Showing papers by "Jeng-Shyang Pan published in 2020"

Improved Binary Grey Wolf Optimizer and Its application for feature selection

Abstract: Grey Wolf Optimizer (GWO) is a new swarm intelligence algorithm mimicking the behaviours of grey wolves. Its abilities include fast convergence, simplicity and easy realization. It has been proved its superior performance and widely used to optimize the continuous applications, such as, cluster analysis, engineering problem, training neural network and etc. However, there are still some binary problems to optimize in the real world. Since binary can only be taken from values of 0 or 1, the standard GWO is not suitable for the problems of discretization. Binary Grey Wolf Optimizer (BGWO) extends the application of the GWO algorithm and is applied to binary optimization issues. In the position updating equations of BGWO, the a parameter controls the values of A and D , and influences algorithmic exploration and exploitation. This paper analyses the range of values of A D under binary condition and proposes a new updating equation for the a parameter to balance the abilities of global search and local search. Transfer function is an important part of BGWO, which is essential for mapping the continuous value to binary one. This paper includes five transfer functions and focuses on improving their solution quality. Through verifying the benchmark functions, the advanced binary GWO is superior to the original BGWO in the optimality, time consumption and convergence speed. It successfully implements feature selection in the UCI datasets and acquires low classification errors with few features.

Energy Saving Technology of 5G Base Station Based on Internet of Things Collaborative Control

Abstract: For time and space constraints, 5G base stations will have more serious energy consumption problems in some time periods, so it needs corresponding sleep strategies to reduce energy consumption. Based on the analysis of 5G super dense base station network structure, through the analysis of current situation and user demand, a cluster sleep method based on genetic algorithm is constructed under the support of genetic algorithm, which can realize the dynamic matching of energy consumption in time domain and space, and the low load base station enters the sleep state. In order to verify the performance of the algorithm, the simulation network structure is built on the MATLAB platform, and the advantages of the algorithm in this study are obtained through comparative analysis, and the relevant test parameters are set for the technical performance analysis of this study. The research shows that the method proposed in this paper has a certain energy-saving effect, can meet the energy efficiency requirements of 5G ultra dense base station, and in the ultra dense base station group, the complexity can also meet the system operation requirements, which has a certain degree of practicality, and can provide reference for the follow-up related research.

Quasi-Affine Transformation Evolutionary Algorithm With Communication Schemes for Application of RSSI in Wireless Sensor Networks

Abstract: QUasi-Affine TRansformation Evolutionary algorithm (QUATRE) is a new optimization algorithm based on population for complex multiple real parameter optimization problems in real world. In this paper, a novel multi-group multi-choice communication strategy algorithm for QUasi-Affine TRansformation Evolutionary (MM-QUATRE) algorithm is proposed to solve the disadvantage that the original QUATRE is always easily to fall into local optimization in the strategy of updating bad nodes with multiple groups and multiple choices. We compared it with other intelligent algorithms, the most advanced PSO variant, parallel PSO (P-PSO) variant, native QUATRE and parallel QUATRE (P-PSO) under CEC2013 large-scale optimization test suite. Thus, the performance of MM-QUATRE was verified. The conclusion that the MM-QUATRE algorithm is superior to other intelligent algorithms is proved by the experimental results. In addition, the application results of MM-QUATRE algorithm (MM-QUATRE-RSSI) based on RSSI in WSN node localization were analyzed and studied. The results appear that this method has higher localization accuracy than other similar algorithms.

A Hybrid Differential Evolution Algorithm and Its Application in Unmanned Combat Aerial Vehicle Path Planning

Abstract: CIPDE and JADE are two powerful and effective Differential Evolution (DE) algorithms with strong exploration and exploitation capabilities. In order to take advantage of these two algorithms, we present a hybrid differential evolution algorithm combining modified CIPDE (MCIPDE) with modified JADE (MJADE) called CIJADE. In CIJADE, the population is first partitioned into two subpopulations according to the fitness value, i.e., superior and inferior subpopulations, to maintain the population diversity. The superior subpopulation evolves using the operation defined in MCIPDE. The MCIPDE adds an external archive to the mutation scheme to enhance the population diversity and exploration capability of original CIPDE. While the inferior subpopulation evolves using the operation defined in MJADE. The MJADE modifies the original JADE by adjusting the parameter p in linear decreasing way to balance the exploration and exploitation ability of original JADE. A new crossover operation is designed to original JADE to deal with the problem of stagnation. Furthermore, the parameters CR and F values of CIJADE are updated according to a modified parameter adaptation strategy in each generation. We validate the performance of the proposed CIJADE algorithm over 28 benchmark functions of the CEC2013 benchmark set. The experimental results indicate that the proposed CIJADE performs better than the eleven popular stateof-the-art DE variants. What's more, we apply the proposed CIJADE to deal with Unmanned Combat Aerial Vehicle (UCAV) path planning problem. The simulation results show that the proposed CIJADE can efficiently find the optimal or near optimal flight path for UCAV.

