Chaos Map Research Articles

A hybrid Harris hawks-moth-flame optimization algorithm including fractional-order chaos maps and evolutionary population dynamics

This paper proposes a modified version of a contemporary metaheuristic named Harris Hawks Optimizer (HHO) that mimics the foraging strategies used by Harris hawks. It is first argued that exploration ability of HHO is weaker than its exploitation. In addition, the initial position of hawks has the greatest impact on the convergence of the solutions in a similar manner to other metaheuristic algorithms. Then, we applied the Fractional-Order Gauss and 2xmod1 Chaotic Maps to generate the initial population as well as applying the operators of the Moth-Flame Optimization (MFO) to improve the exploration of HHO. In addition, the concept of evolutionary Population Dynamics (EPD) is applied to prevent premature convergence and stagnation in local optima. The method proposed in this work is called FCHMD and evaluated using a set of thirty-six mathematical functions and five engineering problems. The results of the FCHMD are compared with a number of well-known metaheuristics. It can be observed that the FCHMD algorithm outperforms its competitors on the majority of case studies.

An Image Encryption Algorithm with Hermite Chaotic Polynomials and Scan Pattern

In today’s digital world, massive amount of sensitive information is being generated in the form of image and further it is shared via Internet. Maintaining the confidentiality of these data has become a major issue due to security vulnerability present in the network and transmission media. Image encryption algorithms are developed by various researchers to permit only authorized users to access and view sensitive images. This paper presents a novel image encryption scheme based on Hermite polynomials chaos function. First, random key stream is generated by using Hermite polynomial with different initial and incremental values of the variables. Next, the original image is scrambled with scan pattern to rearrange the pixels position. The scrambled image is XORed with the random key stream to get the encrypted image. The proposed method is experimented and observed that it is efficient and confirms the confusion and diffusion properties of a secure image encryption method. Large key space, low relation between the pixels of encrypted image, and sensitivity to initial seed value of the key are the strength of the proposed image encryption method.

One-time-pad cipher algorithm based on confusion mapping and DNA storage technology.

In order to solve the problems of low computational security in the encoding mapping and difficulty in practical operation of biological experiments in DNA-based one-time-pad cryptography, we proposed a one-time-pad cipher algorithm based on confusion mapping and DNA storage technology. In our constructed algorithm, the confusion mapping methods such as chaos map, encoding mapping, confusion encoding table and simulating biological operation process are used to increase the key space. Among them, the encoding mapping and the confusion encoding table provide the realization conditions for the transition of data and biological information. By selecting security parameters and confounding parameters, the algorithm realizes a more random dynamic encryption and decryption process than similar algorithms. In addition, the use of DNA storage technologies including DNA synthesis and high-throughput sequencing ensures a viable biological encryption process. Theoretical analysis and simulation experiments show that the algorithm provides both mathematical and biological security, which not only has the difficult advantage of cracking DNA biological experiments, but also provides relatively high computational security.

Spectrum-based multi-fault localization using Chaotic Genetic Algorithm

Abstract Context: In the field of software engineering, the most complex and time consuming activity is fault-finding. Due to increasing size and complexity of software, there is a necessity of automated fault detection tool which can detect fault with minimal human intervention. A programmer spends a lot of time and effort on software fault localization. Various Spectrum Based Fault Localization (SBFL) techniques have already been developed to automate the fault localization in single-fault software. But, there is a scarcity of fault localization technique for multi-fault software. In our study, we have found that pure SBFL is not always sufficient for effective fault localization in multi-fault programs. Objective: To address the above challenge, we propose an automated framework using Chaos-based Genetic Algorithm for Multi-fault Localization (CGAML) based on SBFL technique. Methods: Traditional Genetic Algorithm (GA) sometimes stuck in local optima, and it takes more time to converge. Different chaos mapping functions have been applied to GA for better performance. We have used logistic mapping function to achieve chaotic sequence. The proposed technique CGAML first calculates the suspiciousness score for each program statement and then assigns ranks according to that score. The statements having smaller rank means there is a high probability of the statements to be faulty. Results: Five open-source benchmark programs are tested to evaluate the efficiency of CGAML technique. The experimental results show CGAML gives better results for both single-fault and multi-fault programs in comparison with existing spectrum-based fault localization techniques. Conclusion: E X A M metric is used to compare the performance of our proposed technique with other existing techniques. Smaller E X A M score denotes the higher accuracy of the technique. The proposed framework generates smaller E X A M score in comparison with other existing techniques. We found that, overall CGAML works on an average 8.5% better than GA for both single-fault and multi-fault software.

