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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