A Compact Pigeon-Inspired Optimization for Maximum Short-Term Generation Mode in Cascade Hydroelectric Power Station

Abstract: Pigeon-inspired optimization (PIO) is a new type of intelligent algorithm. It is proposed that the algorithm simulates the movement of pigeons going home. In this paper, a new pigeon herding algorithm called compact pigeon-inspired optimization (CPIO) is proposed. The challenging task for multiple algorithms is not only combining operations, but also constraining existing devices. The proposed algorithm aims to solve complex scientific and industrial problems with many data packets, including the use of classical optimization problems and the ability to find optimal solutions in many solution spaces with limited hardware resources. A real-valued prototype vector performs probability and statistical calculations, and then generates optimal candidate solutions for CPIO optimization algorithms. The CPIO algorithm was used to evaluate a variety of continuous multi-model functions and the largest model of hydropower short-term generation. The experimental results show that the proposed algorithm is a more effective way to produce competitive results in the case of limited memory devices.

Optimizing Ontology Alignment in Vector Space

Abstract: Ontology matching technique aims at determining the identical entities, which can effectively solve the ontology heterogeneity problem and implement the collaborations among ontology-based intelligent systems. Typically, an ontology consists of a set of concepts which are described by various properties, and they define a space such that each distinct concept and property represents one dimension in that space. Therefore, it is an effective way to model an ontology in a vector space, and use the vector space based similarity measure to calculate two entities’ similarity. In this work, the entities’ structure information is utilized to model an ontology in a vector space, and then, their linguistic information is used to reduce the number of dimensions, which can improve the efficiency of the similarity calculation and entity matching process. After that, a discrete optimization model is constructed for the ontology matching problem, and a compact Evolutionary Algorithm (cEA) based ontology matching technique is proposed to efficiently address it. The experiment uses the benchmark track provided by Ontology Alignment Evaluation Initiative (OAEI) to test our proposal’s performance, and the comparing results with state-of-the-art ontology matching systems show that our approach can efficiently determine high-quality ontology alignments.

A Parallel Multi-Verse Optimizer for Application in Multilevel Image Segmentation

Abstract: Multi-version optimizer (MVO) inspired by the multi-verse theory is a new optimization algorithm for challenging multiple parameter optimization problems in the real world. In this paper, a novel parallel multi-verse optimizer (PMVO) with the communication strategy is proposed. The parallel mechanism is implemented to randomly divide the initial solutions into several groups, and share the information of different groups after each fixed iteration. This can significantly promote the cooperation individual of MVO algorithm, and reduce the deficiencies that the original MVO is premature convergence, search stagnation and easily trap into local optimal search space. To confirm the performance of the proposed scheme, the PMVO algorithm was compared with the other well-known optimization algorithms, such as gray wolf optimizer (GWO), particle swarm optimization (PSO), multi-version optimizer (MVO), and parallel particle swarm optimization (PPSO) under CEC2013 test suite. The experimental results prove that the PMVO is superior to the other compared algorithms. In addition, PMVO is also applied to solve complex multilevel image segmentation problems based on minimum cross entropy thresholding. The application results appear that the proposed PMVO algorithm can achieve higher quality image segmentation compared to other similar algorithms.

