Gurobi官方实例指南：模型构建、优化与参数调整

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"GurobiDemo.pdf 是Gurobi官方提供的一个实例教程，旨在帮助用户了解和使用Gurobi优化器。这份文档包含了各种示例，涵盖了从基础模型加载、解决到高级特性的使用，如参数调整、自动参数调优、不一致性的诊断和处理、MIP启动、模型数据分离、回调函数等。此外，还提供了C和C++的源代码示例，用于进一步学习和实践Gurobi API的用法。" Gurobi是一款强大的数学优化求解器，广泛应用于线性规划（LP）、整数规划（MIP）、二次规划（QP）以及更复杂的优化问题。以下将详细阐述GurobiDemo中的关键知识点： 1. **模型加载与解决**：Gurobi提供了一种方便的方式来加载和解决从文件中读取的模型。用户可以通过API函数加载模型，并调用优化器来寻找最优解。 2. **构建模型**：Gurobi允许用户从头开始构建优化模型，包括定义决策变量、目标函数和约束条件。用户可以使用Gurobi的API函数创建线性、二次或者更复杂的表达式。 3. **额外建模元素**：除了基本的线性和二次表达式，Gurobi支持多种建模元素，如逻辑约束、特殊 ordered sets (SOS)、二次约束、一般约束等，以处理各种复杂优化问题。 4. **修改模型**：在模型构建完成后，用户可以随时修改模型，添加或删除变量、约束，甚至改变目标函数。 5. **参数调整**：Gurobi有许多参数可以调整，以优化求解性能。例如，可以更改求解器的精度、时限、内存限制等。 6. **自动化参数调优**：Gurobi提供了参数调优工具，能够自动测试不同的参数组合以找到最佳设置。 7. **处理不一致性**：当遇到不可行的模型时，Gurobi提供了诊断工具帮助用户找出问题并修复模型。 8. **MIP启动**：对于混合整数规划问题，MIP启动策略可以利用已知解决方案或部分解决方案作为起点，提升求解速度。 9. **模型数据分离**：在Python中，Gurobi支持模型数据的分离，使得数据管理更加灵活。 10. **回调函数**：回调功能允许用户在求解过程中插入自定义代码，实现定制化行为，如剪枝、分支决策或自定义搜索策略。 11. **源代码示例**：GurobiDemo提供了C和C++语言的源代码示例，涵盖了各种优化问题，如工作调度、设施定位、旅行商问题等，这些示例有助于用户理解如何使用Gurobi API来构建和解决实际问题。通过学习和实践GurobiDemo中的内容，用户将能更好地掌握Gurobi的使用，解决各种实际的优化挑战。无论是初学者还是经验丰富的优化专家，这份文档都是宝贵的参考资料。

double[][][] x = model.get(GRB.DoubleAttr.X, vars);

We should point out one important subtlely in our interface. We use a lazy update approach to

building and modifying a model. When you make changes, they are added to a queue. The queue

is only ﬂushed when you optimize the model (or write it to a ﬁle). In the uncommon situation

where you want to query information about your model before optimizing it, you should call the

update method before making your query.

2.4 Additional modeling elements

Examples: genconstr, multiobj, piecewise, qcp, qp, sos

A mathematical programming model in its traditional form consists of a linear objective, a

set of linear constraints, and a set of continuous or integer decision variables. Gurobi supports a

number of additional modeling constructs. In addition to linear constraints, Gurobi also supports

SOS constraints, quadratic constraints, and general constraints. In addition to a single linear

objective, Gurobi also supports quadratic objectives, piecewise-linear objectives, and multiple linear

objectives. Consult the corresponding examples from the Gurobi distribution for simple examples

of how to use each of these modeling elements.

2.5 Modify a model

Examples: diet, feasopt, ﬁxanddive, lpmod, sensitivity, workforce3, workforce4, workforce5

This section considers model modiﬁcation. Modiﬁcation can take many forms, including adding

constraints or variables, deleting constraints or variables, modifying constraint and variable at-

tributes, changing constraint coeﬃcients, etc. The Gurobi examples don’t cover all possible modi-

ﬁcations, but they cover the most common types.

diet

This example builds a linear model that solves the classic diet problem: to ﬁnd the minimum cost

diet that satisﬁes a set of daily nutritional requirements. Once the model has been formulated and

solved, it adds an additional constraint to limit the number of servings of dairy products and solves

the model again. Let’s focus on the model modiﬁcation.

