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Codebooks with small cross-correlation amplitude have extensive applications in many fields including code division multiple access (CDMA) communications systems, space-time codes, and compressed sensing. In this paper, a class of asymptotically optimal codebooks was constructed, and the maximum inner-product of these presented codebooks was determined by using properties of character sums over finite fields. Furthermore, these codebooks provided new parameters.

Knowledge Graphs (KGs) have become a pivotal knowledge representation tool in machine learning, not only providing access to existing knowledge but also enabling the discovery of new knowledge through advanced applications. Among the scalable reasoning methods used for such applications, distributed graph embedding approaches, particularly GNNs, have become popular for large-scale graph-related tasks. However, many of these methods have limitations in their interpretability and fail to take into account structural similarity in their representation. Hyperdimensional Computing (HDC), also known as Vector Symbolic Architecture (VSA), addresses this issue by using well-defined cognitive operations on distributed representations of symbolic concepts. This work proposes and evaluates a new vector symbolic graph representation, CLOG, that preserves approximate structural similarity beyond edge correspondence and fundamentally differs from previous methods. The model's effectiveness in graph representation is evaluated through theoretical analysis, graph reconstruction experiments, and link prediction task, highlighting its efficiency and accuracy. This approach significantly advances the field by enhancing the capabilities of HDC in graph representation, representing a notable improvement over existing methods.

The Pareto dominance-based evolutionary algorithms can effectively address multiobjective optimization problems (MOPs). However, when dealing with many-objective optimization problems with more than three objectives (MaOPs), the Pareto dominance relationships cannot effectively distinguish the nondominated solutions in high-dimensional spaces. With the increase of the number of objectives, the proportion of dominance-resistant solutions (DRSs) in the population rapidly increases, which leads to insufficient selection pressure. In this paper, to address the challenges on MaOPs, a knee point-driven many-objective evolutionary algorithm with adaptive switching mechanism (KPEA) is proposed. In KPEA, the knee points determined by an adaptive strategy are introduced for not only mating selection but also environmental selection, which increases the probability of generating excellent offspring. In addition, to remove dominance-resistant solutions (DRSs) in the population, an interquartile range method is adopted, which enhances the selection pressure. Moreover, a novel adaptive switching mechanism between angle-based selection and penalty for selecting solutions is proposed, which is aimed at achieving a balance between convergence and diversity. To validate the performance of KPEA, it is compared with five state-of-the-art many-objective evolutionary algorithms. All algorithms are evaluated on 20 benchmark problems, i.e., WFG1-9, MaF1, and MaF4-13 with 3, 5, 8, and 10 objectives. The experimental results demonstrate that KPEA outperforms the compared algorithms in terms of HV and IGD in most of the test instances.

Excellent mechanical properties, including residual stress, ductility and strength, are important requirements for bone implants. In order to achieve this effect, titanium samples were manufactured by selective laser melting, and the prepared parts were subsequently subjected to three different heat treatment, which were 550 °C, 650 °C and 750 °C for 2 h, respectively. The results show that for as-built sample, relatively short lath-shaped α grains and a few needle-shaped α′ grains were present. After heat treatment, the α grains became thicker and longer, and the α′ grains became more. As the heat treatment temperature increases from 550 °C to 750 °C, the size of the lath-shaped α grains gradually decreases, and the small-sized needle-shaped α′ grains become denser. Moreover, the tensile strength, elongation and shrinkage of specimens increased as the heat treatment temperature increased. The fine microstructure of heat-treated samples also significantly promoted the improvement of tensile properties. The fracture mechanism of the specimens changed from brittle fracture to a mixed mode including ductile and brittle fracture, so that the tensile strength and ductility of the heat-treated specimens were well combined.

Abstract We employ a time series of Sentinel‐1 differential radar interferometry data from 2018 to detect the variability in grounding line position of the Fisher, Mellor, and Lambert glaciers, which drain about 47 billion tons of ice per year from East Antarctica. We observe kilometer‐scale tidal migration, two orders of magnitude larger than expected for ice flowing over a hard bed. The migration is not in phase with changes in oceanic tide. In two estuaries underlaid by subglacial channels, we observe two states of migration that switch on and off over time scales of several weeks. The range of vertical motion reveals a water column thickness of 2–20 cm. Such intrusions of seawater over wide grounding zones are not accounted for in physical models. Including them will add vigorous melting of grounded ice that will enhance the sensitivity of glaciers to ocean warming and increase projections of mass loss.