Improved Compact Cuckoo Search Algorithm Applied to Location of Drone Logistics Hub

Abstract: Drone logistics can play an important role in logistics at the end of the supply chain and special environmental logistics. At present, drone logistics is in the initial development stage, and the location of drone logistics hubs is an important issue in the optimization of logistics systems. This paper implements a compact cuckoo search algorithm with mixed uniform sampling technology, and, for the problem of weak search ability of the algorithm, this paper combines the method of recording the key positions of the search process and increasing the number of generated solutions to achieve further improvements, as well as implements the improved compact cuckoo search algorithm. Then, this paper uses 28 test functions to verify the algorithm. Aiming at the problem of the location of drone logistics hubs in remote areas or rural areas, this paper establishes a simple model that considers the traffic around the village, the size of the village, and other factors. It is suitable for selecting the location of the logistics hub in advance, reducing the cost of drone logistics, and accelerating the large-scale application of drone logistics. This paper uses the proposed algorithm for testing, and the test results indicate that the proposed algorithm has strong competitiveness in the proposed model.

A parallel WOA with two communication strategies applied in DV-Hop localization method

Abstract: Wireless sensor network (WSN) can effectively help us monitor the surrounding environment and prevent the occurrence of some natural disasters earlier, but we can only get the information of the surrounding environment correctly if we know the locations of nodes. How to know the exact positions of nodes is a strict challenge in WSN. Intelligent computing algorithms have been developed in recent years. They easily solve complex optimization problems, especially for those that cannot be modeled mathematically. This paper proposes a novel algorithm, named parallel whale optimization algorithm (PWOA). It contains two information exchange strategies between groups, and it significantly enhances global search ability and population diversity of the original whale optimization algorithm (WOA). Also, the algorithm is adopted to optimize the localization of WSN. Twenty-three mathematical optimization functions are accustomed to verifying the efficiency and effectiveness of the novel approach. Compared with some existing intelligent computing algorithms, the proposed PWOA may reach better results.

Identifying correctness data scheme for aggregating data in cluster heads of wireless sensor network based on naive Bayes classification

Abstract: Wireless sensor network (WSN) has been paid more attention by scholars due to the practical communication of a system of devices to transfer information gathered from a monitored field through wireless links. Precise and accurate data of aggregating messages from sensor nodes is a vital demand for a success WSN application. This paper proposes a new scheme of identifying the correctness data scheme for aggregating data in cluster heads in hierarchical WSN based on naive Bayes classification. The collecting environmental information includes temperature, humidity, sound, and pollution levels, from sensor nodes to cluster heads that classify data fault and aggregate and transfer them to the base station. The collecting data is classified based on the classifier to aggregate in the cluster head of WSN. Compared with some existing methods, the proposed method offers an effective way of forwarding the correct data in WSN applications.

Identification Failure Data for Cluster Heads Aggregation in WSN Based on Improving Classification of SVM

Abstract: Wireless sensor network (WSN) has been paid more attention due to its efficient system of communication devices for transferring information from a target environment to the base station (BS) through wireless links. Precise collecting information from sensor nodes for aggregating data in Cluster Head (CH) is an essential demand for a successful WSN application. This paper proposes a new scheme of identifying collected information correctness for aggregating data in CHs in hierarchical WSN based on improving classification of Support vector machine (SVM). The optimal parameter SVM is implemented by an improved flower pollination algorithm (IFPA) to achieve classification accuracy. The collecting environmental information like temperature, humidity, etc., from sensor nodes to CHs that classify data fault, aggregate, and transfer them to the BS. Compared with some existing methods, the proposed method offers an effective way of forwarding the correct data in WSN applications.

An efficient surrogate-assisted quasi-affine transformation evolutionary algorithm for expensive optimization problems

Abstract: Many real-world engineering optimization problems usually need a lot of time for function evaluations or have massive decision variables. It is still a big challenge to address these problems effectively. Recently, surrogate-assisted meta-heuristic algorithms have drawn increasing attention, and have shown their potential to deal with such expensive complex optimization problems. In this study, a surrogate-assisted quasi-affine transformation evolutionary (SA-QUATRE) algorithm is proposed to further enhance the optimization efficiency and effectiveness. In SA-QUATRE, the global and the local surrogate models are effectively combined for fitness estimation. The global surrogate model is built based on all data in the database for global exploration. While, the local surrogate model is constructed with a predefined number of top best samples for local exploitation. Meanwhile, both the generation- and individual-based evolution controls as well as a top best restart strategy are incorporated in the global and the local searches. To enhance the exploration and the exploitation capabilities, the global search uses the mean of the population to be evaluated with the expensive real fitness function, while the local search chooses the individual with the best fitness according to the surrogate for real evaluation. The proposed SA-QUATRE is compared with five state-of-the-art optimization approaches over seven commonly used benchmark functions with dimensions varying from 10 to 100. Moreover, the proposed SA-QUATRE is also applied to solve the tension/compression spring design problem. The experimental results show that SA-QUATRE is promising for optimizing computationally expensive problems.

