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Questions tagged [optimization]

Questions about problems that entail selecting the best element from some set of available alternatives, and methods to solve them.

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1answer
64 views

Variant of interval scheduling with varying task durations

I am probably just missing the correct term for my problem to find the solution but here it goes: I have a set of tasks with a given duration and an interval for each task in which it has to be ...
4
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1answer
146 views

How to produce nonzero absolute differences between neighboring numbers on a circle as long as possible?

I apologize for the lack of an even better title. The main reason I couldn't find a better one is because I have a problem that I cannot find reference anywhere. I am pretty sure it has a name, but I'...
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86 views

NodeJS vs Golang Performance [closed]

I was testing performance of NodeJS vs GoLang with a very simple script. Situation one is three nested for loops to do a Sin calculation and Situation two is just one for loop. It turns out that for ...
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0answers
22 views

Sparse feasible solution $|x|_0\le k$ for system of linear inequalities $A x \le b$

Suppose the set of linear inequalities $Ax\le b$, in which $A\in\mathbb{R}^{m\times n},x,b\in\mathbb{R}^n$ is given. Is it possible to determine in polynomial time with regard to $m$ and $n$ if there ...
4
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1answer
54 views

Is there an algorithm that can find a solution that solves the most number of equations in a linear system of equations?

My apologies if this question makes no sense. I am trying to find an algorithm that can solve a linear system of equations. Unlike most problems like this, this algorithm does not need to find a ...
4
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1answer
272 views

Minimize sum of squares of rows in matrix when sum of columns have some constraint

I'm looking for an algorithm that can find any matrix $a_{j,i}$ such that $$ \sum_{i \in I} \left(\sum_{j\in J} a_{j,i}\right)^2 $$ is minimal, while also for each $j\in J$ satisfying the constraint ...
3
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2answers
51 views

Optimization Problem when calculating fitness is expensive

I need to solve an optimization problem, maximizing fitness in a set of around 1 million solutions. Calculating the fitness of any solution is very time consuming, taking around 5 minutes. Therefore, ...
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1answer
49 views

On the proof of NP-Hardness of the Cardinality Constrained Quadratic Knapsack Problem

in Polyhedral Study of the Cardinality Constrained Knapsack Problem the authors prove that the Cardinality Constrained Knapsack Problem is NP-Hard by reducing PARTITION to it. Besides, it's easy to ...
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0answers
48 views

How to minimize the number of gates of an arithmetic circuit?

A circuit is simply a DAG, with some input wires, some output wires, and some operations on the vertices. Consider an arithmetic circuit where the only operations are addition ($+$) and ...
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1answer
556 views

How does the problem of “Scheduling to Minimize Lateness” exhibit optimal substructure?

The problem of "Scheduling to Minimize Lateness" is as follows (Section 4.2 of the book "Algorithm Design" by Jon Kleinberg and Eva Tardos): Input: A finite set $J = {J_1, J_2, \ldots, J_n}$ of $n$ ...
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38 views

models/formalism for optimization algorithms?

In Wolpert's "No free lunch theorems for optimization", he uses the following formalism for an optimization algorithm: Let $X$ be a finite space of which an element has to be chosen, and let $Y$ be a ...
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1answer
25 views

What is the difference between the study of Evolutionary algorithm vs. Optimization?

I have a course named "Evolutionary Algorithm". But, our teacher is always mentioning the word "Optimization" in his lectures. I am confused. Is he actually teaching Optimization? If yes, why is the ...
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1answer
157 views

Optimal substructure and dynamic programming for a variant of the rod cutting problem

The rod-cutting problem described in Section 15.1 of CLRS, 3rd edition is the following. Given a rod of length $n$ inches and a table of prices $p_i$ for $i = 1, 2, \ldots, n$, determine the ...
2
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1answer
42 views

How hard is it to decide if there exists a strict improvement of a given solution of an NP-complete problem?

Take the Set Cover problem as an example. When we ask if there is a set of size k that covers all the elements, the problem is NP-complete. Now if we ask, for a given set $S$ of size $k$, if there ...
2
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1answer
51 views

Optimal assignment of +-1 values to vertices in a graph

Let $(V, E)$ be a simple connected undirected graph, $f: V \to \{-1, +1\}$, and $g: E \to \{-1, +1\}$. The function $g$ is completely defined by $f$, while $f$ is something we get to choose. The only ...
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1answer
70 views

Knapsack-type problem where the objective function is a ratio

I have a problem where I have a number of proposed initiatives each with a cost and payoff. I need to select a subset of these initiatives in order to maximize the ROI for the selected set as a whole ...
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0answers
89 views

Specific quadratic 0-1 knapsack problem solvable in linear time?

