Questions tagged [algorithms]

For questions related to the design or implementation of algorithms (exact or heuristic) for solving optimization problems.

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8
votes
1answer
207 views

Specific algorithms to compute the LP-relaxation of the Set-Cover problem

One of the most commonly known combinatorial problems is the set cover problem, which states that given a collection of sets $S = \{s_1, \dots, s_m\}$ and a universe of elements $U = \bigcup_{i=1}^m ...
1
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0answers
61 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 ...
6
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2answers
69 views

Optimizing MIP Parameters For Various Data Sets

I have a MIP that runs for several different data sets. For each data set the MIP runs multiple times, once for each time period in the data set, and each time period is independent. I've experimented ...
6
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3answers
119 views

How to find all descendant vertices of all vertices in a big DAG (Directed acyclic graph)?

A simple algorithm may be traverse all vertices, and perform DFS for every vertex. However, the computational complexity is $O(n(n+m))$, where $n$ and $m$ are the number of vertices and edges in the ...
3
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1answer
82 views

A variant of maximum sum subarray problem?

This is related to the foillowing Q on Cross Validated https://stats.stackexchange.com/questions/483002/experimental-design-problem-with-goofy-constraints which I am trying to answer, but the ...
4
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1answer
123 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
70 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
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 ...
2
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0answers
31 views

Algorithms for finding step sizes which satisfy the Wolfe conditions?

I am a student studying optimization, and I am interested in algorithms which finds step sizes satisfying the Wolfe (or strong Wolfe) conditions. I do know of one book which provides such an algorithm:...
6
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1answer
149 views

Why is this version of the algorithm more efficient?

I am a student self-studying Optimization, and I am reading about the Conjugate Gradient Method in Numerical Optimization by Nocedal & Wright, and they present two different algorithms for it. ...
2
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2answers
159 views

How to correct this scheduling algorithm?

I have a scheduling problem to solve. It's a resource-constrained project scheduling problem with time-varying resource availabilities. The objective is minimizing tardiness. The full detailed model ...
2
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0answers
40 views

Decision-making algorithm for dynamic load balancing

I'm researching a subject of balancing the load between two black-box systems (with some twists). I thought that I could record latest response time log from each of those systems and process such a ...
4
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0answers
93 views

Does anyone have the criss cross algorithm programming code to solve linear programming problems?

I have a project that requires programming code for the simplex algorithm and criss-cross algorithm. The purpose of this project is to compare the two methods. I've tried to find it, but the ...
5
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0answers
36 views

Relative Weakness of Rolling Horizon Optimization

I am running a fairly complex and dynamic(multi-period) model, and as a result of the complexity, solvers are not able to solve the problem in a reasonable time frame. I have since discovered the ...
1
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0answers
44 views

Rolling Horizon in Pyomo

I am trying to figure out how one could write a rolling horizon algorithm in PYOMO to speed up the solution of a model that I am building. My understanding of the Rolling Horizon Algorithm is that you ...
6
votes
2answers
137 views

Find a point inside non-empty difference of ellipsoids

Given two ellipsoids \begin{align}\mathcal{E}_1 &= \{ X \mid X^\top A_1 X + 2B_1^\top X + C_1 \leq 0\}\\\mathcal{E}_2 &= \{ X \mid X^\top A_2 X + 2 B_2^\top X + C_2 \leq 0\}\end{align} are ...
3
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1answer
87 views

Linear programming explanation in Algorithms by Sanjoy Dasgupta

I am reading about simplex algorithms in a textbook titled Algorithms by Dasgupta-Papadimitriou-Vairani. On each iteration, simplex has two tasks: Check whether the current vertex is optimal (and if ...
10
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1answer
143 views

Lagrangian Relaxation bound greater than optimal solution

I am working on a Lagrangian relaxation for a minimization MIP. Everything seemed to be working fine before I started to run a batch of instances. Checking the log results for one of the instances ...
7
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2answers
217 views

The general meaning of “constraint relaxation” in the context of the Shortest Path Problem

I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges") [...][the use of the term "relaxation"] is historical. The outcome of a relaxation ...
11
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5answers
764 views

How to implement a “generic” solver for scheduling problems?

I have been accepted for an internship for 6 months. The aim of this internship is to implement a "generic" solver for scheduling/production planning problems. This solver will bill a small prototype ...
7
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1answer
99 views

Design choices on how to implement several algorithms for the same problem

When one is interested in solving a problem but considering different objective functions the choice is easy, a class for problem, a class for solution and a class by algorithm then in the main ...
8
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1answer
61 views

Speed of convergence for minimizing Rosenbrock's function

I am minimizing $f(x_1,x_2) = 100(x_2-x_1^2)^2 + (1-x_1)^2$, where I try many algorithms to compare with each other. All of the algorithms find the optimal solution $(1,1)$ quickly, so I am not ...
6
votes
1answer
123 views

When does the Junction Tree Algorithm work better than Variable Elimination?

