Symmetry, Volume 10, Issue 11 (November 2018) – 129 articles

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities. Full article

It is generally assumed that the initial integration of visual information is limited in its spatial extent. Of particular interest is the extent to which image symmetries are detected and integrated. Here we studied the spatial extent of visual integration in textures constructed from wallpaper symmetry groups. Using tools from statistical physics, we obtained images ranging from symmetric ones to completely random ones, whereas the textural elements were of the same quality. Results show that the psychometric curves for 3 × 3 motif repetitions are similar to those of images having more repetitions, whereas an equivalent physical scaling of the images does not alter the performance. Full article

Large numbers of images are produced in many fields every day. The content security of digital images becomes an important issue for scientists and engineers. Inspired by the magic cube game, a three-dimensional (3D) permutation model is established to permute images, which includes three permutation modes, i.e., internal-row mode, internal-column mode, and external mode. To protect the image content on the Internet, a novel multiple-image encryption symmetric algorithm (block cipher) with the 3D permutation model and the chaotic system is proposed. First, the chaotic sequences and chaotic images are generated by chaotic systems. Second, the sender permutes the plain images by the 3D permutation model. Lastly, the sender performs the exclusive OR operation on permuted images. The simulation and algorithm comparisons display that the proposed algorithm possesses desirable encryption images, high security, and efficiency. Full article

Radar electronic reconnaissance is an important part of modern and future electronic warfare systems and is the primary method to obtain non-cooperative intelligence information. As the task requirement of radar electronic reconnaissance, it is necessary to identify the non-cooperative signals from the mixed signals. However, with the complexity of battlefield electromagnetic environment, the performance of traditional recognition system is seriously affected. In this paper, a new recognition method based on optimal classification atom and improved double chains quantum genetic algorithm (IDCQGA) is researched, optimal classification atom is a new feature for radar signal recognition, IDCQGA with symmetric coding performance can be applied to the global optimization algorithm. The main contributions of this paper are as follows: Firstly, in order to measure the difference of multi-class signals, signal separation degree based on distance criterion is proposed and established according to the inter-class separability and intra-class aggregation of the signals. Then, an IDCQGA is proposed to select the best atom for classification under the constraint of distance criterion, and the inner product of the signal and the best atom for classification is taken as the eigenvector. Finally, the extreme learning machine (ELM) is introduced as classifier to complete the recognition of signals. Simulation results show that the proposed method can improve the recognition rate of multi-class signals and has better processing ability for overlapping eigenvector parameters. Full article

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach. Full article

The new product development process (NPD) is considered to be the key factor of competition among different markets. The identification of a suitable material is an important issue in the conception and improvement of new products. Material selection is seen as an important multi-criteria decision making (MCDM) problem in engineering because of the requirement of considering multiple criteria from different dimensions. Improper material selection may negatively affect the success of a firm. The purpose of this study is to specify the importance of selection attributes, which are considered to evaluate washing liquid that meets the needs of both customers and firms. Then, it objects to choose the most appropriate alternative among various formulations. A fuzzy MCDM methodology based on quality function deployment (QFD), 2-tuple fuzzy linguistic representation, and linguistic hierarchies is presented. QFD is used to incorporate customer requirements into the evaluation process. The 2-tuple fuzzy modeling and linguistic hierarchies are employed to combine multi-granular data given by experts. Finally, the fuzzy COPRAS (Complex Proportional Assessment) method is used to choose the most suitable alternative. The implementation of the developed method is presented by a case study conducted on a detergent manufacturer located in Turkey. Full article

We introduce refined concepts for neutrosophic quantum computing such as neutrosophic quantum states and transformation gates, neutrosophic Hadamard matrix, coherent and decoherent superposition states, entanglement and measurement notions based on neutrosophic quantum states. We also give some observations using these principles. We present a number of quantum computational matrix transformations based on neutrosophic logic and clarify quantum mechanical notions relying on neutrosophic states. The paper is intended to extend the work of Smarandache by introducing a mathematical framework for neutrosophic quantum computing and presenting some results. Full article

