Questions tagged [algorithms]

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

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3
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1answer
61 views

Does Dijkstra's algorithm find the optimal solution for a weighted and directed shortest paths problem?

I was wondering to know whether Dijkstra's algorithm can find the optimal solution for a weighted and directed shortest paths problem where: 1) for each arc $(i,j)$, $i>j$ and 2) it is not always ...
4
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1answer
83 views
+50

Which constructive heuristics exist for the time-dependent TSP?

A constructive heuristic is a type of heuristic method which starts with an empty solution and repeatedly extends the current solution until a complete solution is obtained. (Wikipedia) Which ...
5
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1answer
81 views

Find Extreme direction of equality constraints

I think this is a very basic question, but I failed to find an algorithm for this... When I have a set of inequality constraints, $Ax \leq b$ as my feasible region, I can set $b = 0$ and find $n-1$ ...
5
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1answer
117 views

Quickest shortest path algorithm

I want to do a shortest path algorithm. My direct and not acyclic graph contains only positive numbers. I have to do the scan for all pairs of nodes in complete depth in python. My graph is big (...
0
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1answer
53 views

Trouble implementing a line-search algorithm

I am trying to implement a simple line-search algorithm in Julia. I am new to Julia programming, so I am learning it on the go. I'd like to ask for some help, if possible, to correct an error while ...
1
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1answer
87 views

Method (Algorithm) and Objective used in Gurobi Model

How can I find out which method or algorithm was used to solve my model? When I use GRB.IntParam.Method- to output the method, I get ...
2
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1answer
63 views

Bounding box fusion with constraints

I have N bounding boxes that I want to fuse/merge given some constraints. Each bounding box has a label. Goal: The main goal is to minimize ...
3
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1answer
220 views

Algorithms for sparse linear systems

I've long wondered this, but what is the algorithm(s) implemented in modern linear equation solvers for sparse systems? The obvious answer I can think of is Gauss-Jordan with a bunch of tricks to make ...
4
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1answer
56 views

Greedy algorithms for assignment problems — prediction doesn't match simulation

I'm considering the following basic assignment problem: a group of $n$ people is to be assigned, in one-to-one fashion, a set of $n$ jobs. Write $C_{ij}$ for the cost incurred when person $i$ gets ...
9
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2answers
411 views

How to maximize “contrast” between nodes on a graph?

I have an undirected graph such as the one shown below. I can make up to 3 choices about the color of each node. The edge weights are equal to the difference between the nodes, given by the "...
2
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3answers
167 views

Are there any standard “tests” that determine if a model will not optimize / no solution?

As the title says, what are the tests for optimality or non-optimality I can build into my procedure and code to alert me that the model is going to be infeasible so I need to revise my constraints? ...
8
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1answer
219 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 ...
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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 ...
6
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2answers
75 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
204 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
91 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
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 ...
5
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0answers
81 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
252 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
38 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:...
7
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1answer
154 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
175 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
46 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 ...
5
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0answers
123 views

A good memoryless elevator strategy?

Could you OR whizkids please help me out with this one: https://stackoverflow.com/questions/61854621/a-good-memoryless-elevator-strategy Surely somebody has solved this before. How do you classify ...
4
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0answers
113 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
38 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 ...
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0answers
65 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
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2answers
143 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
94 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
180 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
402 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
963 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
102 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
90 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
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1answer
193 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
113 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
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1answer
135 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
222 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
109 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
160 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
856 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
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3answers
245 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
76 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
2k 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
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1answer
400 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
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3answers
262 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
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2answers
332 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 ...