Today, many-objective optimization problems have attracted widespread attention. There are significant advantages of the grid-based algorithm in solving multi-objective problems. Grid-based algorithm could offer a transformation of objectives and further distinguish the non-dominated solutions. However, the advantages of grid have not been fully exploited. For example, the traditional homogeneous grid divisions can’t sufficiently reveal the similarity of adjacent solutions. And overemphasizing the selection pressure may cause the diversity decline of grid. To exploit the potentialities of grid, an inhomogeneous grid-based evolutionary algorithm (named IGEA) is proposed. IGEA applies a dynamic inhomogeneous grid division approach and redefining the coordinate assignment of individuals, which makes the dominance relationship more obvious. IGEA also applied the shift-based density estimation (SDE) strategy in discriminating the non-dominated solutions in grid coordinate. SDE can provide a good balance of convergence and diversity. The IGEA compares with several state-of-the-art evolutionary algorithms against the regular and irregular many-objective optimization problems. The experimental results demonstrate that IGEA is very competitive against the peer algorithms in terms of providing a good balance between convergence and diversity.

In order to achieve good adaptability, medical bone implants for clinical applications need to have porous characteristics. From a biological and mechanical point of view, the design of porous structures requires both suitable porosities to facilitate cell ingrowth and suitable strength to avoid implant damage. To handle the multiobjective optimization problems of porous structure design, this work introduced an improved multi-objective optimization algorithm, which is called a multi-swarm multi-objective evolutionary algorithm based on decomposition (MSMOEA/D), and the main idea is a multi-swarm strategy. After a predetermined algebraic evolution, the whole swarm was evenly divided into several parts, and the elite non-dominated sorting mechanism was used to select the individuals with excellent performance and poor performance in the sub-swarms to exchange information between the sub-swarms. The performance of the MSMOEA/D algorithm was verified and validated on 12 constraint two-objective and three-objective benchmark functions and compared with MOEA/D, MOEADM2M, and MOEADDRA algorithms in terms of generational distance indicators. The solutions obtained by the proposed MSMOEA/D algorithm were accurate. Finally, the proposed MSMOEA/D algorithm was applied to optimize the constructed RS porous structure, and the porous optimized models with porosities of 50%, 60% and 70% were obtained.

With the continuous development of E-commerce, warehouse logistics is also facing emerging challenges, including more batches of orders and shorter order processing cycles. When more orders need to be processed simultaneously, some existing task scheduling methods may not be able to give a suitable plan, which delays order processing and reduces the efficiency of the warehouse. Therefore, the intelligent warehouse system that uses autonomous robots for automated storage and intelligent order scheduling is becoming mainstream. Based on this concept, we propose a multi-robot cooperative scheduling system in the intelligent warehouse. The aim of the multi-robot cooperative scheduling system of the intelligent storage is to drive many robots in an intelligent warehouse to perform the distributed tasks in an optimal (e.g., time-saving and energy-conserved) way. In this paper, we propose a multi-robot cooperative task scheduling model in the intelligent warehouse. For this model, we design a maximin-based multi-objective algorithm, which uses a one-by-one update scheme to select individuals. In this algorithm, two indicators are devised to discriminate the equivalent individuals with the same maximin fitness value in the environmental selection process. The results on benchmark test suite show that our algorithm is indeed a useful optimizer. Then it is applied to settle the multi-robot scheduling problem in the intelligence warehouse. Simulation experiment results demonstrate the efficiency of the proposed algorithm on the real-world scheduling problem.

Surrogate-assisted evolutionary algorithms have received a surge of attentions for their promising ability of solving expensive optimization problems. Existing surrogate-assisted evolutionary algorithms usually adopt the regression models and the binary classification models to guide the evolution of the population for solving the multiobjective optimization problems. However, the regression models will make the algorithm to be increasingly computation-expensive as the number of objectives increases, while the use of the binary classification models might suffer from the poor diversity since the diversified information of solutions cannot be reflected in these classification models. For this issue, this paper proposes a surrogate-assisted many-objective evolutionary algorithm using the cooperation of the multi-classification and regression models to improve the search quality while reducing the computational cost. Our approach includes two parts: At the model training stage, a multi-classification model is constructed to divide the whole population into several classes for ensuring diversity, a distance regression model and an angle regression model are used to select solutions with better convergence and diversity in each class; At the evolution stage, a coevolutionary framework is used to guide the evolution according to a new selection criterion. Experimental results verify the effectiveness of the proposed algorithm on a set of expensive test problems with up to 10 objectives.

