# Questions tagged [algorithms]

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

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### 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:...
103 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. ...
140 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 ...
39 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 ...
87 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 ...
34 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 ...
37 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 ...
136 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 ...
84 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 ...
136 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 ...
152 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 ...
655 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 ...
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 ...
58 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 ...
118 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?
80 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 ...
113 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 ...
213 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 ...
99 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 ...
137 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 ...
396 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 ...
194 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 $d$ ...
71 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 ...
1k 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 ...
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 ...
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 ...
388 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 ...
224 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 ...
323 views

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 ...
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 ...
450 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. ...
255 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 ...
169 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: ...