Combinatorial optimization Puns

There is recent interest in incorporating algorithms as layer in neural network. In our recent work (COPS) at NeurIPS'21 we tackle a similar task with the following questions:

1. Is it possible to train a pipeline containing neural networks & combinatorial optimization?
2. Is such pipeline extendible to real-world large scale tasks?
3. Using 1, 2 can we create a fully differentiable approach for panoptic segmentation?

We answer all of the above questions with yes and show benefits, insights into training such hybrid pipelines.

Contribution 1: Backprop through combinatorial optimization (CO) layers: There has been much recent work in this direction but such methods were not previously applied to:

a. Large scale tasks

b. Non-optimal CO solvers.

We extend previous work of [1] to compute better gradient estimates and obtain faster convergence.

Contribution 2: Transformation for backward pass: Previous works for gradient estimation through CO x* = \argmin_{x in C} <c,x> apply loss on x* and perturb costs c by incoming loss gradient on x*. This is not the case for panoptic segmentation. Our scenario is (x*, z*) = \argmin_{x in C, z in D(x)} <c,x> and loss is applied on z*. Here we need to perturb the costs associated with z* (which does not exist). To remedy this problem we solve a different CO problem in the backward pass to compute gradients w.r.t c.

Contribution 3: We show a differentiable surrogate of panoptic quality metric.

TLDR:

1. Backprop. possible through CO for large scale tasks even with non-optimal CO solver.
2. To achieve 1. we smooth gradients in backward pass
3. Solve another CO problem in backward pass for optimizing variables not appearing in objective.
4. Propose a Panoptic segmentation approach with fewer hyperparams. & better results than comparable approaches. Code available at: https://github.com/aabbas90/COPS

[1] - Black-box backprop: https://arxiv.org/abs/1912.02175

I published a paper in a peer-reviewed journal titled "Neural Knapsack: A Neural solver for the Knapsack problem" Article

Now I want to do my PhD in the same topic in Europe or Canada but can not find any research group or a supervisor that would be interested.

I did other projects, have quite good knowledge in deep learning and applied fields as Computer Vision

Can any one help me?

I would like to hear your suggestions on an approach to learn more about combinatorial optimization. What would be some good books or courses on the subject, what are some interesting problems where application of it is being researched, if you want a job that involves the topic what should you look for, etc. Feel free to share anything you find interesting about combinatorial optimization.

Anyone taken this class before? How much work is it, and would you recommend this class for a CS major?

Hello geniuses I need some help with few questions for a Master course, the question include some linear programming/optimization and first fit algorithms

https://preview.redd.it/tncknz5dayv61.jpg?width=2703&format=pjpg&auto=webp&s=7da497ae286ea6a07fb6df0d39818f348af4dff3

Layout Embedding via Combinatorial Optimization
Janis Born, Patrick Schmidt, and Leif Kobbelt
Eurographics 2021 Full Paper

This paper received an honorable mention for the Günter Enderle best paper award! 🏅Congratulations 🥳

We consider the problem of injectively embedding a given graph connectivity (a layout) into a target surface. Starting from prescribed positions of layout vertices, the task is to embed all layout edges as intersection-free paths on the surface. Besides merely geometric choices (the shape of paths) this problem is especially challenging due to its topological degrees of freedom (how to route paths around layout vertices). The problem is typically addressed through a sequence of shortest path insertions, ordered by a greedy heuristic. Such insertion sequences are not guaranteed to be optimal: Early path insertions can potentially force later paths into unexpected homotopy classes. We show how common greedy methods can easily produce embeddings of dramatically bad quality, rendering such methods unsuitable for automatic processing pipelines. Instead, we strive to find the optimal order of insertions, i.e. the one that minimizes the total path length of the embedding. We demonstrate that, despite the vast combinatorial solution space, this problem can be effectively solved on simply-connected domains via a custom-tailored branch-and-bound strategy. This enables directly using the resulting embeddings in downstream applications which cannot recover from initializations in a wrong homotopy class. We demonstrate the robustness of our method on a shape dataset by embedding a common template layout per category, and show applications in quad meshing and inter-surface mapping.

EG digilib
PDF in EG digilib

Hi,

I have a quick question about an optimization problem that I am facing and I just need some pointers to what to search for when it comes to solving it. The problem is structured as follows (simplified version):

Choice 1:

Part 1_1
Part 1_2
Part 1_3

Choice 2:

Part 2_1
Part 2_2

Choice 3:

Part 3_1
Part 3_2
Part 3_3
Part 4_3

With the constraints that some parts does not fit together (eg Part 1_1 and Part 2_1 does not fit so if. I choose Part 1_1 i can't choose Part 2_1 and vice versa). Each part has a cost and I wish to minimize this cost, thereby selecting the optimal (cheapest) set of parts. I also have to select one and only one from each Choice.

