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11
votes
1answer
82 views

CPLEX allows manually inserted solutions to violate lazy constraints

I am using CPLEX 12.9 to solve a mixed integer linear programming problem. Some of my constraints are enforced through a legacy LazyConstraintCallback. Heuristic solutions are inserted through a ...
7
votes
1answer
158 views

Floating points in ORtools

I'm trying to solve an RCPSPDc model (maximizing the net present value instead of a makespan). The objective function is: $\sum\limits_{j \in \text{Tasks}} e^{-\theta\cdot s_{j}}\cdot p_{j}$, where $...
10
votes
2answers
302 views

Current Issues of Interest

What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
6
votes
1answer
101 views

GUROBI Re-optimize a model

(For Linear Programming) I am aware of CPLEX's reoptimize methods. If I am not wrong, if you solve a problem and after that you add a new constraint, then you can call the reoptimize method for not to ...
11
votes
1answer
150 views

k-means/k-medoids Clustering Implementation in CPLEX Java

I am trying to model a grouping algorithm as k-means clustering problem, by referring to the general definition as mentioned in Wikipedia. In my system, I have $N$ nodes that I want to group in $m$ ...
8
votes
0answers
53 views

Which Constraint solver is extensible to CSP algorithms?

I am novice to constraint programming and I need to implement the following algorithms. Backtacking Conflict-based backjumping AC partial lookahead MAC Forward checking Forward checking + dom ...
14
votes
2answers
170 views

Customer clustering to solve very large-scale VRPs

I am looking for references that used customer aggregation to solve large-scale Vehicle Routing Problems. By aggregation, I mean clustering the customers together and representing them with one node ...
10
votes
1answer
99 views

RCPSP minizinc model

I'm working on a resource‐constrained project scheduling problem (RCPSP) in Minizinc but I have problems with the running times when the dataset is big (like 400 jobs, 2 resources, 1,000 precedences, ...
7
votes
1answer
76 views

Variant of job shop scheduling problem

I'm looking to identify a problem in the literature that I'm currently solving. I have a set of jobs each having a set of operations. Each operation has a duration. An operation may be done by a ...
8
votes
1answer
82 views

Complexity comparision between purely BLP and MILP problems?

Could someone please comment and answer on the complexity of purely binary linear programming (BLP) and mixed-integer linear programming (MILP)? In MILP, we have both binary and continuous variables ...
9
votes
1answer
97 views

How to remove or replace sub tour elimination constraints in the VRP variant models?

In many of vehicle routing problems variant (VRP), which can be formulated using MIPs, to avoid creating sub tour, we need to use sub tour elimination constraints (SEC). One of the known SEC is (I ...
4
votes
1answer
112 views

CPLEX Python API

I am trying to run the following optimization problem at Python by using the CPLEX API: $$\min \{x_1 + x_2\ | \ x_1 \geq 3, x_2 \geq 2, 2x_1 + x_2 \geq 9\} $$ I just want to give a matrix of ...
6
votes
1answer
72 views

Interface for Cbc - COIN-OR

I would like to code some IP/MIP models in python and test them with an open-source solver. As of now, I only know the Cbc - COIN-OR open-source solver. I have already tried the or-tools interface, ...
7
votes
1answer
91 views

Design choices on how to implement several algorithms for the same problem

When one is interested in solving a problem but considering different objective functions the choice is easy, a class for problem, a class for solution and a class by algorithm then in the main ...
3
votes
2answers
133 views

Problem with big-M in CPLEX OPL

I have a model for the no-wait flow shop scheduling problem, that utilizes the linear ordering variables, and there is a constraint with big-M. When I implement the model in ...
10
votes
0answers
88 views

Sources to learn about Sample Average Approximation for practitioners

I want to start learning Stochastic Programming, beginning with SAA (Sample Average Approximation) and keeping a practitioner's perspective in mind, i.e. I would like my sources to collectively cover ...
11
votes
1answer
260 views

Metaheuristic to solve general MIPs

Many papers formulate their (NP-hard) problem as ILP or MILP and then show Cplex/Gurobi are unable to solve instances of a certain size. Then they introduce a meta-heuristic solution approach to solve ...
14
votes
3answers
940 views