Aiming at the shortcomings of the Harris hawks optimization algorithm (HHO), such as poor initial population diversity, slow convergence speed, poor local optimization ability, and easily falling into local optimum, a Harris hawks optimization algorithm (CCCHHO) integrating multiple mechanisms is proposed. First, the population diversity is enhanced by the initialization of the chaotic method. Second, the cosine function is used to better simulate the characteristics of the periodic change of the energy of the prey in the repeated contests with the group of hawks, to better balance the exploration and exploitation of the algorithm. Third, Cauchy mutation on the optimal individual in the exploration phase is performed, and the characteristics of the Cauchy distribution to enhance the diversity of the population are used, which can effectively prevent the algorithm from falling into the local optimum. Fourth, the local optimization ability of the algorithm by using the ergodicity of the chaotic system in the exploitation phase to perform a chaotic local search for the optimal individual is enhanced, which can effectively jump out after the algorithm falls into the local optimum. Finally, we use the elite individuals of the population to guide the position update of the population’s individuals, fully communicate with the dominant individuals, and speed up the convergence speed of the algorithm. Through the simulation experiments on CCCHHO with 11 different benchmark functions, CCCHHO is better than the gray wolf optimization algorithm (GWO), the Salp swarm algorithm (SSA), the ant lion optimization algorithm (ALO), and three improved HHO algorithms in terms of convergence speed and optimization accuracy, whether it is a unimodal benchmark function or a multimodal benchmark function. The experimental results show that CCCHHO has excellent algorithm efficiency and robustness.

Summary: Singlet fission is known to improve solar energy utilization by circumventing the Shockley-Queisser limit. The two essential steps of singlet fission are the formation of a correlated triplet pair and its subsequent quantum decoherence. However, the mechanisms of the triplet pair formation and decoherence still remain elusive. Here we examined both essential steps in single crystalline hexacene and discovered remarkable anisotropy of the overall singlet fission rate along different crystal axes. Since the triplet pair formation emerges on the same timescale along both crystal axes, the quantum decoherence is likely responsible for the directional anisotropy. The distinct quantum decoherence rates are ascribed to the notable difference on their associated energy loss according to the Redfield quantum dissipation theory. Our hybrid experimental/theoretical framework will not only further our understanding of singlet fission, but also shed light on the systematic design of new materials for the third-generation solar cells. : Spectroscopy; Theoretical Photophysics; Quantum Phenomena Subject Areas: Spectroscopy, Theoretical Photophysics, Quantum Phenomena

Abstract The ant colony optimization algorithm is an effective way to solve the problem of unmanned vehicle path planning. First, establish the environment model of the unmanned vehicle path planning, process and describe the environmental information, and finally realize the division of the problem space. Next, the biomimetic behavior of the ant colony algorithm is described. The ant colony algorithm has been improved by adding a penalty strategy. This penalty strategy can enhance the utilization of resources and guide the ants to explore other unknown areas by using the worse value in the search history to enhance the volatility of the pheromone.

The design of flexible wearable electronic devices that can shield electromagnetic waves and work in all weather conditions remains a challenge. We present in this work a low-cost technology to prepare an ultra-thin carbon fabric–graphene (CFG) composite film with outstanding electromagnetic interference shielding effectiveness (EMI SE) and electro-photo-thermal effect. The compatibility between flexible carbon fabric skeleton and brittle pure graphene matrix empowers this CFG film with adequate flexibility. The reticular fibers and porous structures play a vital role in multiple scattering and absorption of electromagnetic waves. In the frequency range of 30–1500 MHz, the CFG film can achieve a significantly high EMI SE of about 46 dB at tiny thickness (0.182 mm) and density (1.4 g cm−3) predominantly by absorption. At low safe voltages or only in sunlight, the film can self-heat to its saturation value rapidly in 40 s. Once the electricity or light supply is stopped, it can quickly dissipate heat in tens of seconds. A combination of the EMI SE and the prominent electro-photo-thermal effect further enables such a remarkable EMI shielding film to have more potential applications for communication devices in extreme zones.

There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC) for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell’s pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.

This paper proposes a novel artificial bee colony algorithm with dynamic population (ABC-DP), which synergizes the idea of extended life-cycle evolving model to balance the exploration and exploitation tradeoff. The proposed ABC-DP is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. ABC-DP is then used for solving the optimal power flow (OPF) problem in power systems that considers the cost, loss, and emission impacts as the objective functions. The 30-bus IEEE test system is presented to illustrate the application of the proposed algorithm. The simulation results, which are also compared to nondominated sorting genetic algorithm II (NSGAII) and multi-objective ABC (MOABC), are presented to illustrate the effectiveness and robustness of the proposed method.

