Questions tagged [combinatorial-optimization]

For questions about optimization over a discrete solution space.

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3
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1answer
71 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 ...
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0answers
20 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
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1answer
56 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 ...
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0answers
52 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}...
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0answers
46 views

How to treat with equality constraints in whale optimization algorithm? [duplicate]

Whale optimization is one of the metaheuristic algorithms which used to find the optimal solution to unconstrained optimization problems. I have an objective function : $x_1+2 x_2−6 x_3≥0$, subject to ...
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0answers
92 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
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3answers
278 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 ...
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2answers
98 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 ...
1
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1answer
70 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 ...
5
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2answers
177 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
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1answer
124 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 ...
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1answer
67 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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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 ...
4
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0answers
61 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
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2answers
160 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
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1answer
59 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
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1answer
96 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
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2answers
351 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'...
6
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1answer
146 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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0answers
62 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
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1answer
139 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 ...
5
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0answers
74 views

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 ...
3
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1answer
95 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 ...
5
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1answer
191 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 ...
4
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2answers
67 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 ...
3
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1answer
247 views

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 ...
11
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1answer
130 views

Branch and Price algorithm is exact?

I know that the Column Generation algorithm delivers an exact solution when you are solving a linear programming optimization problem. I want to know that, does this column generation approach deliver ...
5
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0answers
41 views

Mixing time exponent above threshold temperature for Glauber dynamics or annealing

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 ...
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0answers
48 views

What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money $m$ to spend over $r$ different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
5
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2answers
149 views

How to linearize a quadratic constraint to add it then via a callback function

Suppose we have a positive continuous variables $0 \le x \le UB$ where $UB$ is a known upper bound. How can we linearize the term $x^2$? Detailled problem: Suppose that via a callback we compute a ...
4
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2answers
251 views

Combinatorial Optimization using AMPL

I want to solve the following integer programming problem using AMPL. The problem is the following (It was already asked on mathstackexchange.com, but I need to know how to solve it using AMPL): Let $...
3
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1answer
138 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 $\{P1,...,P6\}$. We have three 3D printers $\{M1,M2,M3\}$ which we can use to ...
3
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2answers
123 views

Limit number of switches in employee scheduling problem

Here is a scheduling problem I need to solve. Given the demand for 2 positions in 1 week with 3 shifts per position, I need to allocate the employees accordingly with some extra operational ...
4
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0answers
91 views

Can this problem be modelled with a transformation from a known TSP with profits?

The profitable tour problem (PTP) is defined on a graph $G=(V,E)$ with $|V|=n$, where each vertex $i \in V$ has an associated prize $m_i \geq 0$ and each edge $e \in E$ has an associated cost $c_e \...
3
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0answers
49 views

What are the efficient ways to model this scheduling problem and ways to improve running time

There are $N - \{1 \ldots N\}$ jobs, each with processing time $p_j$, to be scheduled on $M - \{1 \ldots M\}$ machines over span of $D - \{1 \ldots D\}$ days and while working $T - \{1 \ldots E \ldots ...
1
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3answers
204 views

Using big M values for a constraint

I want to enforce $x_{i,j}=x_{k,j}\implies z_i \neq z_k$ where $k = i-1$ so I used \begin{align}z_k + 1 - (x_{i,j} - x_{k,j})) \leq z_i \leq z_k - 1 - (x_{i,j} - x_{k,j})\quad\text{for each $j$}\end{...
2
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1answer
166 views

Does this problem fall into any common problem definition…Knapsack maybe?

I am struggling to find a representative problem formulation for this optimization challenge. I have implemented a MILP in Matlab, but the run time is taking more then a day. My goal is to see if it ...
1
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1answer
53 views

Derived variables of when a decision variable appears?

I am dealing with a multi-travelling passenger problem. $x_{i,j}$ is a binary variable that allocate a passenger $i$ to a vehicle $j$, every vehicle can carry only $n_{pv}$ passenger where $i \in \{1,...
3
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2answers
119 views

Could DOcplex.CP recognize that it solves the graph coloring minimization problem?

I created a graph coloring DOcplex.CP model inspired by this example. However, I do not know the number of colors in advance. The goal is to minimize the number of colors (i.e., get as close as ...
2
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1answer
67 views

Same values constraint and grouping of variables

In a linear program, I would like some variables to: 1. Take the same values 2. Group some variables i.e. some variables should take same values or lie within certain percentage. 3. All different ...
7
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1answer
235 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}...
5
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1answer
384 views

Where can I find resources to learn mathematical modelling for real life operation research problems like combinatorial optimization?

I find it hard to form math models for real life operations research problems, how can I learn this? Any books, tutorials available?
8
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1answer
143 views

Heuristic Search Planning Tree Leading to Worse TSP Solutions than Naive Greedy

I'm doing a Traveling Salesman Problem (TSP) homework for a coursera optimization course. My first attempt was a regular naive greedy approach, from each point, moving to the closest node (that hadn't ...
6
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1answer
73 views

Maximum weight b-matching with global cardinality constraint

Suppose $A$ is an $n$-by-$n$ symmetric matrix whose entries are all nonnegative. $A_{ii} = 0$ for all $i$. We want to find an $n$-by-$n$ binary ($0/1$ valued) matrix $X$ that maximizes $$\sum_{ij} A_{...
4
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1answer
66 views

How to model $A_i=B_i$ for only one $i$

I would like to model the following: Only one of the following equalities can hold. $$(A_1 = B_1)\quad\text{OR}\quad(A_2 = B_2)\quad\text{OR}\quad\dots\quad\text{OR}\quad(A_k = B_k)$$ I can ...
5
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2answers
262 views

How to model If $A \le B$ then $Y = 1$, otherwise $Y = 0$

Somehow I don't get it right. I would like to model the following conditional: If $A\le B$ then $Y=1$ otherwise $Y=0$ where $A, B$ are reals and $Y$ is binary. I can model as follows: $Y \cdot A \le B$...
12
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2answers
204 views

Restoring a list from differences

Given a list of (absolute valued) pair differences ordered and with duplicates removed, how can we recover/reconstruct the list that generated these differences? We do not know anything about the ...
10
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2answers
340 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.
9
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1answer
107 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+...
23
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5answers
825 views

What's the current status of the Vehicle Routing Problem in the logistics industry?

After a bit of reading I think I've been able to conclude that state-of-the-art VRP can get solutions for 100~500 stops. My question is around how this actually affects logistics (like Amazon for ...