Questions tagged [combinatorial-optimization]

For questions about optimization over a discrete solution space.

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44 views

Building blocks for unimodular matrices

I read Chapter 19.4 of Schrijver(1986) and get to know that every totally unimodular matrix can be produced by taking operations on network matrices and two certain matrices. I find that some paper ...
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1answer
137 views

Bin Packing with CP Solver

[ [0,5], [0,4], [1,6], [2,4], [3,6], [3,2], [4,5], [5,5], [6,4], [7,3], [8,2], [8,3], [9,5], [10,3]] ...
6
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2answers
318 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 ...
4
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1answer
89 views

Lot-sizing problem variant

I have a the following optimization problem: I have mandates,(e,g. to deliver 100 tonnes of products) that I need to schedule its delivery during the month (day 2: deliver 40 Tonnes, day 15: deliver ...
5
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4answers
406 views

Solving Capacitated VRP with multiple various sized vehicles

I am looking to form a Capacitated VRP problem like this: I have 40,000 dropping locations with Demands of each point available I have 5-6 types of vehicles available with different capacities and ...
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0answers
85 views

How to approach this Truck Utilisation problem?

The problem statement currently I have is very broad (or you can say very vague at the same time): I have a number of dropping locations (Customer locations) I have the location of the HUB I have a ...
5
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2answers
484 views
5
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2answers
477 views

Combinatorial optimization, implementation needed

I have k sets of items. I want to choose n items from each set, $n \cdot k$ items total. I would like to choose the $n \cdot k$ items under some optimization criterion, e.g. that the sum of the $\...
0
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0answers
49 views

Lower bound very bad. How to improve?

I have the following MILP: \begin{alignat}{2} \nonumber \mbox{minimize } \quad & \phi = \sum_{i=1}^{m-1} \sum_{f=1}^{F} \sum_{\underset{\bar{f} \neq f}{\bar{f}=1}}^F \sum_{h \in H} \left( D_{f \...
4
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1answer
154 views

Why are the bounds 3 and 6 instead of 7, in this binary expansion of a slack variable in this QUBO problem?

I've recently started to study how to formulate optimization problems as QUBO models through this paper/tutorial: https://arxiv.org/pdf/1811.11538.pdf One of the steps is to transform the inequalities ...
4
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3answers
268 views

Is there a Bin Packing Library similar to TSPLIB?

I have concluded there is not, or if there is it's not openly published? I am trying to identify if there are "top solutions/formulations" for the 3d BPP. Looking to apply in a parcel ...
3
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0answers
58 views

Linearization of a quadratic model, what is the difference while using gurobi?

I have a quadratic model of parking $N$ cars in $S$ separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ...
7
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1answer
93 views

Terrain Ruggedness Index for optimization problem

If I want to study the smoothness of the energy landscape of a cost function, is there any metric similar to Terrain Ruggedness Index used in geology?
7
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4answers
402 views

Learning local search operator selection

I'm just reading [1]. 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 ...
1
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2answers
97 views

Combinatorial Optimization Problem using IBM ILOG CPLEX

Consider the combinatorial optimization problem described as below. Let $D=(V,A)$ be a directed graph with $V$ the set of vertices and $A$ the set of arcs, i.e., $A=\{(i,j)\mid i,j\in V\}$. On each ...
2
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1answer
64 views

Finding the minimum of a group of timings

I would like to seek some modeling advice on the following: Say for instance I have 5 nodes representing workstations of the operation of 5 jobs, and that I have less than 5 vehicles. Say I have two ...
5
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0answers
117 views

Maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider sub-vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of ...
7
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93 views

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 ...
5
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2answers
93 views

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 ...
2
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1answer
184 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 ...
4
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1answer
72 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?
3
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1answer
257 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 ...
4
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1answer
187 views

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 ...
2
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1answer
44 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 ...
4
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1answer
120 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 ...
1
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1answer
61 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 ...
7
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4answers
1k views

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 ...
3
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2answers
310 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 ...
4
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1answer
74 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?
2
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2answers
100 views

Should I process the data or add a new constraint to achieve the target?