Branch and Bound Implementation

Branch and Bound (B&B) is a general solution approach to solve combinatorial optimisation problems. I was wondering how B&B is implemented in practice. Although it may be relevant, but I am ...
7
votes
1answer
225 views

Finding the optimal, spatially compact set of grid cells

I have a regular grid of cells, maybe square, maybe hexagonal. Each cell has a numeric value associated with it. How can I find a subset of cells that are: a connected, compact set and have an ...
2
votes
0answers
72 views

Branch and Cut algorithm

Could someone please explain what is the point of this added cut? Also how was it deduced? Could someone please give some examples of this sort? As I've been searching for such examples but did not ...
7
votes
0answers
88 views

Connection between solver and Julia's JuMP Package

I'm looking for ways or tips to connect a solver with the JuMP Package. I started reading the manual of Math Opt Interface (I don't know the right terms, but I'll call it the Backend of the JuMP), ...
5
votes
1answer
157 views

VRP package for R

I work almost exclusively in R and Rstudio, and have found it to be an excellent ecosystem for data analysis and OR, including discrete event simulation, Monte Carlo simulation, MILP, and the ...
8
votes
1answer
80 views

Problem solvable $\Rightarrow$ subproblems solvable if feasible region closed, convex?

Let $c \in \mathbb{R}^n$, $M \subseteq \mathbb{R}^n$ such that the problem \begin{align}P:\quad\min_{x \in \mathbb{R}^n}&\quad c^\intercal x\\\textrm{s.t.}&\quad x \in M\end{align} is solvable....
8
votes
1answer
52 views

Speed of convergence for minimizing Rosenbrock's function

I am minimizing $f(x_1,x_2) = 100(x_2-x_1^2)^2 + (1-x_1)^2$, where I try many algorithms to compare with each other. All of the algorithms find the optimal solution $(1,1)$ quickly, so I am not ...
8
votes
0answers
62 views

Adjusting duals heuristically

I am solving a scheduling problem-to find shifts and task schedules- using column generation. In essence, it is a set covering problem with additional constraints. The problem seems to be that the ...
27
votes
3answers
352 views

What are best practices to make optimization user interfaces intuitive for the user?

For many operations research applications a user will often be in charge of making the final decision and will use the optimization algorithms software as a part of their planning flow. Therefore, ...
5
votes
1answer
370 views

Single KKT solution for a simple problem: proof of being minimizer

I have a very simple problem: $$ \begin{align*} \begin{array}{ll} \min\limits_{x_1,x_2} & -x_1x_2 \\ \text{s.t.} & x_1 + x_2 - 2 = 0. \end{array} \end{align*} $$ The KKT system gives me $x_1^*...
8
votes
1answer
106 views

Why isn't $x_2+x_3+x_4\le 2$ a cutting plane?

In my textbook, to generate cutting planes, they tell you to proceed as follows: A procedure for generating cutting planes: Select a ($\le$) constraint that has only nonnegative coefficients. ...
7
votes
1answer
88 views

Dynamic programming example

I am going to buy a family car at the beginning of the New Year. I am going to stay in the UK for the next 4 years. I am considering the possibility of being a customer of company A which sells ...
10
votes
1answer
246 views

LP sum of variables that are above a threshold

I am trying to code a constraint of the form: $$\sum_i y_i < K\,\text{where}\,\begin{cases}y_i = x_i\quad\text{if}\,x_i>k_i\\0\quad\text{otherwise}.\end{cases}$$ In other words, I want to ...
11
votes
0answers
135 views

Tools to implement branch-and-price algorithms

As far as I know, implementing a branch-and-price algorithm is a task far from trivial. However, there are tools such as SCIP or the BCP framework of COIN-OR that help implement such algorithms. I ...
8
votes
1answer
461 views

Travelling salesman problem with given number of locations to visit

There's a great example here of how to find a solution to the travelling salesman problem: ...
5
votes
2answers
457 views

Integer programming problem

I have the following exercise: Stockco is considering four investments. Investment 1 will yield a net present value (NPV) of \$16,000; investment 2, an NPV of \$22,000; investment 3, an NPV of \$12,...
5
votes
1answer
106 views

How is Big M calculated?

