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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Making change optimally

Consider that a currency system has $k$ denominations $d_0, d_1, ... d_{k-1}$. $d_0, d_1, ... d_{k-1}$ are such that $d_0 < d_1 < ... < d_{k-1}$ and $d_i$ divides $d_j$ for all $0<=i<j&...
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Verifying the minimum cost from each node to a sink node in linear time

Problem Statement: Let $G= (V, E)$ be a directed graph with costs $c_e \in \mathbb{R}$ on each edge $e \in E$. There are no negative cycles in $G$. Suppose there is a sink node $t \in V$, and for ...
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Minimum amount of rectangles to create a 2-dimensional matrix

From this codegolf question. Consider an $r$ by $c$ matrix of nonnegative integers, called $M$. You also have a zero matrix of the same dimensions, called $N$. A "move" consists of replacing a ...
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Given we restrict the time and memory allowed what bounds can we place on a halting decider?

If a program is given as much memory and as much time to execute as it wants, then the halting problem is undecidable, and by Rice's theroem all non-trivial, semantic properties of programs like that ...
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Change the structure from 3SAT to 1in3 3SAT

There is a variable set V = {x1,x2,x3} and clause set C1={x1,x2,-x3} C2={x1,-x1,-x2} C3={-x1,-x2,x3} C4={x2,x3,-x3}. For this structure, no matter each variable is positive or negative, the clause can ...
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How well do multi objective optimization algorithms such NSGAii scale when there are many objectives (for example 10 or more)?

What I'm trying to figure out is what happens when using a multi objective optimization algorithm such as NSGA-ii and instead of trying to find the usual 2/3 objectives, I use 10 or many more ...
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What is the difference between derivative free optimization and derivative optimization in terms of advantages/disadvantages?

I understand the basic operation of the algorithms however i'm unclear as to when to use one over the other and what advantages/disadvantages they offer over each other. Also as an aside, if anyone ...
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How to input random values (constraints) of any variables in case of formulating Linear Programming Problem?

Suppose, Min 2x+3y Subject to, x=2,x=5,x=7 y=5, y=9 is a linear program. Where x holds the values 2 or 5 or 7 and y holds the values 5 or 9. Then what should the correct ...
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Minimize same placed elements in a list of permutations (Heap)

I'm trying to optimize the permutations generated from a set of n elements. Here is the pitch: I have a set of 6 elements $\{1,2,3,4,5,6\}$ and I want to create 10 permutations. I could use Heap ...
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How to identify a continuous shape and break it into minimum number of rectangles?

The input in this case is going to be coordinates in 2D of the vertices of the shape. There will be no curves, but the shape can have holes. The algorithm or program needs to identify the continuous ...
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How is ellipsoid method a polynomial-time algorithm for LP?

I have always thought that the ellipsoid algorithm is an algorithm which can be used to solve LP in polynomial-time. However, what confuses me is the dependence on the ratio of volumes of the balls (...
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metaheuristics vs exact and traditional algorithms

Recently, my friend has submitted a paper and solved a problem with an exact method. Surprisingly, a reviewer asked him why he used an exact method instead of the popular metaheuristics algorithms! We ...
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Optimization palletizing and dispatch

I have the following situation: I have to find the most optimal days to palletize and to dispatch pallets to 22 different destination. The demand for each destination varies, ranging from 3 to 12 ...
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93 views

Is this variation of the assignment problem NP-hard, and does it have a name?

I’m trying to solve a problem very similar to the assignment problem, with a few twists. The problem has a certain amount of workers, and a certain amount of tasks - workers is always >= tasks. Each ...
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Creating a waste-optimizing algortihm for cutting a 1d block

I have a one-dimensional block of material. I run an analysis that divides the material into usable and unusable regions. In a manufacturing process, said material is cut and the unusable regions ...
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Is this a good way of generating diverse solutions to a problem using a genetic algorithm?

Imagine a complicated blackbox-esque system that has 20 inputs and 5 outputs. I have a set of criteria I am able to use to construct a fitness function. I run a genetic algorithm to deduce values ...
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How to prove the optimization version problem (whose decision version is NP-complete) can be solved in poly-time iff P=NP?

I have proved the decision version of my problem be $\mathcal{NP}$-complete. And I know that if I can solve the optimization version in poly-time, then I can just to compare the obtained minimum (or ...
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Obtaining the dual variables of an optimisation problem with second order cone constraints solved using Gurobi

I'm solving an optimisation problem with linear and second order cone constraints, in other words the problem is convex and should have dual variables. I'm using Julia with JuMP to formulate the ...
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Algorithm for selecting a sample that's as spread out as possible?

I have a large database of data with dates. There are large gaps and large chunks of data without gaps. I want to get a sample of this data such that the dates are as spread out as possible (i.e. as ...
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Is there an algorithm that provides the highest possible “sum of satisfaction” for a priority based distribution problem?

Let's say we have n (e.g. 6) children and a box of candy. The box has k (e.g. 8) different flavours, and m (e.g. 4) piece of candy in each flavour. This question is specifically about the cases where ...
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Is it possible to compute a whole convolution layer at once?

I have an input of 32×32×3 and I want to feed it to a convolution layer that output 32×32×16 feature maps. I know that I can compute a single feature map as matrix multiplication. But my question is, ...
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What kind of standard deviation must be used in optimization algorithms?

I would like to ask about the standard deviation of objective function value. There are two types of standard deviations: Population standard deviation Sample standard deviation In metaheuristic ...
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Minimization with asymptotic assumption

Given the function $g(n,m)=\min\Big\{f(a,b)+f(n-a,c)+f(n,m-bc)\Big|\\a,b,c\ \ \text{with} \left\{\begin{matrix} a,\ b,\ n-a,\ c,\ m-bc \geq 0 \\ b\leq a! \\ c\leq (n-a)! \\ \end{matrix}\right. \Big\}...
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59 views

Loop Invariant Code Motion - am I missing something?