I have an MILP as below $\begin{equation} \begin{array}{*{35}{l}} \underset{d_{u,c}}{\max}\hspace{1mm}\hspace{1mm}\sum_{u=1}^{U}\sum_{c=1}^{C}d_{u,c}\omega_{u,c}\\ \text{}\text{subject to }\text{ C1:}...
3
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1answer
185 views

Formulation of Assignment problem as integer programming

We need to maintain as quickly as possible a complex system. In particular, we need to replace six of its components $\{P_1,\ldots,P_6\}$. We have three 3D printers $\{M_1,M_2,M_3\}$ which we can use ...
7
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1answer
194 views

Square packing variant

I saw the following problem and was looking for references about the problem. The problem is stated as “The green field is the empty area, the dark green 2x2 blocks are trees and the grey area is the ...
4
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1answer
35 views

Finding an augmenting path or cycle in weighted graph

Suppose we are given a (simple) graph with non-negative edge weights, along with a matching $M$, which may or may not be max weight. I know that $M$ will be max weight if and only if the graph does ...
7
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2answers
876 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 ...
2
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0answers
68 views

Materials or sample code for column generation book (GERAD 25th Anniversary Series)

As far as I know, one of the interesting resource to learn the basic concept of the decomposition methods is column generation book (GERAD 25th Anniversary Series), which has been mentioned in some ...
4
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1answer
113 views

k -MST problem based on Miller-Tucker-Zemlin subtour elimination constraints

Where can I find the formulation of the $k$-MST ($k$-minimum spanning tree) problem as (mixed) integer linear program based on Miller-Tucker-Zemlin subtour elimination constraints (MTZ)?
4
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1answer
69 views

Does the facility layout problem with zero and one matrices have a specific name?

I have an facility layout problem where the flow between any two departments is either zero or one. Also the distance between each location pair has the same nature (zero or one). I am curious whether ...
7
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1answer
461 views

Minimum vertex cover and linear programming

Suppose we have a graph G. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex $v_{i}$ we have the variable $x_{i}$, for each edge $v_{i}...
-4
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1answer
71 views

How to change a function from Min(F(x)) to -Max(-F(x))?

I have not a good knowledge in math field, I am working on multi objective functions, and I have two maximization functions, and one minimize function, where: Max (X,Y) = X+Y Max (L,M) = Sum (LC + MD)...
5
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1answer
164 views

0-1 knapsack with non-linear objective function

There's efficient algorithms for solving the 0-1 knapsack problems when the objective function is just a sum of profits. I am dealing with the following problem with non-linear objective function: $$\...
2
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2answers
68 views

Parallel scheduling with precedence constraints and variable job length

I have $N$ jobs and $M$ machines and want to minimize the makespan, i.e. the total time to finish all jobs. Some jobs have precedence constraints and can only be started once other jobs are finished. ...
3
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0answers
71 views

Optimal Seat Allocation Problem

I have to do an operations research assignment based on optimal seat allocation. The problem goes something like this. There are 5 rooms in an office each with a separate seating capacity. We now have ...
3
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1answer
103 views

What are the flow based formulations?

What are the flow-based formulations? For what optimization problems are they applied, and in which form? Which are the specificities of such a formulation? Also, the same question for the time staged ...
2
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1answer
68 views

Maximum bipartite matching with breakpoints in edge weight function

I am looking for an analogy to the problem I am facing or better yet a paper or even code. I have: Nodes from set A and B. Edges are from a single A to many B. I am framing a max bipartite matching ...
1
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0answers
27 views

MILP formualtion for Two-level minimum dominating set (MDS) problem?

I'm working on an optimization problem which is kind of finding the minimum dominating set (MDS) or the minimum vertex set (MVS) in an undirected graph. given the MILP formulation for both problems, I ...
6
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2answers
401 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'...
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0answers
65 views

Can I combine two objective functions if they have a relation between them?

I will use a meta-heuristic algorithm, to maximize the following objective functions: Objective function 1 $=\sum\limits_{r=1}^{M} \sum\limits_{s=r+1}^{M} \sum\limits_{j=r+1}^{N} (r_{rj}w_j - r_{sj}...
2
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2answers
190 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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0answers
98 views

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 ...
3
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2answers
108 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 ...