Symbiotic Organism Search Algorithm with Multi-Group Quantum-Behavior Communication Scheme Applied in Wireless Sensor Networks

Abstract: The symbiotic organism search (SOS) algorithm is a promising meta-heuristic evolutionary algorithm. Its excellent quality of global optimization solution has aroused the interest of many researchers. In this work, we not only applied the strategy of multi-group communication and quantum behavior to the SOS algorithm, but also formed a novel global optimization algorithm called the MQSOS algorithm. It has speed and convergence ability and plays a good role in solving practical problems with multiple arguments. We also compared MQSOS with other intelligent algorithms under the CEC2013 large-scale optimization test suite, such as particle swarm optimization (PSO), parallel PSO (PPSO), adaptive PSO (APSO), QUasi-Affine TRansformation Evolutionary (QUATRE), and oppositional SOS (OSOS). The experimental results show that MQSOS algorithm had better performance than the other intelligent algorithms. In addition, we combined and optimized the DV-hop algorithm for node localization in wireless sensor networks, and also improved the DV-hop localization algorithm to achieve higher localization accuracy than some existing algorithms.

An Improved Slime Mold Algorithm and its Application for Optimal Operation of Cascade Hydropower Stations

Abstract: A recently modern stochastic optimization algorithm has been developed by observing the life of slime mold physarum polycephalum in nature. The algorithm is called the slime mold algorithm (SMA) with an excellent exploratory capacity and exploitation inclination. Still, slipping into optimal local is easy to happen and slowly converges speed while dealing with complicated problems. This article proposes a new process of improving SMA (namely ISMA) by adapting the weight coefficient and cooperating the reverse learning strategy in the expression of agents updating locations to enhance the algorithm’s optimization performance. Many selected benchmark functions and the optimal operation of cascade reservoirs are applied to evaluate the performance of the proposed algorithm. Comparisons of the proposed approach’s results with the various algorithms under the case situations show that the recommended solution produces better performance than the different competing algorithms.

Sine Cosine Algorithm with Multigroup and Multistrategy for Solving CVRP

Abstract: Sine Cosine Algorithm (SCA) has been proved to be superior to some existing traditional optimization algorithms owing to its unique optimization principle. However, there are still disadvantages such as low solution accuracy and poor global search ability. Aiming at the shortcomings of the sine cosine algorithm, a multigroup multistrategy SCA algorithm (MMSCA) is proposed in this paper. The algorithm executes multiple populations in parallel, and each population executes a different optimization strategy. Information is exchanged among populations through intergenerational communication. Using 19 different types of test functions, the optimization performance of the algorithm is tested. Numerical experimental results show that the performance of the MMSCA algorithm is better than that of the original SCA algorithm, and it also has some advantages over other intelligent algorithms. At last, it is applied to solving the capacitated vehicle routing problem (CVRP) in transportation. The algorithm can get better results, and the practicability and feasibility of the algorithm are also proved.

A Scheme of Color Image Multithreshold Segmentation Based on Improved Moth-Flame Algorithm

Abstract: A recently developed swarm intelligence algorithm by studying the natural moth’s biological behavior is called Moth-Flame Optimization (MFO). The advantages of MFO conclude a simple structure and a robust selection capability. Still, it is easy to be trapped falling into optimal local, and slow search converges. This study suggests a new process improving MFO by hybridizing Levy flight and logarithmic functions for its formula of flame updating to enhance the optimization performance of the algorithm. In the experimental section, a set of benchmark functions of CEC2013 and the multi threshold image segmentation are used to evaluate the proposed method performance. Compared results of the proposed methods with the different algorithms in the same condition scenarios show that the suggested approach provides better results than the various algorithms in the competitions.

Phasmatodea population evolution algorithm and its application in length-changeable incremental extreme learning machine

Abstract: Extreme learning machine (ELM) is an effective classification and prediction learning algorithm based on feedforward neural network (FNN). This paper presents the Phasmatodea (stick insect) population evolution algorithm (PPE), which is different from other algorithms, in which each solution represents a population and has two attributes: quantity and growth rate. Combining the concept of similar evolution and the model of population competition, it is a new local search method. The algorithm is compared with the other algorithms on benchmark functions and engineering problems. Then use it to enhance a variant of the ELM model. The results show that the proposed algorithm has a certain competitiveness.

