# Questions tagged [algorithms]

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

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### Resources about Busacker & Gowen algorithm

I have a relatively hard time understanding the Busacker & Gowen algorithm. I could not find any resources on it, contrary to Ford-Fulkerson method that is described in Comen's "Introduction ...
1 vote
46 views

### Making a batch of related linear problems more efficient

I have a linear system that is of the form $$My = b \\ L \leq y \leq U$$ i.e. all of the $y_i$ are potentially bounded, and there are various linear relationships between them. I want to find the ...
1 vote
84 views

### Optimization algorithm for space debris

I'm currently working on a research project to optimize the recovery of space debris. We have to recover 50 pieces of space debris with the minimum number of missions possible. The missions are sent ...
1 vote
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### Understanding the L-shaped-method and the different variants of it

I am currently trying to understand the integer L-shaped-method/stochastic version of Benders Decomposition because I have practical problem MIP that is stochastic and thus has very good decomposition ...
1 vote
67 views

### How do I check convergence in stochastic Benders?

So in the deterministic version of Benders, the main process works like this: I initialize my x-vector (Integer variables from the master problem) and solve the dual subproblem (SP). I add an ...
26 views

### Error while using subgradient method to update lagrange multipliers

I am trying to implemet the subgradient method in Lagragian relaxation to update the multiplier lamda which has three dimension, I have ecountered an Except error, it looks the is bugs in the code. it ...
54 views

### Finding lower bound (maximization problem) in Lagrangian Relaxation with subgradient method

I have tried to implement a toy problem (MIP) from the literature using Lagrangian Relaxation with the subgradient method, I implemented it correctly and I got the upper bound which is updated at each ...
121 views

### Is OCN=DOCN decidable?

One-Counter Nets (OCNs) are finite-state machines equipped with an integer counter that cannot decrease below zero and cannot be explicitly tested for zero. An OCN $A$ over alphabet $\sum$ accepts a ...
113 views

### Find an algorithm for quickly computing results to a given equation

There is an equation: 280a + 80b + 75c + 50d + 25e - 30f - 42g = R a, b, c, d, e, f, g - those are modifiers. They're strictly ...
1 vote
202 views

### Best algorithm for scheduling interviews

I posted the same question on stackoverflow and immediately referred to post it here. I want to think about the best algorithm which let the interviewer meet maximum number of candidates. Suppose that ...
153 views

### Simplest Quadratic Programming algorithm for teaching

Can anyone recommend a straightforward quadratic programming (QP) algorithm suitable for an undergraduate engineering class? I'm interested in finding an algorithm that they can easily grasp and ...
103 views

### Finding the minima of a multivariable function with constraints

I have a multivariable function (9 variables), and I want to find where the function records a minimum value. The function is as follows: It also has a few constraints: I tried a brute force ...
86 views

### The linearization of the logical constraints

I know the logical constraints can be linearized by either the logical representation of whose relation, (for pure binary variables e.g. CNF/DNF) or for general form by using Big-M formulation. As I ...
2k views

### How can I solve this algorithmic task in Python?

I am trying to solve this task: There are three datasets: first data on offices in cities: each city has a certain number of offices and each office has its own capacity of employees. Second, data on ...
76 views

### How to find the maximum probability of satisfying the conditions in all combinations of arrays

for example, I got a list of tokens and each token's number of characters(length) is length = [2, 1, 1, 2, 2, 3, 2, 1, 1, 2, 2, 2] and here is the list of each ...
70 views

### Flow problem with flow demands

Recently I found a subproblem in a project I am working with. This problem is a sort of flow variant, as you will see. And I am looking for literature-related articles and also fast approaches for ...
255 views

### Is Dantzig-Wolfe decomposition an example of a divide and conquer algorithm?

Typical Divide and Conquer algorithm solves a problem using following three steps: Divide: This involves dividing the problem into smaller sub-problems. Conquer: Solve sub-problems by calling ...
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### 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 (...