Analysis and optimization of gear skiving parameters regarding interference and theoretical machining deviation based on chaos map

The gear skiving has gained more and more attention from researchers because of high efficiency and high precision. However, if skiving parameters are not properly selected in the actual machining process, the interference between the flank face of the cutter and the machined tooth surface would occur, and the theoretical machining deviation would obviously affect the machining accuracy of the workpiece. In view of this, the influences of skiving parameters on interference and theoretical machining deviation are analyzed by means of edge-scanning surface. Then, a parameter optimization model is built by taking the minimum theoretical machining deviation as optimization objective, and taking machining efficiency as well as no-interference as the constraints. According to the characteristics of this model, an algorithm is proposed based on chaos map. A machining example shows that the algorithm is feasible and effective.

Probabilistic routing protocol with firefly particle swarm optimisation for delay tolerant networks enhanced with chaos theory

In this paper, we propose a proactive routing paradigm for delay tolerant networks (DTN) using probabilistic routing implemented via firefly particle swarm optimisation and optimised by chaos maps. DTN is a specific class of networks where there is absence of an end to end connectivity among nodes and are characterised by long or variable delays, asymmetric data rates and high error rates. The routing scheme considers the constrained environment of DTN nodes and implements a meta-heuristic paradigm to facilitate data transfer. The chaos maps further enhance the probabilistic routing parameters controlling brightness and ageing by randomising them. The protocol is implemented on ONE simulator and its performance is compared with traditional DTN routing schemes across delivery probability, average latency, overhead ratio and buffer utilisation. The simulation results show that our proposed protocol performs better than its contemporary ant PRoPHET protocol across the various performance metrics.

Physical Layer Encryption and System Performance Enhancement Algorithm Based on Chaos Mapping in OFDM-PON

Physical Layer Encryption and System Performance Enhancement Algorithm Based on Chaos Mapping in OFDM-PON

Quantum Chaotic Butterfly Optimization Algorithm With Ranking Strategy for Constrained Optimization Problems

Nature-inspired metaheuristic optimization algorithms, e.g., the butterfly optimization algorithm (BOA), have become increasingly popular. The BOA, which adapts the food foraging and social behaviors of butterflies, involves randomly defined, algorithmic-dependent parameters that affect the exploration and exploitation strategies, which negatively influences the overall performance of the algorithm. To address this issue and improve performance, this paper proposes a modified BOA, i.e., the quantum chaos BOA (QCBOA), that relies on chaos theory and quantum computing techniques. Chaos mapping of unpredictable and divergent behavior helps tune critical parameters, and the quantum wave concept helps the representative butterflies in the algorithm explore the search space more effectively. The proposed QCBOA also implements a ranking strategy to maintain balance between the exploration and exploitation phases, which is lacking in conventional BOAs. To evaluate reliability and efficiency, the proposed QCBOA is tested against a well-utilized set of 20 benchmark functions and travelling salesman problem which belongs to the class of combinatorial optimization problems. Besides, the proposed method is also adopted to photovoltaic system parameter extraction to demonstrate its application to real-word problems. An extensive comparative study was also conducted to compare the performance of QCBOA with that of the conventional BOAs, fine-tuned particle swarm optimization (PSO) algorithm, differential evolution (DE), and genetic algorithm (GA). The results demonstrate that, chaos functions with the quantum wave concept yield better performance for most tested cases and comparative results in the rest of the cases. The speed of convergence also increased compared to the conventional BOAs. The proposed QCBOA is expected to provide better results in other real-word optimization problems and benchmark functions.

A Hybrid Sparrow Search Algorithm Based on Constructing Similarity

Sparrow search algorithm (SSA) is easy to fall into local convergence and convergence stagnation. In order to solve these problems, this paper introduced Circle chaos map into the original SSA to improve its global search ability at the beginning of iteration. Meanwhile, it introduced T-distribution variation to affect the sparrow population position update rules in different iteration periods. Finally, we constructed the “similarity function” to measure the “dispersion” of the sparrow population, and formulated the search rules of the sparrow population under different “dispersion”. In order to test the specific optimization performance of the proposed algorithm, the test results of 54 test functions are compared with those of 9 other algorithms which are widely used, and then the test results are analyzed using non-parametric tests in statistics. At the same time, this paper introduces this algorithm into three concrete engineering test problems for testing. The results of these tests all prove that the proposed algorithm has stronger global optimization ability and higher convergence precision compared with other algorithms.