A Novel Pigeon-Inspired Optimization Based MPPT Technique for PV Systems

Abstract: The conventional maximum power point tracking (MPPT) method fails in partially shaded conditions, because multiple peaks may appear on the power–voltage characteristic curve. The Pigeon-Inspired Optimization (PIO) algorithm is a new type of meta-heuristic algorithm. Aiming at this situation, this paper proposes a new type of algorithm that combines a new pigeon population algorithm named Parallel and Compact Pigeon-Inspired Optimization (PCPIO) with MPPT, which can solve the problem that MPPT cannot reach the near global maximum power point. This hybrid algorithm is fast, stable, and capable of globally optimizing the maximum power point tracking algorithm. Therefore, the purpose of this article is to study the performance of two optimization techniques. The two algorithms are Particle Swarm Algorithm (PSO) and improved pigeon algorithm. This paper first studies the mechanism of multi-peak output characteristics of photovoltaic arrays in complex environments, and then proposes a multi-peak MPPT algorithm based on a combination of an improved pigeon population algorithm and an incremental conductivity method. The improved pigeon algorithm is used to quickly locate near the maximum power point, and then the variable step size incremental method INC (incremental conductance) is used to accurately locate the maximum power point. A simulation was performed on Matlab/Simulink platform. The results prove that the method can achieve fast and accurate optimization under complex environmental conditions, effectively reduce power oscillations, enhance system stability, and achieve better control results.

Securing Fingerprint Template Using Blockchain and Distributed Storage System

Abstract: Biometrics, with its uniqueness to every individual, has been adapted as a security authentication feature by many institutions. These biometric data are processed into templates that are saved on databases, and a central authority centralizes and controls these databases. This form of storing biometric data, or in our case fingerprint template, is asymmetric and prone to three main security attacks, such as fake template input, template modification or deletion, and channel interception by a malicious attacker. In this paper, we secure an encrypted fingerprint template by a symmetric peer-to-peer network and symmetric encryption. The fingerprint is encrypted by the symmetric key algorithm: Advanced Encryption Standard (AES) algorithm and then is uploaded to a symmetrically distributed storage system, the InterPlanetary File system (IPFS). The hash of the templated is stored in a decentralized blockchain. The slow transaction speed of the blockchain has limited its use in real-life applications, such as large file storage, hence, the merge with IPFS to store just the hashes of large files. The encrypted template is uploaded to the IPFS, and its returned digest is stored on the Ethereum network. The implementation of IPFS prevents storing the raw state of the fingerprint template on the Ethereum network in order to reduce cost and also prevent identity theft. This procedure is an improvement of previous systems. By adopting the method of template hashing, the proposed system is cost-effective and efficient. The experimental results depict that the proposed system secures the fingerprint template by encryption, hashing, and decentralization.

3-D Terrain Node Coverage of Wireless Sensor Network Using Enhanced Black Hole Algorithm

Abstract: In this paper, a new intelligent computing algorithm named Enhanced Black Hole (EBH) is proposed to which the mutation operation and weight factor are applied. In EBH, several elites are taken as role models instead of only one in the original Black Hole (BH) algorithm. The performance of the EBH algorithm is verified by the CEC 2013 test suit, and shows better results than the original BH. In addition, the EBH and other celebrated algorithms can be used to solve node coverage problems of Wireless Sensor Network (WSN) in 3-D terrain with satisfactory performance.

Applying Adaptive and Self Assessment Fish Migration Optimization on Localization of Wireless Sensor Network on 3-D Te rrain.

Abstract: This paper presents an improved fish migration optimization (FMO), which adopts novel update equations of individuals and energy. A chieftain concept is introduced and it can attract individuals to exploitation around it. Therefore, the novel algorithm reduced the randomness and improved the convergence ability of the original algorithm. A more flexible update equation of energy is introduced which adjusts the amplitude of energy increase of individuals according to its fitness quality. The performance of the new algorithm is verified by CEC 2013 benchmark function. Besides, the novel algorithm is applied in solving the localization problem of Wireless Sensor Network (WSN) on 3-D terrain.

