scholarly journals Automated Generation of EQ-Algebras through Genetic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 861
Author(s):  
Hashim Habiballa ◽  
Eva Volna ◽  
Martin Kotyrba
Keyword(s):  
Genetic Algorithms ◽  
Time Complexity ◽  
Computing Time ◽  
Genetic Approach ◽  
Fuzzy Logics ◽  
Genetic Operators ◽  
Automated Generation ◽  
Finite Algebras ◽  
Automated Production ◽  
Mutation Ratio

This article introduces an approach to the automated generation of special algebras through genetic algorithms. These algorithms can be also used for a broader variety of applications in mathematics. We describe the results of research aiming at automated production of such algebras with the help of evolutionary techniques. Standard approach is not relevant due to the time complexity of the task, which is superexponential. Our research concerning the usage of genetic algorithms enabled the problem to be solvable in reasonable time and we were able to produce finite algebras with special properties called EQ-algebras. EQ-algebras form an alternate truth–value structure for new fuzzy logics. We present the algorithms and special versions of genetic operators suitable for this task. Then we performed experiments with application EQ-Creator are discussed with proper statistical analysis through ANOVA. The genetic approach enables to automatically generate algebras of sufficient extent without superexponential complexity. Our main results include: that elitism is necessary at least for several parent members, a high mutation ratio must be set, optional axioms fulfilment increases computing time significantly, optional properties negatively affect convergence, and colorfulness was defined to prevent trivial solutions (evolution tends to the simplest way of achieving results).

Assembly Planning: A Genetic Approach

1998 ◽  
Author(s):  
Shiang-Fong Chen
Keyword(s):  
Genetic Algorithms ◽  
Fitness Function ◽  
Assembly Planning ◽  
Genetic Approach ◽  
Genetic Operators ◽  
Complex Problems ◽  
All Solutions ◽  
Assembly Problem ◽  
Optimal Assembly

Abstract The difficulty of an assembly problem is the inherent complexity of possible solutions. If the most suitable plan is selected after all solutions are found, it will be very time consuming and unrealistic. Motivated by the success of genetic algorithms (GAs) in solving combinatorial and complex problems by examining a small number of possible candidate solutions, GAs are employed to find a near-optimal assembly plan for a general environment. Five genetic operators are used: tree crossover, tree mutation, cut-and-paste, break-and-joint, and reproduction. The fitness function can adapt to different criteria easily. This assembly planner can help an inexperienced technician to find a good solution efficiently. The algorithm has been fully implemented. One example product is given to show the applications and results.

Minimization of total trim loss occurring in pipe cutting in shipbuilding with genetic algorithm

2021 ◽  
pp. 147509022199169
Author(s):  
Abdullah Türk ◽  
Dursun Saral ◽  
Murat Özkök ◽  
Ercan Köse
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Search Space ◽  
Cutting Process ◽  
Genetic Operators ◽  
Critical Stage ◽  
Different Types ◽  
Trim Loss ◽  
Pipe Systems

Outfitting is a critical stage in the shipbuilding process. Within the outfitting, the construction of pipe systems is a phase that has a significant effect on time and cost. While cutting the pipes required for the pipe systems in shipyards, the cutting process is usually performed randomly. This can result in large amounts of trim losses. In this paper, we present an approach to minimize these losses. With the proposed method it is aimed to base the pipe cutting process on a specific systematic. To solve this problem, Genetic Algorithms (GA), which gives successful results in solving many problems in the literature, have been used. Different types of genetic operators have been used to investigate the search space of the problem well. The results obtained have proven the effectiveness of the proposed approach.

scholarly journals A GENETIC BASED TECHNIQUE FOR THE DETERMINATION OF POWER SYSTEM TOPOLOGICAL OBSERVABILITY

2014 ◽  
pp. 16-21
Author(s):  
S. Vazquez-Rodriguez ◽  
R. J. Duro
Keyword(s):  
Genetic Algorithms ◽  
Power Systems ◽  
Power System ◽  
Spanning Tree ◽  
Point Of View ◽  
Genetic Operators ◽  
Building Process ◽  
Phenotype Transformation

In this paper we have addressed the problem of observability of power systems from the point of view of topological observability and using genetic algorithms for its determination. The objective is to find a way to determine if a system is observable by establishing if a spanning tree of the system that verifies certain properties with regards to the use of available measurements can be obtained. To this end we have developed a genotype-phenotype transformation scheme for genetic algorithms that permits using very simple genetic operators over integer based chromosomes which after a building process can become very complex trees. The procedure was successfully applied to standard benchmark systems and we present some results for one of them.

Modelling time complexity of micro-genetic algorithms for online traffic control decisions

2019 ◽  
Vol 11 (2) ◽  
pp. 141
Author(s):  
Bassant Abdelrahman ◽  
Kenan Hazirbaba ◽  
Omar Mughieda ◽  
Ghassan Abu Lebdeh
Keyword(s):  
Genetic Algorithms ◽  
Traffic Control ◽  
Time Complexity ◽  
Online Traffic

Modelling time complexity of micro-genetic algorithms for online traffic control decisions

2019 ◽  
Vol 11 (2) ◽  
pp. 141
Author(s):  
Ghassan Abu Lebdeh ◽  
Kenan Hazirbaba ◽  
Omar Mughieda ◽  
Bassant Abdelrahman
Keyword(s):  
Genetic Algorithms ◽  
Traffic Control ◽  
Time Complexity ◽  
Online Traffic

A Mathematical Setting for Fuzzy Logics

1997 ◽  
Vol 05 (03) ◽  
pp. 223-238 ◽  
Author(s):  
Mai Gehrke ◽  
Carol Walker ◽  
Elbert Walker
Keyword(s):  
Fuzzy Logic ◽  
Propositional Logic ◽  
Normal Forms ◽  
Unit Interval ◽  
Fuzzy Logics ◽  
Real Numbers ◽  
Truth Values ◽  
Finite Algebras ◽  
Finite Algorithms ◽  
Interval Valued

The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.

A FAST ALGORITHM FOR COMPUTING SAMPLE ENTROPY

2011 ◽  
Vol 03 (01n02) ◽  
pp. 167-186 ◽  
Author(s):  
YING JIANG ◽  
DONG MAO ◽  
YUESHENG XU
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Fast Algorithm ◽  
Time Complexity ◽  
Computing Time ◽  
Sample Entropy ◽  
Computational Costs ◽  
Tree Data ◽  
Input Time ◽  
Tree Data Structure

Sample entropy is a widely used tool for quantifying complexity of a biological system. Computing sample entropy directly using its definition requires large computational costs. We propose a fast algorithm based on a k-d tree data structure for computing sample entropy. We prove that the time complexity of the proposed algorithm is [Formula: see text] and its space complexity is O(N log N), where N is the length of the input time series and m is the length of its pattern templates. We present a numerical experiment that demonstrates significant improvement of the proposed algorithm in computing time.

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