Questions tagged [algorithms]

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

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How to solve assignment problem with additional constraints?

The assignment problem is defined as: Let there be n agents and m tasks. Any agent can be assigned to perform any task, incurring some costs that may vary depending on the agent-task assignment. We ...
4 votes
1 answer
93 views

Efficiently updating latest finish times via Critical-Path-Method

For a Resource-Constrained-Project-Scheduling problem, I need to calculate Critical-Path-Method (CPM) values for each of the activities. These values are: Earliest Start (ES) Earliest Finish (EF) ...
5 votes
2 answers
464 views

Julia JuMP successive optimization

I am using Julia's JuMP package to solve a cutting-plane method. Namely, I solve a sub-problem, find the most-violated constraint in the master problem, add that to ...
1 vote
2 answers
138 views

How to solve assignment problem with type constraints?

There are $n$ jobs and $m$ machines. Assigning job $i$ to machine $j$ yields a profit of $c_{ij}$. Each job has a type $t_i$. Machine $j$ can take on up to $a_j$ jobs, but the number of job types must ...
4 votes
0 answers
71 views

Is this weighted feedback concept a known, solved, problem?

Imagine a fairly standard Thumbs Up/Down feedback system. For each piece of content they consume, every user has the ability to give a binary positive/negative feedback that piece of content. They're ...
22 votes
6 answers
3k 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 ...
5 votes
0 answers
97 views

How many clues make Sudoku polynomial

Consider a $n^2 \times n^2$ grid sudoku. Define a clue to be composed of a coordinate $x$ and $y$ of the grid and a value $z$. The goal is given $n$ and a set of clues, to find one solution to the ...
7 votes
3 answers
366 views

Combining Multiple Cost Values in Shortest Path Problem

I am trying to solve a shortest path problem through Dijkstra's algorithm. However in my case, cost between nodes (nodes $i$ and $j$) are more than one- two nodes are compared based on two different ...
0 votes
1 answer
131 views

Algorithms and analytical solution methods/tools to solve an optimization problem for a particular objective function

I have the following objective function: \begin{equation} \min_{I_{i,v}} \ \sum^{N_v}_{v}\sum^{TT_v}_{i} \ C_{loss,cyc} \end{equation} where $I_{i,v}$ is the only positive decision variable. $...
2 votes
2 answers
117 views

Minimizing a KS function

For convex functions $f_i, \ i \in I$, the KS function is defined as the following for any $\rho > 0$: $$KS[\{ f_i \}_{i \in I}](x):= (1/ \rho) \ln \left[ \sum_{i \in I} \exp(\rho f_i(x)) \right].$$...
7 votes
2 answers
393 views

Optimization Solution Framework

I am working through Pascal Van Hentenryck's excellent discrete optimization course on Coursera. While the course certainly touches on it in some ways, I am looking for more of a framework in terms of ...
2 votes
1 answer
72 views

Check if there exists a vector that satisfies a set of inequalities but violates another set of inequalities

Problem Given rectangular matrices $A$, $B$ and vectors $\vec{a}$, $\vec{b}$, how to check if there exists an $\vec{x}$ that satisfies the following conditions? $\vec{x} \succcurlyeq \vec{0}$ is true....
2 votes
0 answers
42 views

Importance of Polynomial Time Approximation algorithm for special case [closed]

I am an MSc student, searching for an interesting topic in operations research for NP-hard problems. I need your opinion and recommendation about: "Searching a polynomial time approximation ...
0 votes
0 answers
65 views

How to prove that given algorithm from shortest path always finds the optimal solution?

The greedy approach which is used here is explained below. For finding the stops where the user should make a stop, first declare a dynamic vector to store all the stops. Take a flag as a starting ...
3 votes
0 answers
58 views

Polynomial Time Solution For a Mixed-Integer Linear Programming Specific Case

Consider the following mixed-integer linear programming (MILP): \begin{equation*} \begin{array}{ll@{}ll} \text{maximize} & 1 & \\ \text{subject to}& x_{i} \geq 0, &i=1 ,\dots, m\\ ...
9 votes
2 answers
373 views

Mixed-Integer Linear Programming With Free Variables

In the classic Mixed-Integer Linear Programming (MILP), the variables are fixed to be either integer or real. I am interested in the following MILP variant, where only one thing different from the ...
1 vote
0 answers
38 views

What is the role of parameters in whale optimization algorithm?

I am trying to understand how the whale optimization algorithm works. When I see the mathematical model of this algorithm there are some parameters I want to understand what they mean and what their ...
2 votes
2 answers
94 views

Best way to solve a optimization problem with no objective function?

I have a MILP but fixed the objective function, so at each iteration is constant.Therefore, I solve a constraint satisfaction problem. Is there an algorithm to solve this kind of problem fast? I have ...
7 votes
2 answers
185 views

What strategies to use for Scheduling of Connected Sequences?

I'm given a problem in which I need to schedule multiple sequences. The goal is to minimize the makespan. I'm allowed to elongate all tasks, but I cannot reduce their width nor disconnect any of the ...
2 votes
1 answer
458 views

How to compute the minimum number of vehicles required

I am trying to solve the following problem: I have a set of $N$ requests that must be processed by vehicles. I do not know the locations of these requests. Requests can be processed by a same vehicle, ...
1 vote
1 answer
133 views

Christofides algorithm, transform from Eulerian tour to Hamiltonian cycle

How do I do the change from an Eulerian tour to a Hamiltonian cycle in the Christofides algorithm? In the original paper from Christofides (1976)1 I found that A Hamiltonian circuit $i$ of $G$ can be ...
4 votes
1 answer
143 views

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 ...
3 votes
1 answer
307 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 ...
5 votes
1 answer
145 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 (...
5 votes
1 answer
99 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 $n-1$ ...
0 votes
1 answer
61 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 vote
1 answer
161 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 votes
1 answer
89 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 ...
4 votes
1 answer
229 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 ...
5 votes
0 answers
124 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 ...
9 votes
2 answers
453 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 "...
4 votes
1 answer
82 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 ...
2 votes
2 answers
259 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
3 answers
179 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 votes
1 answer
234 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 ...
6 votes
3 answers
590 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 ...
6 votes
2 answers
87 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 ...
3 votes
1 answer
128 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 votes
1 answer
218 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 votes
0 answers
129 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 ...
7 votes
1 answer
166 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. ...
3 votes
1 answer
260 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 votes
0 answers
45 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:...
1 vote
2 answers
220 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 ...
10 votes
1 answer
251 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 ...
2 votes
0 answers
49 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 votes
0 answers
150 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 votes
0 answers
46 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 ...
6 votes
2 answers
148 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 ...
1 vote
0 answers
122 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 ...