In recent years, symbiosis as a rich source of potential engineering applications and computational model has attracted more and more attentions in the adaptive complex systems and evolution computing domains. Inspired by different symbiotic coevolution forms in nature, this paper proposed a series of multi-swarm particle swarm optimizers called PS2Os, which extend the single population particle swarm optimization (PSO) algorithm to interacting multi-swarms model by constructing hierarchical interaction topologies and enhanced dynamical update equations. According to different symbiotic interrelationships, four versions of PS2O are initiated to mimic mutualism, commensalism, predation, and competition mechanism, respectively. In the experiments, with five benchmark problems, the proposed algorithms are proved to have considerable potential for solving complex optimization problems. The coevolutionary dynamics of symbiotic species in each PS2O version are also studied respectively to demonstrate the heterogeneity of different symbiotic interrelationships that effect on the algorithm’s performance. Then PS2O is used for solving the radio frequency identification (RFID) network planning (RNP) problem with a mixture of discrete and continuous variables. Simulation results show that the proposed algorithm outperforms the reference algorithms for planning RFID networks, in terms of optimization accuracy and computation robustness.

Over the last few decades, evolutionary algorithms (EAs) have been widely adopted to solve complex optimization problems. However, EAs are powerless to challenge the constrained optimization problems (COPs) because they do not directly act to reduce constraint violations of constrained problems. In this paper, the robustly global optimization advantage of artificial bee colony (ABC) algorithm and the stably minor calculation characteristic of constraint consensus (CC) strategy for COPs are integrated into a novel hybrid heuristic algorithm, named ABCCC. CC strategy is fairly effective to rapidly reduce the constraint violations during the evolutionary search process. The performance of the proposed ABCCC is verified by a set of constrained benchmark problems comparing with two state-of-the-art CC-based EAs, including particle swarm optimization based on CC (PSOCC) and differential evolution based on CC (DECC). Experimental results demonstrate the promising performance of the proposed algorithm, in terms of both optimization quality and convergence speed.

A novel state estimation algorithm based on the parameters of a self-learning unscented Kalman filter (UKF) with a model parameter identification method based on a collaborative optimization mechanism is proposed in this paper. This algorithm can realize the dynamic self-learning and self-adjustment of the parameters in the UKF algorithm and the automatic optimization setting Sigma points without human participation. In addition, the multi-algorithm collaborative optimization mechanism unifies a variety of algorithms, so that the identification method has the advantages of member algorithms while avoiding the disadvantages of them. We apply the combination algorithm proposed in this paper for state of charge (SoC) estimation of power batteries and compare it with other model parameter identification algorithms and SoC estimation methods. The results showed that the proposed algorithm outperformed the other model parameter identification algorithms in terms of estimation accuracy and robustness.

A hybrid coevolution particle swarm optimization algorithm with dynamic multispecies strategy based on K-means clustering and nonrevisit strategy based on Binary Space Partitioning fitness tree (called MCPSO-PSH) is proposed. Previous search history memorized into the Binary Space Partitioning fitness tree can effectively restrain the individuals’ revisit phenomenon. The whole population is partitioned into several subspecies and cooperative coevolution is realized by an information communication mechanism between subspecies, which can enhance the global search ability of particles and avoid premature convergence to local optimum. To demonstrate the power of the method, comparisons between the proposed algorithm and state-of-the-art algorithms are grouped into two categories: 10 basic benchmark functions (10-dimensional and 30-dimensional), 10 CEC2005 benchmark functions (30-dimensional), and a real-world problem (multilevel image segmentation problems). Experimental results show that MCPSO-PSH displays a competitive performance compared to the other swarm-based or evolutionary algorithms in terms of solution accuracy and statistical tests.

Ordered mesoporous Fe2O3 supported gold nanoparticles with a desired specific surface area and porous structure (Au/meso-Fe2O3) was successfully fabricated with a hard templating method by using KIT-6 as the template. The morphology and physico-chemical properties of Au/meso-Fe2O3 were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM) and transmission electron microscope (TEM), etc. The gold nanoparticles are highly dispersed on the surface of the mesoporous Fe2O3. The catalytic performance of the synthesized catalyst was studied for the aerobic oxidation of benzylic alcohols in β−O−4 linked lignin model dimers to the corresponding carbonyl products under atmosphere pressure. Au/meso-Fe2O3 shows an enhanced activity for the aerobic oxidation of 1-phenylethanol in comparison with that of Au/bulk-Fe2O3. The promoted catalytic activity is related to the confined porous structure of mesoporous Fe2O3 and more boundaries contact between gold and meso-Fe2O3, which shows that the porous structure of the support has a significant influence on the activity of gold catalysts.