I am interested in a simple variant of the quadratic knapsack problem. Let $\{w_1, \ldots, w_n\} \in \{0,1\}$ be $n$ weights and $\{v_1, \ldots, v_n\} \in \mathbb{R}$ be $n$ values. Furthermore, ...
4
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0answers
115 views

One-sided, distance-optimal polyline reduction to a given number of vertices

So I have been battling this rather peculiar problem: given the following input (on an euclidean plane): point p polyline l integer n p is not inside of the convex hull of l find a new polyline l', ...
3
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1answer
45 views

Maximizing quantities/length in buckets to match each other

I have a use case, real one, and I'm trying to come up with an efficient maximization algorithm to solve it. I'll try to simplify, with a simple analogue, and after will explain the real world use ...
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0answers
21 views

In multiobjective optimization, how to calculate the distance to reference point?

In multiobjective optimization, what does the distance exactly means, is it: 1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space). <...
2
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1answer
350 views

Finding paths with minimum intersections

Given a graph and a set of origin-destination $\langle o_i,d_i\rangle$ pairs. The goal is computing a set of paths such that every pair has a path and number of common vertices between paths is ...
3
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2answers
69 views

Finding pairs of numbers in array whose reciprocals sum to 1

Given an array of numbers. Find all pairs of numbers satisfying the condition $1/a + 1/b < 1$. For example: Input: $2, 3, 1, 0.5, 3, 1.6$. Output: $(2,3), (3,2), (3,3), (3,1.6), (1.6,3)$. We can ...
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2answers
46 views

How to create constraints for Mixed integer linear problem?

i am a beginner to Discrete optimization domain. I am working on the real world problem, i.e., Scheduling of hybrid appliances. I have hybrid appliances which can ...
4
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1answer
128 views

search problem vs optimization problem

This is mostly a terminological question: Is there a fundamental difference between "optimization problems" and "search problems"? Apologies if this is an obvious question As I understand it, we can ...
1
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1answer
32 views

How do I model this expression maximization problem as a Knapsack problem?

Given two arrays of the same length $n$: $A = \{a_1,a_2,\dots,a_n\}$, $B = \{b_1,b_2,\dots,b_n\}$, I have to maximize the following expression: $$\frac{a_{i_1} + a_{i_2} + a_{i_3}+ \dots + a_{i_k}}...
2
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0answers
57 views

Inexact cover, or cover with gaps

Dancing Links: wikipedia article, research paper is an implementation of algorithm X for exact cover problem. In the Knuth's research papaer, linked above it is shown how Polymino problem (that is ...
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0answers
32 views

Job shop scheduling with events that should be completed simultaneously

I'm working on a scheduling algorithm that schedules a set of events with an event duration to a set of agents with various working times. However, some events require more than one agent to be ...
1
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1answer
34 views

Is there a generic algorithm to optimally combine elements by some arbitrary scoring method?

I'm looking for a generic algorithm to optimally combine elements of a list. I'm not sure if it even exists, but I believe some kind of divide-and-conquer algorithm could exist. In my specidifc case, ...
3
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1answer
123 views

Weird behaviour of softmax derivative?

I have been implementing some neural networks in MATLAB and recently I noticed a weird thing while implementing softmax derivative: Setting the derivative to one, rather than using the actual ...
3
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2answers
272 views

Maintaining a sorted moving window

I have an array of length $n$ representing a time series of data. I want to implement a moving (sliding) window of length $k < n$ and calculate things like sliding median, sliding quantile, sliding ...
1
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0answers
59 views

How to Optimise Each Multithreading Technique? (Cooperative/Preemptive/Simultaneous)

I am currently in the process of writing an IB Extended Essay on the efficacy of multithreading on increasing the performance of applications. So far, I have been able to deduce that there are three ...
4
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0answers
72 views

Need help figuring out a planning/assignment problem

I'm looking to solve this planning problem. Any pointers or ideas are much appreciated! You have a number of i individuals i = { 1, 2, ..., n } that need to perform tasks. Tasks are performed in ...
1
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1answer
31 views

How important is to formulate a convex optimization for a proposed algorithm?

