# Questions tagged [combinatorial-optimization]

For questions about optimization over a discrete solution space.

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### Characterization for total dual integrality

A problem I study reduces to whether the polyhedron $P=\{\mathbf{x}\mid A\mathbf{x}=\mathbf{1}, \mathbf{x}\geq0\}$ is integral ($A$ is a matrix with coefficients in $\{0,1\}$). I know that the ...
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### MAX-CUT: are there any algorithms or codes for classical computers, that cater to this specific case?

I missed the opportunity to ask this on OR.SE by 24 days! I asked it at CS.SE on 6 May 2019 and OR.SE entered Private Beta on 30 May 2019. It's a problem about minimizing a sum of terms that are ...
134 views

### Efficient solver for multiway number partitioning

I am interested in the following problem. The input is a set of $n$ integers, and a fixed integer $k$. The required output is a partitioning of the integers into $k$ subsets, such that the smallest ...
67 views

### How to prove pseudo-convexity of a discrete function?

Given a general function $f:\Bbb Z\to\Bbb R$ is there a simple way to verify whether $f(x)$ is pseudo-convex or not?
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### Assignment problem with batching costs

I am studying an assignment problem with batching costs, and I would like to know if there is a standard name or algorithm for this problem. I know this problem can be formulated as mixed-integer ...
43 views

### How to define a stationary point of the MINLP problem?

As we all know, KKT point and stationary point are well defined when the optimization variables are continuous in the problem. Now, I want to know whether there exist some special points except for ...
102 views

### 0 1 solution of linear programming problem with only equality constraints

I have a linear programming problem $LP$ where all the variables $x_{i}$ take value in $\left[0, 1\right]$ (that is $0\leq x_{i} \leq 1$). All the constraints are as follow: $a_{1}+a_{2}+a_{3}=1$ that ...
164 views

### Implementing benders decomposition using Lazy and User cuts callback of Cplex

I am trying to implement benders decomposition for a simple fixed charge transportation problem for the purpose of learning. I implemented the classic Benders decomposition successfully by adding ...
55 views

### Minimum vertex cover and linear programming 2

This is a modified version of the algorithm that I have proposed here. Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for ...
112 views

### How to improve the solution in ALNS metaheuristic

I am solving the CVRP with Adaptive Large Neighborhood Search (ALNS) . I used the following construction operators: GreedyInsertion and ...
148 views

### A relaxed version of job shop scheduling

I am working on a formulation for a problem that seems similar to the bin packing problem. My problem variables include items that are to be placed in bins, special events that are conditionally ...
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### What's the name of a finite-capacity bin packing problem trying to minimize the weight of the heaviest bin?

I have a fixed number of bins which are themselves weightless. Each bin can hold only a fixed amount of weight. Not all bins have the same capacity. I also have a fixed number of objects each of which ...
72 views

### Does anybody know the complexity of finding a maximum clique in circulant graphs?

I would be interested in knowing if finding a maximum clique in circulant graphs is NP-hard? Does anybody have any pointers or papers to suggest?
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### How to develop a vehicle routing optimization package? [closed]

I would like to know how vehicle routing software optimizes routes? In demos of this software, they provide the optimal (or a good) route in just a few seconds or minutes with several nodes (maybe 50 ...
315 views

### Learning local search operator selection

I'm just reading . The authors use a neural network to solve capacitated vehicle routing problems through iterative generation of tours by solving a price-collecting traveling salesman problem in ...
105 views

### Relaxation and complexity of two formulations

I have two different MILP formulations for the same scheduling problem with the same complexity but with different running times. Why it is recommended to compare the relaxed versions of each ...
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### What kind of job shop scheduling problem is this and how do I solve it?

I have a production planning / scheduling problem, which I believe is a kind of job shop scheduling problem. But I would like to get some input on what kind of job shop scheduling problem it is and ...
512 views

### Can I use 'SCIP' solver for PYOMO?

I have an MINLP problem to solve where I was initially using 'ipopt' solver but the solution was not sticking to 'binary/boolean/integer' domain type for a variable. I am not sure which free solver ...
137 views

### Literature on “simcity-like” problems

As it will become apparent, my field is not operation-research and so this question will sound very naive. I am sorry for that. I have a set of "buildings" that I want to place on a small 2d ...
75 views

### A discrete location problem

I have a discrete optimization problem in which there are some predetermined nodes in the set A. a vehicle must visit them as the traveling salesman problem. there are some other nodes in the set B ...
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### Combinatorial problem in my daughter’s class

In Denmark, a rather substantial amount of work and effort has gone into reducing bullying in the Danish public schools. Many initiatives, which purposes are to strengthen the unity and solidarity in ...
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### Best known results on the flexible jobshop benchmarks

Is there a website that compiles the best known results on the flexible jobshop problem ? I know there was a blog post/article by Quintiq, a (deleted) blog post on CP Optimizer, some more recent ...
182 views

### implementation of heuristics using C++ to solve operations research problems

can anyone suggest some good books with the implementation of heuristics and matheuristics using C++ to solve operations research problems especially routing problems such as TSP and VRP. also, I need ...
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### distance specific constraint

I have some points with determined coordinates $(a_i,b_i)$. A vehicle can move between these points based on rectangular distance. In more detail, we consider that the path between points is an ...
115 views

### How to represent time window as constraint in a vehicle routing problem

Hi I am trying to solve a vehicle routing problem using Tabu search, I have successfully completed implementation of constraints for CVRP by giving penalties to objective function , how do I implement ...
370 views

### Branch and Price Algorithm

Can branch and price be a good solution approach for a routing problem with min-max objective function? For example, minimizing the max length of any vehicle route in a VRP. In the literature, I haven'...
157 views

### Strong MIP formulations for a large-scale mixed-integer nonlinear feasibility problem

I'm trying to construct a strong MIP formulation for the following integer nonlinear feasibility problem. Informally: We have a $m \times n$ decision matrix of binary variables Each row of the matrix ...
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### How to combine wires into a cable maximizing cable length while minimizing waste?

A customer brought us this problem and we're looking for ideas to help them. It seems to be a flavor of cutting-stock but without the demand profile. They have varied length spools of different types ...
166 views

### Column Generation algorithm

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. but there is a point in calculating the arrival time of the vehicle in each node. the ...
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### Column generation approach for CVRP

I want to use a column generation based heuristic to solve a capacitated Vehicle Routing Problem. I know the basics of the algorithm but I don't have much experience in coding. is there any code about ...
108 views

### A Question on A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet

I am reading A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet to learn the column generation approach, but I have a problem. in section 3.3 ...
204 views

### Column Generation algorithm for vehicle routing problem

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. In more detail, I want to minimize the arrival time of the last vehicle in the depot. I ...
71 views

### How to decide between a inaccurate system and a accurate system with capacity constraints to do a stream of jobs

Let's say you have a list of at most N Jobs to be done which are coming in a stream. There are two kinds of systems that can do the job: System 1: A very fast system, which however, only does the job ...
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### social network analysis - relations between people with weights

I asked this question on datascience.stackexchange but they directed me here. I have a social network represented as a set of people $S$ and individual weights for each of person (weight is the cost ...
It is well-known that the Glauber dynamics will converge in polynomial time to the Gibbs distribution for, say, the Ising model on a d-regular graph at high enough temperatures $T>T_c$. There are ...