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
36 views

Text search by first order formula

I am searching for substrings that satisfy a given first order formula in a moderately sized text. The formula is made out of usual $\wedge, \neg, \exists$ and predicates ...
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1answer
358 views

Transition coverage for a DFA

Let $G$ be a directed graph, with a single source node $s$. I want to find a collection of paths that cover every edge of $G$ (i.e., every edge of $G$ appears in at least one of these paths), where ...
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2answers
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Ant colony optimization for continuous functions

I am trying to do optimization of a voice activity detection function, which is a function with continuous parameters. This is easily accomplished with genetic algorithms, simulated annealing, and ...
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2answers
855 views

Find the smallest summed distances by uniquely pairing elements of one set to elements of another set

As input I have two sets of points in RN, typically for large N, for example N=40. Supose both sets have m elements: S = s1 ... sm T = t1 ... tm Semantically both sets are equal, but due to noise (...
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1answer
153 views

Check constraint under some condition in linear programming

I would like to minimize linear pseudo-boolean function $$\mathrm{obj} = \sum_i c_i \mathrm{sel}_i$$ subject to $$\sum_i c_i sel_i \geq \mathrm{Value} \qquad\qquad(1)$$ where $c_1,\dots c_5, \...
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1answer
137 views

Shortest-depth routing algorithm

This problem came up in a graph network routing context, it can be expressed as follows: Let $n, m > 0$ be integers. Find any smallest list of positive integers $\langle a_1, \cdots, a_k \rangle$...
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1answer
90 views

Fitness functions for low-dimensional parts of cooperative coevolution algorithms

In cooperative coevolution algorithms, a high dimensional vector is broken into smaller vectors, each of which is optimized separately using EAs for fewer dimensions and then recombined. What is the ...
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1answer
241 views

What problem is to the set packing problem, as the hitting set problem to the set cover problem?

Wikipedia says that Set covering is equivalent to the hitting set problem What problem is to the set packing problem, as the hitting set problem is to the set cover problem? Is it that given the ...
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5answers
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Why do low fitness individuals have a chance to survive to the next generation?

I am currently reading and watching about genetic algorithm and I find it very interesting (I haven't had the chance to study it while I was at the university). I understand that mutations are based ...
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2answers
188 views

Is there only one optimal BST?

as i read some material about Optimal BST, i ran into a trouble. for following key i find two optimal BST with Average Cost = 30. 1 optimal BST using Dynamic programming Algorithm and 1 by hand ! ...
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1answer
92 views

Can weighted problem have polynomial complexity if non-weighted problem is NP-complete: hitting set

I am confronted with task to find polynomial time complexity solution for weighted hitting set problem. I have found that usual hitting set problem is NP-complete and therefore the task seems to be ...
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0answers
33 views

Choose m points out of n that form the polytope with the maximum volume in hyperspace

Let's say I have a set $A$ of $n$ points represented by real vectors of length $l$. What type of algorithm would I use to find the subset $B$ of $m$ ($m$ is arbitrary, to be chosen) points that ...
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3answers
9k views

Floyd–Warshall algorithm on undirected graph

I am referring to the algorithm from the Wikipedia page on the Floyd–Warshall algorithm. In case of undirected graphs should I change the assignment statement inside the ...
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1answer
129 views

What is the significance of the vector dimension in semidefinite programming relaxations?

Let's say that we want to design a semi-definite programming approximation for an optimization problem such as MAX-CUT or MAX-SAT or what have you. So, we first write down an integer quadratic ...
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0answers
144 views

A matrix rank problem over finite fields

I have already asked a similar question here, but since I have not got an acceptable answer, I decided to ask a simpler version of the question here. Let $M|\mathbf w$, where $M$ is a matrix and $\...
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1answer
529 views

Distance k-Dominating Set on a Tree

I don't consider myself very good at math, but nevertheless I enjoy solving optimization problems like the ones often asked in ACM ICPC (a college programming competition). I recently came across an ...
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1answer
213 views

Is the length of the shortest quine in a programming language computable?