A novel butterfly-shaped patch antenna for wireless communication is introduced in this paper. The antenna is designed for wideband wireless communications and radio-frequency identification (RFID) systems. Two symmetrical quasi-circular arms and two symmetrical round holes are incorporated into the patch of a microstrip antenna to expand its bandwidth. The diameter and position of the circular slots are optimized to achieve a wide bandwidth. The validity of the design concept is demonstrated by means of a prototype having a bandwidth of about 40.1%. The return loss of the butterfly-shaped antenna is greater than 10 dB between 4.15 and 6.36 GHz. The antenna can serve simultaneously most of the modern wireless communication standards.

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization (HABC), for multilevel threshold image segmentation, which employs a pool of optimal foraging strategies to extend the classical artificial bee colony framework to a cooperative and hierarchical fashion. In the proposed hierarchical model, the higher-level species incorporates the enhanced information exchange mechanism based on crossover operator to enhance the global search ability between species. In the bottom level, with the divide-and-conquer approach, each subpopulation runs the original ABC method in parallel to part-dimensional optimum, which can be aggregated into a complete solution for the upper level. The experimental results for comparing HABC with several successful EA and SI algorithms on a set of benchmarks demonstrated the effectiveness of the proposed algorithm. Furthermore, we applied the HABC to the multilevel image segmentation problem. Experimental results of the new algorithm on a variety of images demonstrated the performance superiority of the proposed algorithm.

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization (HABC), to tackle complex high-dimensional problems. In the proposed multilevel model, the higher-level species can be aggregated by the subpopulations from lower level. In the bottom level, each subpopulation employing the canonical ABC method searches the part-dimensional optimum in parallel, which can be constructed into a complete solution for the upper level. At the same time, the comprehensive learning method with crossover and mutation operator is applied to enhance the global search ability between species. Experiments are conducted on a set of 20 continuous and discrete benchmark problems. The experimental results demonstrate remarkable performance of the HABC algorithm when compared with other six evolutionary algorithms.

This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization, called HABC, to tackle the radio frequency identification network planning (RNP) problem. In the proposed multilevel model, the higher-level species can be aggregated by the subpopulations from lower level. In the bottom level, each subpopulation employing the canonical ABC method searches the part-dimensional optimum in parallel, which can be constructed into a complete solution for the upper level. At the same time, the comprehensive learning method with crossover and mutation operators is applied to enhance the global search ability between species. Experiments are conducted on a set of 10 benchmark optimization problems. The results demonstrate that the proposed HABC obtains remarkable performance on most chosen benchmark functions when compared to several successful swarm intelligence and evolutionary algorithms. Then HABC is used for solving the real-world RNP problem on two instances with different scales. Simulation results show that the proposed algorithm is superior for solving RNP, in terms of optimization accuracy and computation robustness.

Bacterial Foraging Algorithm (BFO) is a recently proposed swarm intelligence algorithm inspired by the foraging and chemotactic phenomenon of bacteria. However, its optimization ability is not so good compared with other classic algorithms as it has several shortages. This paper presents an improved BFO Algorithm. In the new algorithm, a lifecycle model of bacteria is founded. The bacteria could split, die, or migrate dynamically in the foraging processes, and population size varies as the algorithm runs. Social learning is also introduced so that the bacteria will tumble towards better directions in the chemotactic steps. Besides, adaptive step lengths are employed in chemotaxis. The new algorithm is named BFOLS and it is tested on a set of benchmark functions with dimensions of 2 and 20. Canonical BFO, PSO, and GA algorithms are employed for comparison. Experiment results and statistic analysis show that the BFOLS algorithm offers significant improvements than original BFO algorithm. Particulary with dimension of 20, it has the best performance among the four algorithms.

We develop an optimization model for risk management in a virtual enterprise environment based on a novel multiswarm particle swarm optimizer called PS2O. The main idea of PS2O is to extend the single population PSO to the interacting multiswarms model by constructing hierarchical interaction topology and enhanced dynamical update equations. With the hierarchical interaction topology, a suitable diversity in the whole population can be maintained. At the same time, the enhanced dynamical update rule significantly speeds up the multiswarm to converge to the global optimum. With five mathematical benchmark functions, PS2O is proved to have considerable potential for solving complex optimization problems. PS2O is then applied to risk management in a virtual enterprise environment. Simulation results demonstrate that the PS2O algorithm is more feasible and efficient than the PSO algorithm in solving this real-world problem.

