with  their multi-criteria  objective function,  they  exploit
Pareto-optimal  sets. Tang et  al  (2000) model a  steel hot
rolling mill as a multiple  travelling  salesman  problem  and
solve it with a GA. Mayrand  et al (1995) propose another
GA  to  schedule an  aluminum cold  mill  with  different
technological  constraints, while Frontini and Bonhomme
(1999)  describe  a GA for an aluminum  hot line  in Brazil.
4. Algorithm
Our algorithm  can be pided  into  three sequential  steps.
First,  an  insertion  heuristic  (HI) creates  blocks while  taking
care  to  balance the  workload on  the  furnaces. A  first
sequence  of blocks on the mill  is then created  with another
insertion  heuristic  (H2). Finally,  this sequence  is improved
by eliminating  some parts of  it and by using heuristic  H2
again  to reconstruct  it. The main  steps  of this algorithm  are
summarized  in Figure 1.
Objective  function
The  objective  is  twofold  and  involves  minimizing  the  hot mill
idle  time  (in  percent of  total  time)  and  the  penalties
associated  with unsatisfied  preferences.  Due date considera-
tions are included  in  the  latter as  'negative penalties' or
rewards  for scheduling  orders  on time  (see below). The two
objectives are  weighted  and  aggregated into  a  single
objective  function  f,  using weighting  parameters  w, for idle
time and Wp  for penalties,  that  is
f =
wp * Penalty +
wI
* IdleTime  (1)
The weighting  parameters  are  very  important  because  even
small variations  in  their values can drive the  search  in  a
different region  of  the  solution  space. We  exploit  this
property by  generating many  solutions  using  different
weights  (see Section  4.4, for more details).
Penalties
The standard  penalties  are those already  mentioned  in the
previous section for modelling the preferences  associated
with the furnaces  and the mill. Given that only a subset  of
orders  can be scheduled  during  a roll  life, orders  that  are  left
apart  should  also be considered  when  evaluating  the quality
of  a  schedule. Otherwise,  some orders  could be  left apart
forever because their  inclusion would  lead  to  a  serious
degradation  of the  current  schedule.  Consequently,  there  are 摘要本文提出一种启发式算法调度的热轧机铝行业。一个问题是均质化炉之间的紧密耦合,轧机设计哪些需要集成到启发式。还考虑标准技术约束像合金硬度转换、轧辊磨损,均质化代码的兼容性和宽度转换。目标是最小化轧机和空闲时间　　处罚软约束违反与生产质量有关。启发式分为两个阶段。首先,批锭炉构造，这些批次,称为块,然后测序机。数值结果报道来自真实的数据测试实例。
关键词: 生产 制造　调度 测序 启发式方法 热轧机的趋同性 炉
目录 
摘要    1
1 介绍    3
2 问题描述    4
2.1 均质化炉    4 启发式算法热轧机铝英文文献和中文翻译(6):http://www.youerw.com/fanyi/lunwen_16688.html