The length of the shortest program in a given (fixed) programming language that produces a given output is that output's Kolmogorov complexity, which is not a computable function on the set of ...
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2answers
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What is a bicriteria approximation algorithm?

What is a bicriteria approximation algorithm? This keeps coming up in the case of data stream clustering. Is this related to multi-objective optimization? This is where I came across it: cis.upenn....
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1answer
2k views

How to modify Bellman-Ford algorithm for this specific Minimum Cost Flow problem?

I'm trying to design an algorithm for the following optimization problem. Suppose that $G=(V, E)$ is a digraph where $V$ and $E$ are sets of vertices and edges of $G$, respectively. $|V| = n$ and $|E| ...
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1answer
101 views

Fast Consequence FInders

I have been struggling in the search for a modern fast "consequence finder". That is, an implementation based on state-of-the-art theory; things of the ilk of Z3, Prover9, OTTER, etc. To describe ...
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1answer
266 views

Algorithm for cost function maximization

I have a system that takes in 'm' inputs and provides a cost value as an output. The system is a "black box" to me. The inputs can be varied and the corresponding output can be observed, however, I ...
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1answer
167 views

What's the meaning of “Front” in “Pareto-Optimal Front”?

I'm reading a paper about Multi-Objective Optimization Problem. I understand Optimal in Pareto sense, and I even know what is Pareto-Optimal Front somehow. But I can't find a relationship between the ...
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2answers
320 views

Minimizing Cost by minimizing delay

There is a complete binary tree with its leaves as components of some system The values from one node to another gives propagation time for a signal to propagate from one junction to another For the ...
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3answers
2k views

Algorithm to match numbers with minimum number of moves

This is a sort of edit-distance question, and is very easy. I am just quite brain dead on this subject and can't figure it out so far. Given a series of numbers, e.g. ...
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0answers
25 views

Is it possible to do reductions with non-decision problems? [duplicate]

I've recently begun studying reductions in my algorithms class. All the reductions I've seen have been from decision problem $\to$ decision problem. Is it possible to do reductions with non-decision ...
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2answers
94 views

Programming a genetic algorithm with a non-fixed size

I am trying to write a genetic algorithm for a program. Most examples for genetic algorithms use something like this as the input: aaaaaaaaaa and mutate/...
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1answer
111 views

What does “finding an optimal action” for a bandit mean?

In Sutton and Barto's reinforcement learning book, in multi-armed bandit problem a phrase has been used. "finding an optimal action" using greedy/$\epsilon$-greedy algorithm. When it is said that an ...
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1answer
81 views

Minimum weighted arithmetic mean partion?

Assume I have some positive numbers $a_1,\ldots,a_n$ and a number $k \in \mathbb{N}$. I want to partition these numbers into exactly $k$ sets $A_1,\ldots,A_k$ such that the weighted arithmetic mean ...
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3answers
1k views

Interpolation Optimization Problem

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - M by N Matrix). Someone marks some pixels as anchors. Now, you need to ...
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0answers
180 views

Gradient descent vs. Newton's method: which is more efficient?

Using gradient descent in d dimensions to find a local minimum requires computing gradients, which is computationally much faster than Newton's method, because Newton's method requires computing both ...
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1answer
107 views

Application of Combinatorics, Logic and computability theory in physical science: Tiling of Wang Tile with proportionality [closed]

The original problem of Domino Tiling and Wang Tile has great theoretical interest on computability theory... However, the great emerging problem on application of Wang Tile in material science and ...
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1answer
223 views

Maximum Stacking Height Problem

Has the following problem been studied before? If yes, what approaches/algorithms were developed to solve it? Problem ("Maximum Stacking Height Problem") Given $n$ polygons, find their stable, ...
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6answers
13k views

How is Dynamic programming different from Brute force

I was reading up on Dynamic Programming when I came across the following quote A dynamic programming algorithm will examine all possible ways to solve the problem and will pick the best solution. ...
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1answer
77 views

How to optimally seperate a student body?

Students will identify certain students they want to work with. I have therefore decided to split them into two groups where I want to minimize the number of people in Group 1 who want to work with ...
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1answer
977 views

Traveling Salesman: how to use a lower bound?