I think it reminds slightly of a knapsack problem, but not entirely because of the constraints and the need to choose exactly one from each choice. What can this problem be classified as? And if possible, does anyone have a good process for solving this?

Thanks in advance!

I have read one paper where the Travelling Salesman problem is solved using Graph Convolutional Network. So for my master's thesis I have decided that I would solve another combinatorial optimization problem using GCN or GNN, so my question is what optimization problems can be solved using GCN?

Hello, world! I will be finishing my computer science bachelor by the end of march 2021. I've already decided to pursue a master's degree right after I graduate. However, I don't really know what will my research topic be and this is making me really anxious, since the master program demand a ten-page essay of what my research is going to be about (along with a schedule).

I am really interested in combinatorial optimization and everything involving it, such as graph & computation theory, soft computing, AI, operations research, metaheuristics, etc. My undergraduate thesis consisted in the development of a metaheuristic approach for the DARP (Dial-a-Ride Problem), which is a NP-hard problem that can be seen as a "generalized" TSP. I kinda enjoyed working on it, however it was very exhausting, since my advisors did not give a shit about it and I was on my very own. Thus I don't want to continue researching this specific topic (the DARP).

My question is: what are some of the hot topics in these area(s) that could lead into research opportunities? I accept any suggestion in which I can put my mind in some papers. I know this may lead into many different kinds of answers, but anything would be definitely appreciated. Thank you.

Ps: I thought about posting in r/csMajors but I think this question in much more related to CompSci than academia/career issues.

I have been learning python and found the idea of combinatorial optimizing interesting. Does anyone have good code examples of this being used. I currently understand the idea of how to use this optimization technique but am struggling with applying it to a real world scenario.

https://arxiv.org/abs/1811.06128

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art methodologies involve algorithmic decisions that either require too much computing time or are not mathematically well defined. Thus, machine learning looks like a promising candidate to effectively deal with those decisions. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

Authors: Yoshua Bengio, Andrea Lodi, Antoine Prouvost

Do people have ideas about either the course (Combinatorial Optimization) or the instructor (Chaitanya Swamy)?https://uwflow.com/course/co450

Difficulty level, relative to other 400-level courses, style of the prof, etc. Thanks!

The closest description of the problem I am trying to solve would be described as a multi-objective, multi knapsack problem.

The problem:

• I have a number of objects ( red 1, red 2, ..., red 30, blue 1, blue 2, ..., blue 50, green 1, ..., green 25 , purple 1, ..., purple 100, etc )
• Each object has a value associated with it ( some objects worth more than others )
• I have a number of bags, lets say 5 bags
• Each bag can hold a set amount of each type of object. Lets say each bag can hold 1 red item, 3 blue, 4 green, and 5 purple.
• I want to fill bags sequentially, one object to a bag at a time. Once each bag has one object, a 2nd object will be placed until the bags can not hold any more. Once an object is taken, it can not be placed in any other bags.
• End goal, maximize value of each bag. Think of each bag independently wanting to have higher value sum of objects than the other bags, so it would have to decide is it wiser to take a blue value 10 or a green value 8 this turn. In certain circumstances it would be wiser to take the green 8 if the only green objects left are value 1's and there are blue still 8, 9, or 10s.

I was looking into swarm algorithms, specifically ant swarms. I am not sure if this is the best algorithm for solving this sort of problem. If this is the best solution for the problem, does anyone know of any good tutorials on the subject. I am having a difficult time finding free resources. Books on the subject on Amazon are around $100 for some reason.

edit: clarified maximize value goal

Consider a set S composed of a high number of discrete elements. The goal is to determine which subset of n elements of S has the lowest cost.

Does anyone know what's the name of this particular type of problem? Also, which algorithms are able to solve this problem?

Thanks,

Are there any recent works on neural nets solving combinatorial optimization problems like "Pointer Networks"?

As far as I understand, neural net's performance is lower than the handcrafted combinatorial optimization algorithms. Are there any instances where NN outperform classical combinatorial optimization algorithms?

A crime happened in Marriland. n detectives have each, one unique clue. If they can communicate by telephone, what's the minimum number of phonecalls (Cn) that allows all detectives to know all clues.

I can't figure it out. Something to get you started: 2>=C(n+1)-C(n)>=0

Which one is harder?