本文共 2280 字，大约阅读时间需要 7 分钟。

1. callback函数的定义

所谓callback函数，即应用以参数的形式传入API的函数。cplex的callback分为3种：

1. Informational callbacks：不干涉优化过程，仅获取信息。
2. Query callbacks（也叫diagnostic callbacks）：与优化过程相互交涉的获取信息过程。
3. Control callbacks：会改变优化过程的函数。

下面是

2. MIP control callback案例分析

本文案例是一个location问题，有4个备选仓库，9个客户，$x_1$~$x_4$表示是否选择这4个仓库，启用仓库有启动成本。$y_{ij}$表示仓库与客户之间的距离，运输有成本。每个客户只能从一个仓库供货；每个仓库的库存量有限。

# Given a set of locations J and a set of clients C# Minimize#   sum(j in J) fixedCost[j]*used[j] + sum(j in J)sum(c in C)cost[c][j]*supply[c][j]# Subject to#   sum(j in J) supply[c][j] == 1                    for all c in C#   sum(c in C) supply[c][j] <= Capacity[j]* used[j] for all j in J#               supply[c][j] <= used[j]              for all c in C, j in J#               supply[c][j] in { 0, 1 }             for all c in C, j in J#                    used[j] in { 0, 1 }             for all j in J

3. 自定义UserCutCallback

我们可以在主问题中不添加第3条约束，而把它作为UserCutCallback。代码如下：

import sysfrom cplex.callbacks import UserCutCallbackfrom docplex.mp.callbacks.cb_mixin import *from docplex.mp.model import Modelclass MyCutCallback(ConstraintCallbackMixin, UserCutCallback):    # Callback constructor. Model object is set after registration.    def __init__(self, env):        UserCutCallback.__init__(self, env)        ConstraintCallbackMixin.__init__(self)        self.eps = 1e-6        self.nb_cuts = 0    def add_cut_constraint(self, ct):        self.register_constraint(ct)    @print_called("--> custom cut callback called: #{0}")    def __call__(self):        # fetch variable solution values at this point.        sol = self.make_solution()        # fetch those constraints which are not satisfied.        unsats = self.get_cpx_unsatisfied_cts(self.cts, sol, self.eps)        for ct, cut, sense, rhs in unsats:            # Method add() here is CPLEX's CutCallback.add()            self.add(cut, sense, rhs)            self.nb_cuts += 1            print('-- add new cut[{0}]: [{1!s}]'.format(self.nb_cuts, ct))

在主代码中如下：

cut_cb = m.register_callback(MyCutCallback)for l in range_locations:    location_used = used[l]    for c in range_clients:        cut_cb.add_cut_constraint(supply[c, l] <= location_used)print('* add cut constraints callback with {0} cuts'.format(len(cut_cb.cts)))m.cut_callback = cut_cb