In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design. Full article

In this paper, we propose a new scale-free social networks (SNs) evolution model that is based on homophily combined with preferential attachments. Our model enables the SN researchers to generate SN synthetic data for the evaluation of multi-facet SN models that are dependent on users’ attributes and similarities. Homophily is one of the key factors for interactive relationship formation in SN. The synthetic graph generated by our model is scale-invariant and has symmetric relationships. The model is dynamic and sustainable to changes in input parameters, such as number of nodes and nodes’ attributes, by conserving its structural properties. Simulation and evaluation of models for large-scale SN applications need large datasets. One way to get SN data is to generate synthetic data by using SN evolution models. Various SN evolution models are proposed to approximate the real-life SN graphs in previous research. These models are based on SN structural properties such as preferential attachment. The data generated by these models is suitable to evaluate SN models that are structure dependent but not suitable to evaluate models which depend on the SN users’ attributes and similarities. In our proposed model, users’ attributes and similarities are utilized to synthesize SN graphs. We evaluated the resultant synthetic graph by analyzing its structural properties. In addition, we validated our model by comparing its measures with the publicly available real-life SN datasets and previous SN evolution models. Simulation results show our resultant graph to be a close representation of real-life SN graphs with users’ attributes. Full article

In this paper, we propose a new synthetic sampling plan assuming that the quality characteristic follows the normal distribution with known and unknown standard deviation. The proposed plan is given and the operating characteristic (OC) function is derived to measure the performance of the proposed sampling plan for some fixed parameters. The parameters of the proposed sampling plan are determined using non-linear optimization solution. A real example is added to explain the use of the proposed plan by industry. Full article

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz–Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations. Full article

Biometry based authentication and recognition have attracted greater attention due to numerous applications for security-conscious societies, since biometrics brings accurate and consistent identification. Face biometry possesses the merits of low intrusiveness and high precision. Despite the presence of several biometric methods, like iris scan, fingerprints, and hand geometry, the most effective and broadly utilized method is face recognition, because it is reasonable, natural, and non-intrusive. Face recognition is a part of the pattern recognition that is applied for identifying or authenticating a person that is extracted from a digital image or a video automatically. Moreover, current innovations in big data analysis, cloud computing, social networks, and machine learning have allowed for a straightforward understanding of how different challenging issues in face recognition might be solved. Effective face recognition in the enormous data concept is a crucial and challenging task. This study develops an intelligent face recognition framework that recognizes faces through efficient ensemble learning techniques, which are Random Subspace and Voting, in order to improve the performance of biometric systems. Furthermore, several methods including skin color detection, histogram feature extraction, and ensemble learner-based face recognition are presented. The proposed framework, which has a symmetric structure, is found to have high potential for biometrics. Hence, the proposed framework utilizing histogram feature extraction with Random Subspace and Voting ensemble learners have presented their superiority over two different databases as compared with state-of-art face recognition. This proposed method has reached an accuracy of 99.25% with random forest, combined with both ensemble learners on the FERET face database. Full article