Let me preface this question by giving some helpful background material. I'm trying to solve the traveling salesman problem using branch and bound. Concretely, for a partial solution, I'm using the ...
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2answers
131 views

Unknown notation “$e^T$” in a machine learning paper

I'm trying to understand the material in "A Dual Coordinate Descent Method for Large-scale Linear SVM" by Hsieh et. al. (link to paper) There is an equation for the Dual form of an unconstrained ...
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1answer
2k views

Automatic seat assignment algorithm [closed]

I am looking for articles relating to algorithms that deal with automatic selection of seating assignment. I need an algorithm (preferably more than one) that can automatically select a seating place ...
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0answers
128 views

In multi criteria decision making, what notions are there to get a subset of the Pareto set?

In the multi criteria decision making context, let $\mathcal{A}$ be a set of alternatives or choices. Each alternative $\alpha\in \mathcal{A}$ is a vector of $k$ criteria $\alpha=(v_1,v_2,\dots,v_k)$. ...
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0answers
385 views

Trying to understand the Gilmore-Lawler lower bound

For a class project we're developing a software that solves a common optimisation problem. After some research we've found out that our problem is called QAP (Quadratic Asssignment Problem) and the ...
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0answers
710 views

Practical Application of Kadane algorithm

Kadane Algorithm is used to solve the maximum subarray problem which in simpler terms is to find the highest possible value of a continuous sub array in an array. One often cited application of ...
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0answers
50 views

Assigning packages to different points by minimizing distance: is this a known problem?

Imagine we have N houses, on a standard euclidean 2D plane. We also have N "packages", each of which contains several "objects" of different types, let's call them A, B, C, etc. We know the content of ...
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1answer
5k views

Choosing a subset to maximize the minimum distance between points

I have a set of points $C$, and I have the distance between each point $D(P_i,P_j)$. These distances are euclidean but the points are actually in a feature space. From the $C$ points I want to choose ...
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1answer
565 views

Mutation and crossover operations in discrete differential evolutionary operations?

I need to use discrete differential evolutionary algorithm for assigning discrete values from set size $L$ to vectors of size $D$ where $L$ could be smaller, equal or larger than $D$. Elements of ...
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1answer
103 views

How to reformulate my problem as a mixed-integer quadratic problem

I have an unknown $n$-dimensional vector $x$ whose analytical expression depends on the following sum $x = z + Ba$ where the vector $z$ and the matrix $B\in \mathbb{R}^{n\times s}$ are given. So the $...
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2answers
613 views

Suboptimal Solution for a combinatorial problem

I have a cost function $f(X)=\|\hat{X}-X\|_2$ to minimize which depends on a $s\times s$ matrix $X$ where $\hat{X}$ is given and $\|X\|_2=\big(\sum_{i,j}x_{ij}^2\big)^{1/2} $. This matrix $X$ is ...
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5answers
4k views

What is the best way to index lookups on a 2D array of integers that is boundless in x and y?

Lets say you have a data model that consists of a 2D grid of integer points. This grid is sparsely populated and boundless in x and y (up to the max of a 32-bit integer). What is the best way to ...
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1answer
631 views

Boat riddle as a combinatorial optimization problem?

I remember a riddle about a bunch of people on a river bank, and a boat with limited capacity (lets say the boat can transport 2 people at a time). There are various relations between the people like: ...
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1answer
282 views

Bin packing problem or not?

Suppose I have $N$ bins and $M$ items as depicted in the figure below (3 bins and 3 items): Suppose that every bin has unit capacity and the weights of the items depend on the bins used. I want to ...
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0answers
124 views

Boolean formula that agrees with most truth assignments

Let $X_1,\dots,X_n$ be $n$ boolean variables. I have an unknown predicate $P(X_1,\dots,X_n)$ on these boolean variables. Of course, I can view the predicate as a function $f_P : \{0,1\}^n \to \{0,1\}...
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1answer
372 views

Balanced partition problem for N =< 60 and very large sums

I was proposed (in school) to develop an approach to solve optimally the balanced partition problem. I tried the pseudo-linear algorithms but SUM is very large (~1M) and so O(S*N) cant run under ...

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