Differential evolution utilizing a handful top superior individuals with bionic bi-population structure for the enhancement of optimization performance

Abstract: In this paper, we propose a new DE variant incorporating a new mutation strategy and a bionic bi-population structure to enhance the overall performance of the canonical DE algorithm. As it...

A Load Economic Dispatch Based on Ion Motion Optimization Algorithm

Abstract: This paper presents a new approach for dispatch generating powers of thermal plants based on ion motion optimization algorithm (IMA) Electrical power systems are determined by optimization in power balancing, transporting loss, and generating capacity The scheduling power generating units for stabilizing different dynamic responses of the control power system are mathematically modeled for the objective function Economic load dispatch (ELD) gains as the objective function is optimized by applying IMA In the experimental section, several cases of different units of thermal plants are used to test the performance of the proposed approach The preliminary results are compared with the other methods in the literature shows that the proposed plan offers higher effect performance

A novel pigeon-inspired optimization with QUasi-Affine TRansformation evolutionary algorithm for DV-Hop in wireless sensor networks:

Abstract: In modern times, swarm intelligence has played an increasingly important role in finding an optimal solution within a search range. This study comes up with a novel solution algorithm named QUasi-A...

Parallel compact differential evolution for optimization applied to image segmentation

Abstract: A parallel compact Differential Evolution (pcDE) algorithm is proposed in this paper. The population is separated into multiple groups and the individual is run by using the method of compact Differential Evolution. The communication is implemented after predefined iterations. Two communication strategies are proposed in this paper. The first one is to replace the local optimal solution by global optimal solution in all groups, which is called optimal elite strategy (oe); the second one is to replace the local optimal solution by mean value of the local optimal solution in all groups, which is called mean elite strategy (me). Considering that the pcDE algorithm does not need to store a large number of solutions, the algorithm can adapt to the environment with weak computing power. In order to prove the feasibility of pcDE, several groups of comparative experiments are carried out. Simulation results based on the 25 test functions demonstrate the efficacy of the proposed two communication strategies for the pcDE. Finally, the proposed pcDE is applied to image segmentation and experimental results also demonstrate the superior quality of the pcDE compared with some existing methods.

Diversity Teams in Soccer League Competition Algorithm for Wireless Sensor Network Deployment Problem

Abstract: The drawback of several metaheuristic algorithms is the dropped local optimal trap in the solution to complicated problems. The diversity team is one of the promising ways to enhance the exploration of searching solutions in algorithm to avoid the local optimum trap. This paper proposes a diversity-team soccer league competition algorithm (DSLC) based on updating team member strategies for global optimization and its applied optimization of Wireless sensor network (WSN) deployment. The updating team consists of trading, drafting, and combining strategies. The trading strategy considers player transactions between groups after the ending season. The drafting strategy takes advantage of draft principles in real leagues to bring new players to the association. The combining strategy is a hybrid policy of trading and drafting one. Twenty-one benchmark functions of CEC2017 are used to test the performance of the proposed algorithm. The experimental results of the proposed algorithm compared with the other algorithms in the literature show that the proposed algorithm outperforms the competitors in terms of having an excellent ability to achieve global optimization. Moreover, the proposed DSLC algorithm is applied to solve the problem of WSN deployment and achieved excellent results.

Reversible data hiding in dual encrypted halftone images using matrix embedding

Abstract: Reversible data hiding (RDH) is a data-hiding technique that embeds data into cover media such that it can be recovered distortion-free after the embedded data are retrieved. Currently, for RDH in encrypted halftone images (RDH-EH), the original cover image cannot be recovered once the watermark is extracted. In this paper, we present a RDH method for encrypted halftone images based on matrix embedding, which can achieve a high embedding capacity with low distortion. Since minimal information redundancy exists in encrypted halftone images, perfectly reversible algorithms appear to be difficult to implement. Nevertheless, we proposed a completely reversible RDH method for encrypted halftone images with high embedding capacity. To address the drawback of information redundancy, the pixels of the cover image are copied into two images to guarantee reversibility. The watermark is embedded into the first cover image by changing one pixel of each block using syndrome encoding, and into the second cover image by bit replacement. The experimental results show that the halftone image can be completely recovered after the embedded data are extracted. Furthermore, our algorithm can achieve moderate computational complexity, high embedding capacity and high visual quality of marked images. This scheme is suitable for data-hiding applications such as the medical or printing applications where the reversibility is crucial.