meta-heuristic algorithms namely the simulated annealing algorithm (SA) and harmony search algorithm (HSA), in order to minimize the corresponding objective function. The results produced by the numerical study we conducted on the performance of both algorithms are presented and discussed.

References

1.
Schmidt
,
F.
,
Le
,
M. Y.
, and
Monteix
,
S.
,
2003
, “
Modelling of Infrared Heating of Thermoplastic Sheet Used in Thermoforming Process
,”
J. Mater. Process. Technol.
,
143
(1), pp.
225
231
.
2.
Monteix
,
S.
,
Schmidt
,
Y.
,
Le Maoult
,
Y.
,
Ben Yedder
,
R.
,
Diraddo
,
R. W.
, and
Laroche
,
D.
,
2001
, “
Experimental Study and Numerical Simulation of Perform or Sheet Exposed to Infrared Radiative Heating
,”
J. Mater. Process. Technol.
,
119
(
1–3
), pp.
90
97
.
3.
Burkard
,
R.
,
Dell'Amico
,
M.
, and
Martello
,
S.
,
2012
,
Assignment Problems
, Society for Industrial and Applied Mathematics, Philadelphia, PA.
4.
Erchiqui
,
F.
,
Nahas
,
N.
,
Nourelfath
,
M.
, and
Souli
,
M.
,
2011
, “
A Metaheuristic Algorithms for Optimization of Infrared Heating Stage of the Thermoforming Process
,”
Int. J. Metaheuristics
,
1
(
3
), pp.
199
221
.
5.
Bachir
,
C. K.
,
Rebaine
,
D.
,
Erchiqui
,
F.
, and
Fofana
,
I.
,
2015
, “
Metaheuristics as a Solving Approach for the Infrared Heating in the Thermoforming Process
,” Université de Montréal, Montréal, QC, Canada, Technical Report No. GERAD-G-2015-139.
6.
Modest
,
M.
,
2013
,
Radiative Heat Transfer
, 3rd ed.,
Elsevier
,
Oxford, UK
.
7.
Reddy
,
J.
,
1993
,
An Introduction to the Finite Element Method
,
McGraw-Hill
,
New York
.
8.
Garcia
,
D.
,
Burret
,
T.
, and
Boutaous
,
M.
,
2006
, “
Procédé De Thermoformage: Simulation De La Phase De La Mise En Température
,”
Matér. Tech.
,
94
(
5
), pp.
355
370
.
9.
Kyun Lee
,
J. E.
,
Virkler
,
T. L.
, and
Scott
,
C. E.
,
2001
, “
Influence of Initial Sheet Temperature on ABS Thermoforming
,”
J. Polym. Eng. Sci.
,
41
(
10
), pp.
1830
1844
.
10.
Hertz
,
A.
,
2005
, “
Les Méta-Heuristiques: Quelques Conseils Pour En Faire Un Bon Usage
,” Université de Montréal, Montréal, QC, Canada, Technical Report No. GERAD G-2005-03.
11.
Koulmas
,
C.
,
Antony
,
S. R.
, and
John
,
R.
,
1994
, “
A Survey of Simulated Annealing Applications to Operations Research Problems
,”
Omega Int. J. Manage. Sci.
,
22
(
1
), pp.
41
56
.
12.
Zong
,
W.
,
2006
, “
Improved Harmony Search from Ensemble of Music Players
,”
Tenth International Conference
, Bournemouth, UK, Oct. 9–11, pp.
86
93
.
13.
Geem
,
Z. W.
,
2008
, “
Novel Derivative of Harmony Search Algorithm for Discrete Design Variables
,”
Appl. Math. Comput.
,
199
(
1
), pp.
223
230
.
14.
Geem
,
Z. W.
,
Kim
,
J. H.
, and
Loganathan
,
G. V.
,
2001
, “
A New Heuristic Optimization Algorithm: Harmony Search
,”
Simulation
,
76
(
2
), pp.
60
68
.
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