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied. Full article

In this study, the chemical composition and biological activities of the essential oil (EO) extracts (from leaves and cones) of the Tunisian Thuja occidentalis were evaluated. The composition of the leaf EO extract was more complex than that of the cones. The major components of the leaf EO extract were α-Pinene (34.4%), cedrol (13.17%), and β-Phellandrene (8.04%), while the composition of the cone EO extract was characterized by the predominance of α-Pinene (58.55%) and 3-Carene (24.08%). All EO extracts showed much better antioxidant activity than Trolox against 2, 2′-diphenyl-1-picryl hydrazyl (DPPH) radical scavenging, but EOs extracted from leaves exhibited the highest total antioxidant activity. All EOs showed strong antibacterial and antifungal activities against nine tested foodborne microorganisms (Bacillus cereus American Type Culture Collection (ATCC) 1247, Listeria monocytogenes ATCC 7644, Staphylococcus aureus ATCC 29213, Aeromonas hydrophila EI, Escherichia coli ATCC 8739, Pseudomonas aeruginosa ATCC 27853, Salmonella typhimurium NCTC 6017, Aspergillus flavus (foodborne isolate), and Aspergillus niger CTM 10099. The highest antimicrobial activities by disk diffusion assay were recorded for the EOs extracted from leaves, while no difference in potency was marked between leaf and cone EO extracts by the agar dilution method. The most potent antimicrobial activity was recorded among fungi. This study confirms the strong antimicrobial and antioxidant potential of EO extracts from the Tunisian T. occidentalis (from the Sidi Bou Said site), highlighting its potential as a natural preservative against foodborne pathogens, particularly against E. coli and S. typhimurium. Full article

Artificial neural networks (ANN) have attracted significant attention from researchers because many complex problems can be solved by training them. If enough data are provided during the training process, ANNs are capable of achieving good performance results. However, if training data are not enough, the predefined neural network model suffers from overfitting and underfitting problems. To solve these problems, several regularization techniques have been devised and widely applied to applications and data analysis. However, it is difficult for developers to choose the most suitable scheme for a developing application because there is no information regarding the performance of each scheme. This paper describes comparative research on regularization techniques by evaluating the training and validation errors in a deep neural network model, using a weather dataset. For comparisons, each algorithm was implemented using a recent neural network library of TensorFlow. The experiment results showed that an autoencoder had the worst performance among schemes. When the prediction accuracy was compared, data augmentation and the batch normalization scheme showed better performance than the others. Full article

In this paper, we consider a symmetric wireless communication network, i.e., each user is equipped with the same number of antennas. Specifically, this paper studies simultaneous wireless information and power transfer (SWIPT) in a K-user multiple-input multiple-output (MIMO) cognitive radio network where the secondary users (SUs) access the same frequency band as the pre-existing primary user (PU) without generating any interference. The transceivers and power splitting ratio are designed and power allocation is considered in our system model. To guarantee the signal-to-interference-plus-noise ratio (SINR) and harvested energy requirement of the PU, its optimal transceiver and minimal transmitted power are obtained by the technique of semi-definite relaxation (SDR). We design the beamformers of the SUs using the distance between the interference subspaces at the PU and the null space of PU’s desired signal to preserve the PU from the interference caused by the SUs. We aim to maximize the sum rate of all the SUs by jointly designing power splitting ratios and allocating transmission power. Furthermore, to consider the performance fairness of SUs, we propose another approach to maximize the minimum SINR of the SUs. Finally, numerical results are given to evaluate the performance of proposed approaches. Full article

As the size and service requirements of today’s networks gradually increase, large numbers of proprietary devices are deployed, which leads to network complexity, information security crises and makes network service and service provider management increasingly difficult. Network function virtualization (NFV) technology is one solution to this problem. NFV separates network functions from hardware and deploys them as software on a common server. NFV can be used to improve service flexibility and isolate the services provided for each user, thus guaranteeing the security of user data. Therefore, the use of NFV technology includes many problems worth studying. For example, when there is a free choice of network path, one problem is how to choose a service function chain (SFC) that both meets the requirements and offers the service provider maximum profit. Most existing solutions are heuristic algorithms with high time efficiency, or integer linear programming (ILP) algorithms with high accuracy. It’s necessary to design an algorithm that symmetrically considers both time efficiency and accuracy. In this paper, we propose the Q-learning Framework Hybrid Module algorithm (QLFHM), which includes reinforcement learning to solve this SFC deployment problem in dynamic networks. The reinforcement learning module in QLFHM is responsible for the output of alternative paths, while the load balancing module in QLFHM is responsible for picking the optimal solution from them. The results of a comparison simulation experiment on a dynamic network topology show that the proposed algorithm can output the approximate optimal solution in a relatively short time while also considering the network load balance. Thus, it achieves the goal of maximizing the benefit to the service provider. Full article