Because of excessive pollution on the Momiss River, the state of Momiss is going to build pollution control stations. Three sites (1, 2, and 3) are under consideration. Momiss is interested in ...
8
votes
4answers
216 views

Disciplined convex programming representation of $x\sqrt{1-x}$

Anyone have an idea for a disciplined convex programming (DCP) representation of the concave function $x\sqrt{1-x}$, which is defined over the domain $[0,1]$? The Taylor series about $x=0$ is $$x - \...
4
votes
3answers
605 views

Shortest path problem

At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine $i$ years old is given in Table 5. The cost of purchasing a machine at the beginning of each year is ...
4
votes
2answers
303 views

Shortest path problem with boxes

A company sells seven types of boxes, ranging in volume from 17 to 33 cubic feet. The demand and size of each box is given in the following table. The variable cost (in dollars) of producing each box ...
7
votes
2answers
156 views

How can I implement a user-written lazy constraint callback in concert CPLEX with C++?

I am trying to implement a user-written lazy constraint callback in concert CPLEX with C++. Although I know there exists a way to implement callbacks in concert CPLEX with C++ via macros, I am looking ...
6
votes
0answers
55 views

Why does PuLP call copy for addition and how can I avoid it?

Using a for loop to append terms to an expression seems to be much faster than summing a group of terms all at once. Constructing the expression using a for loop uses __iadd__, which does not include ...
4
votes
2answers
83 views

Can I export to .cpo file using OPL?

I have a model written in CPLEX OPL. Is there a way to export the model to .cpo extension? In Python ...
3
votes
0answers
58 views

How can I do this in GAMS?

I am mimicking a GAMS model that was introduced in Soler et al. (2013)1 to compare my new model with its results. In a nutshell, assume we have a variable $t$ that is supposed to only take certain ...
6
votes
0answers
101 views

Cplex is stuck after root node relaxation solution

I am solving an MIP through Benders decomposition (coded both generic and legacy callback versions), by employing Java with Cplex 12.9. For some of the instances, Cplex is stuck for two hours (time ...
5
votes
0answers
51 views

Understanding HardRouteConstraint

I am trying to understand the route constraints in jsprit. While I got the concept of HardActivityConstraint, I am unable to have clarity on HardRouteConstraint. Can someone, preferably with a simple ...
8
votes
1answer
98 views

Equivalence of formulations

I have a simple model such as: \begin{align}\max&\quad z=X_1+X_2+X_3+X_4\\\text{s.t.}&\quad y_1+y_2+y_3+y_4=2\\&\quad X_1 \leq y_1\\&\quad X_2 \leq y_1+y_2\\&\quad X_3 \leq y_2+...
13
votes
4answers
972 views

Implementation gap in logistics

Typically OR-projects steps are: observing a situation, modeling it, solving the model, implementing the solution, and evaluating the situation. In the area of production and logistics, the models ...
4
votes
2answers
117 views

Solving a non-linear non-convex mixed-integer program

The optimization problem that I am dealing with is very similar to this example. In brief, I have some decision variables that can take real values with lower/upper bounds, and some other variables ...
12
votes
2answers
723 views

How to choose between high number of binary variables or fewer number of integer (not only 0 and 1) variables in a IP formulation?

When I have to write the formulation of an IP, I usually have the choice between writing $i\times j$ binary variables with two indices such as $ x_{i,j} $ or, writing $j$ integer variables $x_i$. Is ...
8
votes
1answer
136 views

Integrating genetic algorithm (or other heuristic methods) with CPLEX

[Topic to discuss GA and CPLEX] I've seen some papers trying to integrate genetic algorithm with CPLEX, such as here and here. Although they integrated both, it is done in 2 different steps; that ...
8
votes
2answers
234 views

How can I transform this MILP into an LP problem?

I have a MILP problem with one of the constraints is given below. Sometimes, even for a small-sized problem, the solver takes a very long time to find a solution. What could be an efficient ...
12
votes
2answers
137 views

Dual bounds of integer programming problems

I often read in papers when branch-and-X algorithms are used to solve mixed integer programming problems, that the lower bound (in the minimization case) obtained from solving a linear programming ...

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