I've been implementing LICM for a project, and came upon a strange observation. Let's say we have a loop int i = 10; while (i > 0) { a = 2; i--; } ...
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Finding an optimal machine assigning

I have $m$ machines and $n$ jobs. Each machine has a load capacity. Each job can be only handled by either one or two machine, and each job takes some time to finish. After it finished, new jobs can ...
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42 views

Modelling of minimal NOR-circuit problem with CP

I'm currently working on a Constraint Programming problem which I find difficult to model. Here 's the definition of the problem : " Given a specification of a Boolean function f(x1, ..., xn) in the ...
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Finding “good” order of elements for the purpose of material minimization

I am working with metallic shapes which are curved and highly irregular. The initial order of them is random and by default they are merely sorted by size, which is simple. However the resulting order ...
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235 views

Implementing a job-scheduling problem with multiple dependencies and variable tasks (time frames) using dynamic programming

I'm writing a "Chores Scheduler" in Python. It has to be implemented using dynamic programming and has to take in two types of chores, as below: Regular chores with a start time and end time (a real-...
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A scheduling problem on an oriented graph with multiple constraints

The problem is the following : Data An oriented graph $(V, E)$ : to be understood as a set of partially ordered tasks A map $d: V -> \mathbb{N}$ : to be understood a function mapping tasks to a ...
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Confused between different Structure from Motion pipelines

What is the difference between Global SfM, Incremental SfM, Sequential SfM, Progressive SfM and VSLAM (Visual Simultaneous Localization and Mapping). Is sequential SfM the same as VSLAM ? I have tried ...
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How to judge the searching precision of Particle Swarm Optimization?

As the title mentioned, how can I judge the searching precision of PSO? Is this depending on the velocity of the particles? I would like to give an example to clarify my question: For a 2-D searching, ...
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Optimize an underdetermined system with quartic constraints

I encountered an optimization problem which does not belong to any well-known category of optimization. The system has $M$ (typically $M=120$) real variables and $N$ (typically $N=100$) constraints (...
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Resource allocation / optimization

At work I stumbled across this problem of allocating resources: We are given a set of objects belonging to one of seven possible classes (multiple objects per class are allowed). We distinguish ...
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Kiln optimization problem

Say I have a kiln for making castings. There are 3 shapes. I need to produce the following castings: 102 of A 364 of B 70 of C I can put 50 molds in the kiln at a time. I can have 75 molds made in ...
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Branch and bound Dual Gap

Let's suppose we want to solve the knapsack problem using the Branch and Bound algorithm. I know that the algorithm ends when the optimality gap is = 0. However i have not understood how the dual ...
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34 views

Complexity of linear programming with restricted quadratic constraints

A problem instance is a linear program with the following kind of quadratic inequalities allowed: For some of the variables $x_i$, there is a variable $s_i$ (intuitively for approximating $x_i^2$, and ...
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How would I optimize a tree-like graph with a significant number of redundant nodes?

Recently, I was looking at the underlying data/implementation of a survey application created using a RPA tool. As a user progresses through the survey, the "decisions" reveal a predominantly tree-...
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223 views

Distribute repeated values into bins as evenly as possible

Preface I've asked a very similar question already on stack overflow in a different wording and gotten a working answer under the assumption that there is no way to go through all possibilities (np-...
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40 views

Determining cycle time and and hold time in logic circuits

First I have general question. In a circuit with both logic and D edge flip flop does hold time have to satisfy $t_{hold} < t_{setup}($D-FF$) + t_{pd-min}$(Logic), or is it enough that $t_{hold} \...
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174 views

What is the difference in SMO algorithm for SVM and SMO for one class?

Please let know if this is not the correct forum to ask this question. If not can anyone please tell where can I ask this question? I am trying to understand the difference between the paper : https:/...
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69 views

Stable matching with asymmetric arrays (gale shapley)

I was reading this thread The stable marriage algorithm with asymmetric arrays and started to solve the problem asked in this thread about matching 5 students with 10 dorms. One of the answer ...
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If value of LP relaxation of s-t minimum cuts is P ,then wen can find a s-t cut at most P edges?

My problem is mainly from this lecture notes on convex optimization here page4 Consider a s-t Minimum problem, on unweighted undirected graph $G=(V,E)$,we can formalize in following linear integer ...
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59 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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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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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 ...
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51 views

Compute unknown matrices that minimize a sum

This problem is about working with smart-phone accelerometers. To calibrate accelerometer, I need to find three unknown matrices T, K and B that minimize this sum: $$\sum_{i=0}^N(|g|^2 - |TK(a_i + B)|...
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Optimizing convex function in an online manner

I have a convex function of $n$ variables, $f(x_1,x_2,\dots,x_n)$ and need to find its minimizer. Are there algorithms that can retrieve the minimizer in an online fashion? i.e. solve for $x_1^{(opt)}$...
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137 views

Shortest path between 2 nodes subject to constraints

I am trying to find shortest path between 2 nodes in a graph similar to below: Each edge has a weight assigned to it. Also, the graph is directional with each edge directing from left to right. I ...
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22 views

Evolutionary algorithm - is there a relation between minimum iterations and size of decision variables

I am solving an optimization problem using SPEA2, my problem has three cases with decision variables 25, 50 and 100 in each case. I want to ask if there is some relationship between the number of ...
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How many optimal alignments can be there for a string of length m with a string of length n?

So I was practicing optimal alignment algorithm and I was stuck with this question of finding optimal alignment for a string of length m with a string length n ? Also is it possible to run it in theta(...