The article analyzes Bernoulli’s binary sequences in the representation of empirical events about water usage and continuous expenditure systems. The main purpose is to identify among variables that constitute water resources consumption at public schools, the link between consumption and expenditures oscillations. It was obtained a theoretical model of how oscillations patterns are originated and how time lengths have an important role over expenditures oscillations ergodicity and non-ergodicity. Full article

HIV-2 protease (PR2) is a homodimer, which is an important target in the treatment of the HIV-2 infection. In this study, we developed an in silico protocol to analyze and characterize the asymmetry of the unbound PR2 structure using three levels of protein description by comparing the conformation, accessibility, and flexibility of each residue in the two PR2 chains. Our results showed that 65% of PR2 residues have at least one of the three studied asymmetries (structural, accessibility, or flexibility) with 10 positions presenting the three asymmetries in the same time. In addition, we noted that structural and flexibility asymmetries are linked indicating that the structural asymmetry of some positions result from their large flexibility. By comparing the structural asymmetry of the crystallographic and energetically minimized structures of the unbound PR2, we confirmed that the structural asymmetry of unbound PR2 is an intrinsic property of this protein with an important role for the PR2 deformation upon ligand binding. This analysis also allowed locating asymmetries corresponding to crystallization artefacts. This study provides insight that will help to better understand the structural deformations of PR2 and to identify key positions for ligand binding. Full article

We introduce oracle Turing machines with neutrosophic values allowed in the oracle information and then give some results when one is permitted to use neutrosophic sets and logic in relative computation. We also introduce a method to enumerate the elements of a neutrosophic subset of natural numbers. Full article

This paper proposes the author’s model based on the Fuzzy Analytic Hierarchy Process (FAHP) to improve the efficiency of contractor bidding decisions. The essence of the AHP method is to make pairwise comparisons of available options against all evaluation criteria. The results of these comparisons are recorded in a square matrix in which symmetrical elements are reciprocal. In the expert opinion, a 9-step, bipolar verbal scale was used so that the symmetry of the response was maintained. For contractors from countries where the tendering system is commonly used, the choice of the right tender in which to participate influences their image, financial condition, and their aspiration to succeed. The bid/no bid decision depends on numerous factors associated with the company itself, the environment, and the project concerning the tender. When facing tough competition, contractors search for a solution which increases their chances of winning the tender. The proposed model was based on factors selected by Polish contractors. The original element of the model involves 4 original criteria and 15 sub-criteria for the assessment of investment decision projects to the selection of the most advantageous contract, i.e., the contractor’s participation in the bid. For verbal evaluations describing the criteria, symmetric triangular fuzzy numbers were assigned. The authors performed an extended analysis method combined with FAHP in the model. Fuzzy evaluations underwent elaborate analysis, the aim of which was to specify the synthetic priority weights for each criterion. As a result of the application of the method, to prove that the model works, an example from the Polish construction market was presented in which a bid/no bid decision about four possible tenders was to be taken. Despite the considered example applying to Polish conditions, the proposed model can be used also in other countries. The authors’ rationale is to produce new and more flexible methodologies in order to realistically model a variety of concrete decision problems. Full article

In this paper, a new variable control chart is proposed using multiple dependent-state repetitive sampling by assuming that the data follows a normal distribution having a symmetry property. Its efficiency will be evaluated in terms of in-control and out-of-control average run lengths. The results showed that the proposed chart is better than the existing variable control chart to detect an early shift in the process. An industrial example is given to illustrate the proposed chart in the industry. Full article