Adding constraints to a model that has already been solved is no diﬀerent from adding con-

straints when constructing an initial model. In Python, we can introduce a limit of 6 dairy servings

through the following constraint:

m.addConstr(buy[’milk’] + buy[’ice cream’] <= 6, "limit_dairy")

For linear models, the previously computed solution can be used as an eﬃcient warm start for

the modiﬁed model. The Gurobi solver retains the previous solution, so the next optimize call

automatically starts from the previous solution.

lpmod

Changing a variable bound is also straightforward. The lpmod example changes a single variable

bound, then re-solves the model in two diﬀerent ways. A variable bound can be changed by

modifying the UB or LB attribute of the variable. In C:

error = GRBsetdblattrelement(model, GRB_DBL_ATTR_UB, var, 0.0);

We should add a comment on how parameter settings propagate between diﬀerent models.

When we set the TimeLimit parameter on the base model, then make a copy of that model, the

parameter setting is carried over to the copy. When we set the MIPFocus parameter on the copy,

that parameter change has no eﬀect on the other copies, nor on the original model.

2.7 Automated parameter tuning

Example: tune

The next example we consider is tune, which demonstrates the use of our automated parameter

tuning tool. This tool searches for parameter settings that improve performance on a model. While

you would typically invoke the tool through the command line, using our grbtune program, it can

also be invoked from our APIs. We’ll provide only a cursory description of the tool here. We

recommend that you consult the Parameter Tuning Tool section of the Gurobi Reference Manual

for more precise details.

Our tuning example demonstrates a typical use of the tuning tool. You would start by invoking

the tool on a model. In C:

error = GRBtunemodel(model);

In Java:

model.tune();

This routine solves the model multiple times, with diﬀerent parameter settings, to ﬁnd settings

that improve performance.

Once tuning is complete, you would then use GetTuneResult to retrieve the result. In C:

error = GRBgettuneresult(model, 0);

In Java:

model.getTuneResult(0);

The numerical argument indicates which tuning result to retrieve (0 is the best result, 1 is the

second-best, etc.). This routine loads the requested parameter set into the environment associated

with the argument model.

Once the tune parameter settings have been loaded into the model, you can then call Optimize

to use these parameters to solve the model, or you can call Write to write these parameters to a

.prm ﬁle.

2.8 Diagnose and cope with infeasibility

Examples: feasopt, lp, workforce1, workforce2, workforce3

When solving optimization models, there are some situations where the speciﬁed constraints

cannot be satisﬁed. When this happens, you often need to either identify and repair the root cause

of the infeasibility, or alternatively ﬁnd a set of constraints to relax in order to obtain a feasible

model. The workforce1, workforce2, and workforce3 illustrate these diﬀerent strategies.

Starting with the simplest of the three examples, workforce1 formulates a simple workforce

scheduling model and solves it. If the model is infeasible, it computes an Irreducible Inconsistent

Subsystem (IIS). The user can then inspect this information to understand and hopefully address

the source of the infeasibility in the model.

Example workforce2 is similar, except that if the model is infeasible, the example repeatedly

identiﬁes an IIS and removes one of the associated constraints from the model until the model

becomes feasible. Note that it is suﬃcient to remove one constraint from the IIS to address that

source of infeasibility, but that one IIS may not capture all sources of infeasibility. It is therefore

necessary to repeat the process until the model is feasible.

Example workforce3 takes a diﬀerent approach to addressing infeasibility. Rather than iden-

tifying and removing IIS members, it allows the constraints of the model to be relaxed. Like the

feasopt example, an artiﬁcial variable is added to each constraint. The example sets the objective

on the original variables to zero, and then solves a model that minimizes the total magnitude of

the constraint relaxation.

The feasopt example demonstrates another approach to relaxing an infeasible model. It com-

putes a feasibility relaxation for the infeasible model. A feasibility relaxation is a model that, when

solved, minimizes the amount by which the solution violates the bounds and linear constraints of

the original model. This method is invoked as follows:

In C:

error = GRBfeasrelax(feasmodel, GRB_FEASRELAX_LINEAR, 1,

NULL, NULL, rhspen, &feasobj);

In C++:

feasmodel1.feasRelax(GRB_FEASRELAX_LINEAR, true, false, true);

In C#:

feasmodel1.FeasRelax(GRB.FEASRELAX_LINEAR, true, false, true);

In Java:

feasmodel1.feasRelax(GRB.FEASRELAX_LINEAR, true, false, true);

In Python:

feasmodel1.FeasRelaxS(0, True, False, True);

The arguments to this method select the objective function for the relaxed model, the speciﬁc

set of bounds and constraints that are allowed to be relaxed, and the penalties for relaxing speciﬁc

bounds and constraints.

2.9 MIP starts

Example: facility

A MIP modeler often knows how to compute a feasible solution to their problem. In cases

where the MIP solver is slow in ﬁnding an initial feasible solution, it can helpful for the modeler to

provide a feasible solution along with the model itself. This is done through the Start attribute

on the variables. This is illustrated in the facility example.

The facility example solves a simple facility location problem. The model contains a set

of warehouses, and a set of plants that produce the products required in the warehouses. Each

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