IoD swarms collision avoidance via improved particle swarm optimization

Abstract Drones flights have been investigated widely. In the presence of high density and complex missions, collision avoidance among swarm of drones and with environment obstacles becomes a challenging task and indispensable. This paper aims to enhance the optimality and rapidity of three dimensional IoD path generation by improving the particle swarm optimization (PSO) algorithm. The improvements include using chaos map logic to initialize the population of PSO. Also, adaptive mutation is utilized to balance local and global search. Then, the inactive particles are replaced by new fresh particles to push the solution toward global optimal. Furthermore, Monte Carlo simulation is carried out and the results are compared with slandered PSO and with recent work CIPSO. The results exhibit significant improvement in convergence speed as well as optimal solution which prove the ability of proposed method to generate safety path for IoD formation without collision with terrain obstacle and among drones.

Image Encryption Scheme using Complemented MLCA and Special Chaos Map

Image Encryption Scheme using Complemented MLCA and Special Chaos Map

An efficient image cryptography mechanism based on the hybridization of standard encryption algorithms

In our approach the combination of RC4 and Blowfish algorithms with chaos mapping (RC4BC) has been presented for the image encryption. In the first phase image dataset has been considered. Then weight values have been calculated based on the image pixels. It has been calculated based on the attribute pixel, corelated pixels and the analytical factors of the edges. Then substitution has been performed through RC4 encryption mechanism. The substitution has been performed based on 8 sub blocks for the first time. After that different random substation has been applied based on the reallocation of bytes up to 16 rounds. Final substitution has been performed by the blowfish and chaos mapping. By this method the pixels of the images are rotated and shuffled with the XOR operation along with 16-byte reshuffling in each iteration. A total of 50 rounds have been considered for the shuffling, rotation and mapping. Then for comparative analysis peak signal to noise ratio (PSNR) and mean square error (MSE) have been calculated. Our results show that it is efficient in terms of MSE and PSNR values.

Single-Valley-Extended Solutions with Platforms of FKS Equation

The Feigenbaum–Kadanoff–Shenker (FKS) equation is a nonlinear iterative functional equation, which characterizes the quasiperiodic route to chaos for circle maps. Instead of FKS equation, we put forward the second type of FKS equation. We use the iterative construction method to obtain a new kind of continuous solutions with platforms for this functional equation. We show some properties of these continuous solutions, and give one relationship of some solutions between FKS equation and the second type of FKS equation.

Fault Detection Based on a Combined Approach of FA-CP-ELM with Application to Wind Turbine System

In this paper, a novel wind turbine (WT) fault detection method, based on the Partial Least Squares (PLS), Firefly Algorithm (FA), Chaos Map (CP) and Extreme Learning Machine (ELM), which is proposed and explained in detail. The proposed method includes two procedures: a WT mathematical model with PLS and a prediction model with FA-CP-ELM. Since the WT system is modeled as a system using PLS, the ELM has been optimized by the FA and CP to improve the predictive performance. Then, it’s calculated the residual between the mathematical model and the predicted model. If a fault occurs, the residual will increase accordingly and exceed the tolerance range. Hence, a fault can be detected quickly. To demonstrate the feasibility and effectiveness of the proposed approach, the wind turbine system is tested with a fault point set in this system. According to the results of the example, this proposed method is found to achieve better performance.

Modified Whale Optimization Algorithm Based on Tent Chaotic Mapping and Its Application in Structural Optimization

In this paper, a novel modified whale optimization algorithm based on Tent chaos map and tournament selection strategy (MWOA) was presented. The aim of the improved algorithm is to reduce the possibility of the standard whale algorithm falling into local optimal. During the initialization of the population, in order to increase population diversity and randomness, MWOA cites the Tent chaos map. In the optimization process, in order to improve the development ability of the standard algorithm, the tournament selection strategy was employed to improve the algorithm accuracy. Numerical simulation and example calculation results show that the improved algorithm is superior to the standard WOA algorithm. The improved method provides a new method for truss structure optimization.

Image steganography based on a new hybrid chaos map and discrete transforms

With the development of Internet networks, the importance of information security is becoming more and more significant. Therefore, it is considered necessary to study the existing methods in order to develop them for creating more suitable approaches. Due to the fact that, in the most communication networks image is one of the most popular and widely used communication formats, the method presented in this paper is the image steganography method in transform domain. In order to enhance the image transfer, first of all, we have introduced a hybrid chaotic map based on the sine and Logistic-Tent systems by applying radical function and a variety of trigonometric functions. Furthermore, we have represented some new kinds of shift operators for shuffling pixel positions of the cover image in order to improve resistance of the algorithm against different kinds of attacks. In the proposed algorithms, we have also applied discrete framelet and wavelet transforms on secret and cover images, respectively. To show the ability of the proposed algorithm, the results have been evaluated.

