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    1. Introduction In a standard rolling plant there are three main shops, the foundry, the hot line and the cold line. In the foundry, recycled pieces of aluminum are melted in large furnaces. During this operation, different elements like magnesium or zinc are added to the mixture to obtain a specific alloy. Afterwards, the metal in liquid form is poured into a casting pit to produce ingots. Different dimensions are obtained by changing the casting table. When ingots are solidified and cooled, they are transferred to the hot line. First, they are scalped to eliminate impurities that tend to accumulate on the edges. Then, ingots are heated in homogenizing furnaces to obtain desired mechanical properties and to prepare them for the next operation, where they are rolled in a hot mill at near 6000C. This operation reduces their thickness to a fraction of an inch and produces long sheet coils. In the cold line, coils are processed by different machine centers, like the cold mill, annealing furnaces, and tension leveller to obtain their final desired properties. The sequence of operations often depends on the product and can change in course of operations, as different sequences are equivalent. In this paper, we focus on the hot line, in particular the homogenizing furnaces and the rolling mill. A good synchronization between the furnaces and the mill is very important because any waste time on the hot mill is costly in terms of productivity and energy savings (as the mill must be maintained at the right temperature). On the other hand, the production must satisfy quality standards. Therefore, a good trade-off between quality and efficiency must be found. To  complicate the  matter,  the  process  imposes  specific 23562
    constraints on  the  solution.  Some  must  absolutely be
    satisfied  (hard  constraints),  while others can be relaxed  by
    adding penalties to  the  objective  (soft constraints,  prefer-
    ences).  The goal is to find a good compromise  among  these
    conflicting  objectives,  while  satisfying  hard  constraints.
    The  following Section 2  describes  the  problem under
    study.  Then,  a short  literature  review  is presented  in Section
    3,  followed by a description  of  our heuristic  algorithm  in
    Section 4.  Numerical results are  reported in  Section 5.
    Finally,  the conclusion  is presented  in Section  6.
    2. Problem description
    In a standard  rolling  plant,  ingots  are  casted  in the foundry,
    rolled into coils on  the hot  line and then rolled at  room
    temperature  on the cold  line. The hot line  contains  two main
    machine  centres:  one with  the homogenizing  furnaces  and  the
    other  with  the  mill,  in  that  order.  They  are  described  as  follows:
    2.1. Homogenizing  furnaces
    The goal of homogenization  is to thermically  treat  ingots  to
    obtain  desired  mechanical  properties  and  to have  them  at  the
    right  temperature  for the hot rolling  operation  that follows.
    The heating  time varies  a lot and can take between 10 and
    50  h,  depending  on  the homogenization  code and furnace
    type. Each  ingot has its own code and all codes in a batch
    must be  compatible. The code with  the  longest duration
    determines  the batch code and the heating  time. Although
    this  is not ideal,  ingots  can also be kept  longer  in the  furnace
    as long as a predefined  maximum  time associated  with each
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