Questions tagged [combinatorial-optimization]
For questions about optimization over a discrete solution space.
114
questions
3
votes
1answer
11 views
How to define the upper bound for a binary expansion of a slack variable in Quadratic Unconstrained Binary Optimization (QUBO) models?
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 ...
3
votes
0answers
43 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 ...
-1
votes
0answers
44 views
Combinatorial Analysis : How can I demonstrate the following proposition [closed]
I have to demonstrate the following proposition, but I cant figure out how I might start with it.
Can anyone please help me demonstrating the following mathematical proposal :
The number $g_{s}$ of ...
0
votes
0answers
52 views
How to calculate the time complexity of a Heuristic Algorithm?
I have a binary integer programming problem.
I solve it with a heuristic approach.
How can I calculate the time complexity of the heuristic algorithm?
7
votes
1answer
87 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?
1
vote
2answers
81 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
votes
1answer
63 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 ...
7
votes
0answers
89 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
votes
2answers
77 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 ...
1
vote
1answer
145 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
votes
1answer
70 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?
4
votes
1answer
179 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
votes
1answer
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 ...
3
votes
0answers
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 ...
3
votes
1answer
195 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 ...
1
vote
1answer
57 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 ...
4
votes
1answer
113 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 ...
3
votes
2answers
210 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 ...
7
votes
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 ...
4
votes
1answer
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?
1
vote
2answers
98 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:}...
6
votes
1answer
189 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 ...
3
votes
1answer
31 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 ...
2
votes
0answers
63 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
votes
1answer
111 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
votes
1answer
64 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 ...
-4
votes
1answer
69 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
votes
1answer
139 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
votes
2answers
63 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
votes
0answers
63 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
votes
1answer
97 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 ...
1
vote
0answers
26 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 ...
2
votes
1answer
66 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
vote
0answers
62 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}...
1
vote
0answers
96 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 ...
6
votes
4answers
376 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 ...
3
votes
2answers
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 ...
0
votes
1answer
88 views
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 ...
7
votes
2answers
612 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 ...
6
votes
1answer
138 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 ...
1
vote
1answer
76 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 ...
23
votes
3answers
3k views
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 ...
3
votes
0answers
79 views
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 ...
2
votes
2answers
183 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 ...
2
votes
1answer
60 views
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 ...
4
votes
1answer
120 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 ...
6
votes
2answers
386 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'...
7
votes
1answer
160 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 ...
1
vote
0answers
69 views
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 ...
4
votes
1answer
172 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 ...