Compared with the Variable Elimination algorithm, when does the Junction Tree algorithm work better? For what kind of graph structures? Size of the problem? Sparsity of the network?
11
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0answers
83 views

Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
7
votes
1answer
117 views

How to convert 3D bin packing problem to 2D bin packing approximation?

I'm trying to approximately solve a 3D container loading problem. Is it possible to use 2D bin packing algorithms? If so, how do we make the transformation? What are the conditions needed to make the ...
15
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1answer
214 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
7
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1answer
100 views

Maximize charging, minimize cost

The task pertains to choosing an algorithm based on the data, requirements and constraints. I have a number of electrical devices ($d_1,d_2,\dots,d_n$) with batteries. Throughout the day I will ...
10
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0answers
144 views

Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
16
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1answer
497 views

IPOPT with HSL vs MUMPS

What are the advantages (if any) of using IPOPT with HSL vs MUMPS? HSL has a reputation of being faster, but does it walk the walk? In particular, does HSL scale better for large-scale problems? We ...
10
votes
3answers
217 views

Is the “reverse search” algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities?

Is the "reverse search" algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities? If it is not, then what is? For $m$ inequalities in $d$ ...
6
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0answers
72 views

What are the top three applications (in terms of number of citations) of the “reverse search” algorithm of David Avis?

I can see that this algorithm is quite popular, and that one of the original papers now has 820 citations on Google Scholar. However, what are the most highly cited applications of it? If in Google ...
26
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6answers
2k views

Statistical tests for benchmark comparison

Suppose that you have two algorithms for solving an optimization model, and you want to benchmark their performance over a large set of instances (with only one performance metric, for example, the ...
12
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3answers
1k views

Performance of a branch and bound algorithm VS branch-cut-heuristics

I was trying to solve a moderate scheduling model using an open-source solver. I did two different ways. A) using pure branch and bound algorithm (disable all options). B) using the default setting ...
16
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6answers
3k views

Does the problem of P vs NP come under the category of Operational Research?

I am enrolled in an Operational Research program. I am also interested in Algorithms, and I wish to know whether "P vs NP" is a common point in both of the fields, so that the effort put in ...
8
votes
1answer
392 views

Finding minimum time for vehicle to reach to its destination

Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
10
votes
3answers
241 views

Does the “prize-collecting shortest path problem” exist?

The prize collecting shortest path problem (PCSPP) is a special case of the prize collecting Steiner tree problem (PCSTP) (PCSPP is the PCSTP with only two terminal vertices, namely the source and ...
10
votes
2answers
327 views

Many-to-many Breadth First Search

There is a directed social network with large number of nodes and arcs and there are many instances of the network (nodes are same but arcs change in each instance). You can think of it as a ...
18
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6answers
2k views

List of Implementations for common OR problems

For the TSP there famously is the concord solver (http://www.math.uwaterloo.ca/tsp/concorde.html) which is argubly the fastest exact solver for the TSP. There are many other problems that also show ...
11
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2answers
455 views

Finding an optimal set without forbidden subsets

Given $n$ items, I want to select a set items $S\subseteq\{1,2,\dots,n\}$ that maximize profit. The profit of item $i\in\{1,2,\dots,n\}$ is given by $p_i$ and may be assumed to be non-negative. ...
18
votes
2answers
261 views

Mathematically creating the 'perfect' permutation for reservations in a hostel

I am working at a hostel which uses a reservation system for each room and the beds in the room (e.g. $14$ beds in one room, bed numbers $1-14$.) When we get bookings for multiple people, we assign ...
11
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2answers
173 views

partitioning hub assignment models

When solving large-scale hub assignment models (1000+ candidate hubs and 1000+ demand nodes), it is possible that parts of a cost matrix are not connected to one another. A typical workflow would be: ...
1
vote
2answers
206 views

Is there any way to generate all the possible undirected graphs with unlabeled nodes?

I am looking for an efficient algorithm to generate all of the unique graphs for a given number of nodes. For small instances, the total number of graphs are as follows: n=2 G=2 n=3 G=4 n=4 G=11 ...
10
votes
1answer
125 views

Algorithmic gap for Hochbaum's (greedy) algorithm for (metric) uncapacitated facility location

In Jain et al. (2003)1, at the bottom of page 801, they construct an instance of (metric) uncapacitated facility location for which they claim the greedy (Hochbaum's) algorithm has gap $\Omega\left(\...
11
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2answers
122 views

Neigbourhoods in Large Neighbourhood Search (LNS) algorithms

I have been trying to implement a variant of LNS on a graph for TSP. One of the ways that I can define a neighborhood for TSP is to find $k$-shortest path between two nodes. But the choice of these ...