An improved digital logistic map and its application in image encryption

Chaos maps are widely used in image encryption systems due to their intrinsic advantages such as extreme sensitivity to initial values., ergodicity and pseudo-randomness. 1D Logistic map has attracted the attention of researchers due to its simple structure and easy implementation, but also because of this, the map is easy to be affected by finite precision, resulting in dynamic degradation, at low precision, the sequence generated by this map not only enters a period quickly, but also has a shorter period. Thus, taking 1D Logistic map as an example, we proposed a method to suppress the dynamic degradation of digital chaotic systems by using parameter variables and state variables to influence each other, and using sine function as feedback function to destroy the state space. The simulation results show that the improved logistic mapping with the proposed method has better randomness and higher complexity than the original logistic mapping. To prove the practicability and applicability of the improved chaotic map, we design a new image encryption algorithm, which is suitable for both color image and grayscale image. The numerical results indicate that the proposed algorithm has high encryption efficiency, good resistance to various attacks and certain competitiveness with other encryption algorithms.

Chaotic evolutionary-based image encryption using RNA codons and amino acid truth table

With the increasing use of Internet and mass media, information security has become an important issue in the field of communication. Image encryption is one of the ways to secure information in communications. In this paper, a Chaotic Evolutionary Amino Acid Codons Model (CEAACM) is presented for image encryption. The proposed model consists of four phases. In the first phase, a hidden key is provided using the SHA-256 algorithm for the initial value of the hyper chaos function. In the second phase, the permutation and diffusion of image pixels are done using two bit level permutation and Hyper Chaos Function. In the next phase, RNA and amino acid codons are used for the diffusion operation, and in the fourth phase, the process performed in the previous phases is repeated by the initial population number of the imperialist competition algorithm. Then in the next step, the optimization is performed using the operators of the imperialist competition algorithm. The results show the superiority of the proposed model over other models. In addition, according to the high value of entropy, the proposed model is highly resistant to common attacks.

Full Session Key Agreement Scheme Based on Chaotic Map in Vehicular Ad Hoc Networks

Vehicular ad hoc networks (VANETs) are wireless self-organizing networks, whose communication is conducted through open wireless channels, thus making it vulnerable to various attacks. It is therefore necessary to employ encryption technology to ensure secure communication. In view of the foregoing, key agreement techniques are introduced to VANET communications. The group key agreement (GKA) protocol allows a group of participants to establish a public session key for a secure communication channel over an insecure network. The traditional GKA protocol is inefficient, however, and consumes considerable amounts of resources. With the aim of resolving problems related to information security and privacy preservation in VANETs, this paper proposes a full session key agreement scheme based on chaos mapping. In this paper, the first phase describes the key agreement between the fog server and group administrator; the second phase describes the group key agreement for vehicle nodes in the group where the vehicle can only communicate with vehicles having the same group key without the aid of a trusted key center or centralized key distributor. The proposed scheme is based on Chebyshev chaotic mapping algorithm, in which a chaotic map is utilized to provide a one-way hash; Chebyshev polynomial is also employed to establish a public multi-party key; it avoids the modular multiplication index or scalar multiplication on the elliptic curve. The proposed scheme does not only satisfy the security requirements in VANETs but also performs detailed analysis.

Evolutionary-based image encryption using biomolecules operators and non-coupled map lattice

Information security is one of the important defensive issues in coping with attacks to valuable information of organizations. Image encryption is one of the passive defense tools to provide the information and communication security. In this paper, a chaotic evolutionary biomolecules operators model (CEBOM) was presented for image encryption. The proposed model consisted of three steps. In the first step, a secret key was considered for the initial value of the non-coupled map lattice function using the SHA (Secure Hash Algorithm)-256 algorithm. In the next step (permutation), the optimization process was performed using the tabu search algorithm (TSA) operators and the chaos function for the image with the least correlation, then the operators of the DNA sequence and chaos function were applied to the diffusion operation. The results were indicative of the superiority of the proposed model over other models. In addition, the proposed model was highly robust to common attacks, with the entropy value obtained as 7.9994.