Combinatorial Problems in Algorithmic Differentiation

One of the central issues that must be resolved for a metaheuristic optimization process to work well is the dilemma of the balance between exploration and exploitation. The metaheuristics (MH) that achieved this balance can be called balanced MH, where a Q-Learning (QL) integration framework was proposed for the selection of metaheuristic operators conducive to this balance, particularly the selection of binarization schemes when a continuous metaheuristic solves binary combinatorial problems. In this work the use of this framework is extended to other recent metaheuristics, demonstrating that the integration of QL in the selection of operators improves the exploration-exploitation balance. Specifically, the Whale Optimization Algorithm and the Sine-Cosine Algorithm are tested by solving the Set Covering Problem, showing statistical improvements in this balance and in the quality of the solutions.

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Inversion-free geometric mapping construction: A survey

Computational Visual Media ◽

10.1007/s41095-021-0233-9 ◽

2021 ◽

Vol 7 (3) ◽

pp. 289-318

Author(s):

Xiao-Ming Fu ◽

Jian-Ping Su ◽

Zheng-Yu Zhao ◽

Qing Fang ◽

Chunyang Ye ◽

...

Keyword(s):

Mesh Generation ◽

Optimization Problem ◽

Texture Mapping ◽

Deformation Texture ◽

Research Field ◽

Combinatorial Problems ◽

Open Problems ◽

Nonlinear Constrained Optimization ◽

Construction Methods ◽

Geometric Mapping

AbstractA geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

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Feature Selection and Parameter Optimization of Support Vector Machines Based on Modified Artificial Fish Swarm Algorithms

Mathematical Problems in Engineering ◽

10.1155/2015/604108 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 7

Author(s):

Kuan-Cheng Lin ◽

Sih-Yang Chen ◽

Jason C. Hung

Keyword(s):

Feature Selection ◽

Parameter Optimization ◽

Combinatorial Problem ◽

Combinatorial Problems ◽

Support Vector ◽

Local Optimum ◽

Artificial Fish Swarm Algorithm ◽

Swarm Algorithms ◽

Artificial Fish Swarm ◽

Information And Communication

Rapid advances in information and communication technology have made ubiquitous computing and the Internet of Things popular and practicable. These applications create enormous volumes of data, which are available for analysis and classification as an aid to decision-making. Among the classification methods used to deal with big data, feature selection has proven particularly effective. One common approach involves searching through a subset of the features that are the most relevant to the topic or represent the most accurate description of the dataset. Unfortunately, searching through this kind of subset is a combinatorial problem that can be very time consuming. Meaheuristic algorithms are commonly used to facilitate the selection of features. The artificial fish swarm algorithm (AFSA) employs the intelligence underlying fish swarming behavior as a means to overcome optimization of combinatorial problems. AFSA has proven highly successful in a diversity of applications; however, there remain shortcomings, such as the likelihood of falling into a local optimum and a lack of multiplicity. This study proposes a modified AFSA (MAFSA) to improve feature selection and parameter optimization for support vector machine classifiers. Experiment results demonstrate the superiority of MAFSA in classification accuracy using subsets with fewer features for given UCI datasets, compared to the original FASA.

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Lower bounds for combinatorial problems on graphs

Journal of Algorithms ◽

10.1016/0196-6774(85)90008-2 ◽

1985 ◽

Vol 6 (3) ◽

pp. 393-399 ◽

Cited By ~ 1

Author(s):

Hiroyuki Nakayama ◽

Takao Nishizeki ◽

Nobuji Saito

Keyword(s):

Lower Bounds ◽

Combinatorial Problems

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On the Number of Tetrahedra with Minimum, Unit, and Distinct Volumes in Three-Space

Combinatorics Probability Computing ◽

10.1017/s096354830700884x ◽

2008 ◽

Vol 17 (2) ◽

pp. 203-224 ◽

Cited By ~ 3

Author(s):

ADRIAN DUMITRESCU ◽

CSABA D. TÓTH

Keyword(s):

Unit Volume ◽

Time Algorithm ◽

Combinatorial Problems ◽

List Type ◽

Type Number ◽

Point Sets ◽

Minimum Number ◽

Three Space

We formulate and give partial answers to several combinatorial problems on volumes of simplices determined bynpoints in 3-space, and in general inddimensions.(i)The number of tetrahedra of minimum (non-zero) volume spanned bynpoints in$\mathbb{R}$3is at most$\frac{2}{3}n^3-O(n^2)$, and there are point sets for which this number is$\frac{3}{16}n^3-O(n^2)$. We also present anO(n3) time algorithm for reporting all tetrahedra of minimum non-zero volume, and thereby extend an algorithm of Edelsbrunner, O'Rourke and Seidel. In general, for every$k,d\in \mathbb{N}, 1\leq k \leq d$, the maximum number ofk-dimensional simplices of minimum (non-zero) volume spanned bynpoints in$\mathbb{R}$dis Θ(nk).(ii)The number of unit volume tetrahedra determined bynpoints in$\mathbb{R}$3isO(n7/2), and there are point sets for which this number is Ω(n3log logn).(iii)For every$d\in \mathbb{N}$, the minimum number of distinct volumes of all full-dimensional simplices determined bynpoints in$\mathbb{R}$d, not all on a hyperplane, is Θ(n).

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