Questions tagged [combinatorial-optimization]

For questions about optimization over a discrete solution space.

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9
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3answers
2k views

Are Metaheuristics and Evolutionary Algorithms the "Gold Standard" for the Traveling Salesman Problem?

Are Metaheuristics and Evolutionary Algorithms the "Gold Standard" for the Traveling Salesman Problem? I am interested in learning more about how we have been able to solve the (famous) ...
4
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1answer
407 views

Is the Travelling Salesman Problem Considered as "Gradient Free Optimization"?

I was thinking about the Traveling Salesman Problem the other day - for such types of discrete combinatorial optimization problems, do they have a "loss function"? It seems that there is ...
2
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1answer
43 views

Master Problem Infeasible after Iterations of Unbounded Sub Problem (Generic Benders Decomposition in non Stochastic MILP)

I am dealing with a large problem of MILP problem and interested to apply Benders Decomposition. I have already check the original problem and it was feasible to run in large number of computation ...
22
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5answers
4k views

Why is open source operations research software so far behind open source statistics and machine learning software?

Like many who participate in this site, I work on projects in both operations research (OR) and statistics/machine learning (ML). The different states of open source software in these fields are often ...
6
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3answers
1k views

Solving Logic puzzles through optimization

I have the following "logic puzzle" (I think this is considered as a "scheduling problem"): In this problem, there are 5 basketball players - provided some clues about their ...
3
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2answers
167 views

How to perform clustering of two different sets of entities?

I need to perform clustering of two different entities. Lets say we have transmitters and users. The relation between a transmitters and user is defined by a weight, for example, the weight between ...
4
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1answer
118 views

Adding a group constraint to binary decision variables

I have a problem where I have N binary decision variables where each one of them belongs to a group (Where the number of groups G is less than N) and I have to choose a subset of them to maximize some ...
1
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0answers
42 views

Ordering a set in GAMS

I'm trying to solve a problem very similar to this one, where I'm trying to find an optimal order. How would I actually plug this into GAMS? It gives out a single value rather than an ordering. I ...
2
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1answer
94 views

Number of paths in asymmetric capacitated vehicle routing problem

This seems like a natural question, but I was not able to find an answer. My question is this. Consider a CVRP where $n$ customers have to be serviced by $m$ vehicles on any given day. All the ...
2
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0answers
105 views

Are there hybrid metaheuristic-solvers to solve combinatorial optimization problems?

I have a problem which is formulating a linear program. To solve large instances I implement a metaheuristic to solve my problem. In my problem, I have two objective functions. With my linear program, ...
2
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2answers
67 views

Change the objective function formula change the complexity of a linear program?

I have a linear program, where I can use it with the same constraint to minimize objective 1 or minimize objective 2. I noted that when I use the formula of objective 2 the problem can be solved with ...
3
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0answers
88 views

Sources of Min-Cost Flow Models That Utilize Binary Variables for Transportation Networks

I am looking for articles that include min-cost flow models with binary variables for flow transportation like gas networks, traffic systems, heating systems. Is there any specific place(like OR ...
6
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3answers
211 views

Budgeted max cut heuristic

I am looking for a heuristic that solves a budgeted variant of the max cut problem. Given a graph $G = (V, E)$, if the original problem is to find a partition of $V$ into two subsets $A$ and $B$ where ...
14
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3answers
2k views

Why does the design of heuristics require considerable domain knowledge?

I am from a machine learning (ML) background and am interested in how ML is applied to Combinatorial Optimisation. As such, as I have been reading around the area and have come across the statement ...
2
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2answers
93 views

How to prove that optimizing each component of a system separately gives suboptimal result?

The black-box system shown below has 3 components. They run sequentially to generate a final output from the input. Each component has its own parameters to optimize for better intermediate results (...
3
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1answer
190 views

Discrete problems versus Combinatorial problems

I have seen one explanation about the difference between discrete and combinatorial optimization problems in such a way that "all combinatorial optimization problems are also discrete ...
2
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0answers
61 views

Mathematical model complexity Vs Time Complexity of the model

As far as I know, when we talk about the term of complexity, it referred to the time complexity of the model in which how long does it take to solve a specific mathematical program by a specific ...
3
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1answer
62 views

How to know if a combinatorial optimization problem is linear or not?

I want to know if a combinatorial problem like the knapsack problem is linear or not. And how do we know if a given problem is convex or not?
-1
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1answer
61 views

How to interpret velocity computation in Particle Swarm Optimization?

Please in PSO metaheuristic when we calculate the velocity what is the advantage of using pBest?
2
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0answers
101 views

About combinatorial Benders Cuts

I am solving an OR scheduling problem where I assign the patient to (day,OR) tuple in Master Problem. Once the assignment is made, a subproblem can be solved for each (day,OR) tuple independently ...
2
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1answer
98 views

Adapting a cluster-first-route-second approach for VRP with heterogenous fleet

I have the following data: A fixed depot/facility location Dropping points with demands List of available vehicles (heterogeneous fleets) What I am trying to do is, given the list of vehicles and ...
4
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1answer
298 views

Complexity of navigation with google maps

I was wondering what complexity a simple start-destination task in a routing software would have. Knowing the shortest path problem, it should be in P. Is there anything I am missing?
1
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0answers
46 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 ...
4
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1answer
92 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 ...
3
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1answer
146 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]] ...
3
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0answers
113 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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4answers
427 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 ...
5
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2answers
498 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
57 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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3answers
280 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 ...
4
votes
1answer
188 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 ...
3
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0answers
62 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
95 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
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2answers
162 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
67 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 ...
6
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0answers
97 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 ...
6
votes
2answers
136 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
285 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
78 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
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1answer
197 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
46 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 ...
6
votes
2answers
392 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
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1answer
363 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
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1answer
146 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
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1answer
133 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
354 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
75 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
102 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:}...
7
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1answer
199 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 ...