In this paper, a new approach and framework based on the interval dependent degree for multi-criteria group decision-making (MCGDM) problems with simplified neutrosophic sets (SNSs) is proposed. Firstly, the simplified dependent function and distribution function are defined. Then, they are integrated into the interval dependent function which contains interval computing and distribution information of the intervals. Subsequently, the interval transformation operator is defined to convert simplified neutrosophic numbers (SNNs) into intervals, and then the interval dependent function for SNNs is deduced. Finally, an example is provided to verify the feasibility and effectiveness of the proposed method, together with its comparative analysis. In addition, uncertainty analysis, which can reflect the dynamic change of the final result caused by changes in the decision makers’ preferences, is performed in different distribution function situations. That increases the reliability and accuracy of the result. Full article

Present research in the domain of wireless sensor network (WSN) has unearthed that energy restraint of sensor nodes (SNs) encumbers their perpetual performance. Of late, the encroachment in the vicinity of wireless power transfer (WPT) technology has achieved pervasive consideration from both industry and academia to cater the sensor nodes (SNs) letdown in the wireless rechargeable sensor network (WRSNs). The fundamental notion of wireless power transfer is to replenish the energy of sensor nodes using a single or multiple wireless charging devices (WCDs). Herein, we present a jointly optimization model to maximize the charging efficiency and routing restraint of the wireless charging device (WCD). At the outset, we intend an unswerving charging path algorithm to compute the charging path of the wireless charging device. Moreover, Particle swarm optimization (PSO) algorithm has designed with the aid of a virtual clustering technique during the routing process to equilibrate the network lifetime. Herein clustering algorithm, the enduring energy of the sensor nodes is an indispensable parameter meant for the assortment of cluster head (CH). Furthermore, compare the proposed approach to corroborate its pre-eminence over the benchmark algorithm in diverse scenarios. The simulation results divulge that the proposed work is enhanced concerning the network lifetime, charging performance and the enduring energy of the sensor nodes. Full article

The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented. Full article

Many scholars have attempted to use an encryption method to resolve the problem of data leakage in data outsourcing storage. However, encryption methods reduce data availability and are inefficient. Vertical fragmentation perfectly solves this problem. It was first used to improve the access performance of the relational database, and nowadays some researchers employ it for privacy protection. However, there are some problems that remain to be solved with the vertical fragmentation method for privacy protection in the relational database. First, current vertical fragmentation methods for privacy protection require the user to manually define privacy constraints, which is difficult to achieve in practice. Second, there are many vertical fragmentation solutions that can meet privacy constraints; however, there are currently no quantitative evaluation criteria evaluating how effectively solutions can protect privacy more effectively. In this article, we introduce the concept of information entropy to quantify privacy in vertical fragmentation, so we can automatically discover privacy constraints. Based on this, we propose a privacy protection model with a minimum entropy fragmentation algorithm to achieve minimal privacy disclosure of vertical fragmentation. Experimental results show that our method is suitable for privacy protection with a lower overhead. Full article

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome. Full article

The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane (${\omega }_d$ - ${\omega }_d^{\prime }$ , ${\omega }_d$ and ${\omega }_d^{\prime }$ represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover, ${\omega }_d$ - ${\omega }_d^{\prime }$ plane lies in the thawing region for all three HDE models. Full article

Changhee polynomials were introduced by Kim, and the generalizations of these polynomials have been characterized. In our paper, we investigate various interesting symmetric identities for Carlitz’s type q-Changhee polynomials under the symmetry group of order n arising from the fermionic p-adic q-integral on ${\mathbb{Z}}_p$ . Full article

This paper shows the results of our study on the pick-and-place optimization problem. To solve this problem efficiently, an iterated hybrid local search algorithm (IHLS) which combines local search with integer programming is proposed. In the section of local search, the greedy algorithm with distance weight strategy and the convex-hull strategy is developed to determine the pick-and-place sequence; in the section of integer programming, an integer programming model is built to complete the feeder assignment problem. The experimental results show that the IHLS algorithm we proposed has high computational efficiency. Furthermore, compared with the genetic algorithm and the memetic algorithm, the IHLS is less time-consuming and more suitable in solving a large-scale problem. Full article