I proposed a new sparse coding algorithm which has good results compared to the baselines, however, it has a non-convex optimization framework. I solved the problem using a general solver (e.g. ...
4
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1answer
116 views

Integer Problem Solving with two boolean selection variables

I am trying to solve a two dimensional combinatorial problem. Hereis my input space {{RA1,RA2},{RB1,RB2},{RC1,RC2}} and i have to choose two out of three elements{A,B,C} and one out of two possible ...
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0answers
47 views

Knapsack problem with additional conditions for data objects

I've been trying to theorize how to solve a certain type of problem for months now. Suppose you have a collection of $m$ pre-defined $(d+2)$-dimensional vectors like so: $$(v, s, m_1, \dots, m_{d})$$...
-1
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1answer
37 views

Optimization problems and quantifiers

A simple optimization problem is of form $\max_{x\in\mathcal R}f(x)$. We can quantify as $\exists x\in\mathcal R\forall y\in\mathcal R f(y)\leq f(x)$. The quantification here is $\exists\forall$. ...
1
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1answer
644 views

Fantasy premier league dream team algorithm?

For those of you who are not familiar with FPL, here's a short version. You have players playing as either Goalkeeper, Defender, Midfielder or Forward. Each player has some price (either rounded to .5 ...
2
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1answer
482 views

Optimal way to find maximal sum (with constraints) of array elements

Problem: Find the maximum sum of the elements in an array, with the following constraints: all the elements of the array are non-negative integers each element can either be left out completely from ...
2
votes
1answer
284 views

Parameter sharing / weight constraints in Neural Networks

I would like to train a neural network whose parameters (alternatively, weights) are subject to linear constraints such as $w_{i,j} = w_{i',j'}$, where $w_{i,j}$ denotes the weight from input node $...
2
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1answer
32 views

optimize string search on black-box function

Given a lower-bound predicate function which returns true if an input is greater than or equal to a constant string, what is the optimal way to search for the ...
2
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1answer
17 views

Finding many different minima of nonlinear cost function

Given a nonlinear cost function $G(\vec{x})$ of many variables, does there exist a method that allows one to find successive local minima $\vec{x}_0, \vec{x}_1, \dots$ so that $\vec{x}_n$ is ...
3
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2answers
566 views

Optimal meeting point

I'm interested in studying the problem of the optimal meeting point, which can be described as follow: $n$ individuals who want to gather in a restaurant (for example). They want a fair meeting point ...
1
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1answer
21 views

Finding a non-boundary, local optimum of a non-convex function over a convex feasible region

I have a reasonably smooth non-convex non-monotone function in high(ish) dimensional space, that I wish to find a local minimizer for, over a convex feasible region (the intersection of a ball with a ...
4
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1answer
45 views

Optimal flow in a network with non-constant edges' weights

I've recently come across the problem that seems to be quite interesting but i don't know how to tackle it. I suppose that it might be a special case of maximum flow problem but it seems to be rather ...
3
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1answer
69 views

Find the shortest sub-tree with node deletion

Let $T=(V,E)$ be a tree rooted in $r$ and let $L$ denotes the set of leaves of $T$. For a given $v \in V$, let $C(v)$ be the out-neighors of $v$ i.e. its children in $T$ and $p(v)$ be its in-neighbor ...
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0answers
64 views

Hessian in reinforcement learning

The Hessian of multi-layered network exhibits known behaviour at critical points as shown in [1]. The tools of random matrix theory allow [2] to deduce the asymptotic distribution of the eigenvalues ...
2
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0answers
18 views

Job Shop Problem with dynamic jobs

I've got a problem at hand that's about scheduling tasks to different ressources, basically a simple job shop problem. But: my tasks "branch" dynamically, that is, there are tasks that not only have a ...
3
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1answer
318 views

Which algorithm can calculate an optimal allocation of students to projects?

I am trying to find an algorithm which calculates an optimal and stable allocation of $n$ students to $m$ projects, where each student strictly ranks all projects by preference. The available projects ...
4
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2answers
72 views

Largest weight-limited connected subgraph: NP-complete?

When playing Terra Mystica, it might be useful to predict how many spades you will get throughout the game, and use this information to decide where to build, such that you stand a good chance of ...
4
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2answers
96 views

How to model and solve this problem?

I have a matrix $P \in M_n(\mathbb N)$, where $$ P = \begin{bmatrix} 0 & P_{12} & \ldots & P_{1n}\\ P_{21} & 0 & \ldots & P_{2n}\\ \vdots & \vdots & \ddots &...