减少优化中替代解决方案的大小
我们有一个供应商/仓库（索引 d）和几个工厂（索引 f），在 T < 期间对不同产品 (p) 的需求已知。未来一个月（指数 t）。有一个卡车车队（索引 v），具有不同的卡车类型（索引 k）（例如，其中一些有冰箱），这限制了仅将某些产品运送到该卡车类型。我们在仓库和工厂之间有一组预定义的路线（索引r）（工厂本身之间存在路线）。
卡车从供应商那里装载货物，并按照预先定义的路线，可以访问多个工厂，最后返回仓库进行下一次装载。一个月内，每辆卡车可能多次将货物从仓库运送到工厂 j 。因此变量 x_{p,k,r,f,n,t} 是类型 v（类型 k）的卡车可以从仓库装载并通过路线 r 运至工厂 f 的产品 p 的数量在时间 t。某种类型的车辆受V_k限制。
计数器 n 是一种卡车类型在一个月内将相同产品、路线运送到同一工厂的次数。目标是最小化总成本。 最简单的情况是车辆走depot -> depot -> 路径。工厂 1 ->仓库->一个月内 1 家工厂。在本例中，我们有两个索引 x_{p,k,r,f,1,t} 和 x_{p,k,r,f,2,t}来区分这两轮。 问题是，这个模型产生了许多替代解决方案。例如，如果我们有 4 辆类型为 k 的卡车，则一种解决方案是（我们称之为解决方案 1）：
x_{p,k,r,f,1,t} = 6
x_ {p,k,r,f,2,t} = 4。
另一个解决方案（解决方案 2）是：
x_{p,k,r,f,1,t} = 4 >
x_{p,k,r,f,2,t} = 6.
Whish 与解 1 基本相同（只是顺序改变）。
随着问题规模的扩大，许多不同的解决方案具有相同的总成本。我们想考虑一种方法来减少解决方案空间（替代解决方案），同时保留所有可能的目标值。
We have a supplier/depot (index d) and several factories (index f) with demand known for different products (p) during T month (index t) ahead. There is a fleet of trucks (index v) with different truck types (index k) (e.g., some of them have fridge) which restricts carrying some products just to that truck type. We have a set of pre-defined routes (index r) between depot and factories (there exists routes between factories themselves).
A truck loads goods from the supplier and uses the pre-defined routes in which multiple factories can be visited, and finally gets back to the depot for the next load. In a month each truck may carry goods from the depot to factory j more than once. So variable x_{p,k,r,f,n,t} is the amount of product p that truck type v (of type k) can load from depot and through rout r take to factory f at time t. The vehicles of a type are limited by V_k.
The counter n is the number of rounds in a month that a truck type takes the same product, route, to the same factory. The goal is to minimize the total cost.
The simplest case is where a vehicle takes the path depot -> factory 1 -> depot -> factory 1 in a month. In this case we have two index x_{p,k,r,f,1,t} and x_{p,k,r,f,2,t} to differentiate these two rounds.
Here is the problem, this model generates many alternate solutions. For example if we have 4 trucks of type k, then one solution is (we call it solution 1):
x_{p,k,r,f,1,t} = 6
x_{p,k,r,f,2,t} = 4.
Another solution (solution 2) is:
x_{p,k,r,f,1,t} = 4
x_{p,k,r,f,2,t} = 6.
Whish is basically the same as solution 1 (just the order changes).
As the problem size enlarges, many different solutions have the same total costs. We would like to think of a method to decreasing the solution space (alternate solutions), while keeping all possible objective values.
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查看 CPLEX 解决方案池以及如何设置其过滤器。
Check out Cplex solution pool and how to set its filters.
这是可用于过滤 cplex 解决方案池的参数：
填充限制（生成的解决方案数量）
检查以下链接：
https://www.ibm.com/docs/en/icos/20.1.0?topic=pool-which-parameters-control-solution
This is the parameter that you can use to filter cplex solution pool:
Limit on populate (number of solutions generated)
Check the link below:
https://www.ibm.com/docs/en/icos/20.1.0?topic=pool-which-parameters-control-solution
您应该添加额外的约束来消除对称性。
例如，
将摆脱一些重复的解决方案
在较小的示例中，例如 zoo 示例，
在 OPL CPLEX 中
可能会导致许多重复的解决方案。
额外的约束
将消除一些
You should add additional constraints to get rid of symmetries.
For instance
will get rid of some duplicate solutions
In a smaller example like the zoo example,
in OPL CPLEX
may lead to many duplicate solutions.
The additional constraint
willget rid of some