Bacterial Foraging Optimization (BFO) is a recently developed nature-inspired optimization algorithm, which is based on the foraging behavior of E. coli bacteria. Up to now, BFO has been applied successfully to some engineering problems due to its simplicity and ease of implementation. However, BFO possesses a poor convergence behavior over complex optimization problems as compared to other nature-inspired optimization techniques. This paper first analyzes how the run-length unit parameter of BFO controls the exploration of the whole search space and the exploitation of the promising areas. Then it presents a variation on the original BFO, called the adaptive bacterial foraging optimization (ABFO), employing the adaptive foraging strategies to improve the performance of the original BFO. This improvement is achieved by enabling the bacterial foraging algorithm to adjust the run-length unit parameter dynamically during algorithm execution in order to balance the exploration/exploitation tradeoff. The experiments compare the performance of two versions of ABFO with the original BFO, the standard particle swarm optimization (PSO) and a real-coded genetic algorithm (GA) on four widely-used benchmark functions. The proposed ABFO shows a marked improvement in performance over the original BFO and appears to be comparable with the PSO and GA.

Multiobjective optimization has been a difficult problem and focus for research in fields of science and engineering. This paper presents a novel algorithm based on artificial bee colony (ABC) to deal with multi-objective optimization problems. ABC is one of the most recently introduced algorithms based on the intelligent foraging behavior of a honey bee swarm. It uses less control parameters, and it can be efficiently used for solving multimodal and multidimensional optimization problems. Our algorithm uses the concept of Pareto dominance to determine the flight direction of a bee, and it maintains nondominated solution vectors which have been found in an external archive. The proposed algorithm is validated using the standard test problems, and simulation results show that the proposed approach is highly competitive and can be considered a viable alternative to solve multi-objective optimization problems.

This paper presents a novel optimization model called hierarchical swarm optimization (HSO), which simulates the natural hierarchical complex system from where more complex intelligence can emerge for complex problems solving. This proposed model is intended to suggest ways that the performance of HSO-based algorithms on complex optimization problems can be significantly improved. This performance improvement is obtained by constructing the HSO hierarchies, which means that an agent in a higher level swarm can be composed of swarms of other agents from lower level and different swarms of different levels evolve on different spatiotemporal scale. A novel optimization algorithm (named PS2O), based on the HSO model, is instantiated and tested to illustrate the ideas of HSO model clearly. Experiments were conducted on a set of 17 benchmark optimization problems including both continuous and discrete cases. The results demonstrate remarkable performance of the PS2O algorithm on all chosen benchmark functions when compared to several successful swarm intelligence and evolutionary algorithms.

Artificial Bee Colony (ABC) is one of the most recently introduced algorithms based on the intelligent foraging behavior of a honey bee swarm. This paper presents an extended ABC algorithm, namely, the Cooperative Article Bee Colony (CABC), which significantly improves the original ABC in solving complex optimization problems. Clustering is a popular data analysis and data mining technique; therefore, the CABC could be used for solving clustering problems. In this work, first the CABC algorithm is used for optimizing six widely used benchmark functions and the comparative results produced by ABC, Particle Swarm Optimization (PSO), and its cooperative version (CPSO) are studied. Second, the CABC algorithm is used for data clustering on several benchmark data sets. The performance of CABC algorithm is compared with PSO, CPSO, and ABC algorithms on clustering problems. The simulation results show that the proposed CABC outperforms the other three algorithms in terms of accuracy, robustness, and convergence speed.

Bacterial Foraging Optimization (BFO) is a novel optimization algorithm based on the social foraging behavior of E. coli bacteria. This paper presents a variation on the original BFO algorithm, namely, the Cooperative Bacterial Foraging Optimization (CBFO), which significantly improve the original BFO in solving complex optimization problems. This significant improvement is achieved by applying two cooperative approaches to the original BFO, namely, the serial heterogeneous cooperation on the implicit space decomposition level and the serial heterogeneous cooperation on the hybrid space decomposition level. The experiments compare the performance of two CBFO variants with the original BFO, the standard PSO and a real-coded GA on four widely used benchmark functions. The new method shows a marked improvement in performance over the original BFO and appears to be comparable with the PSO and GA.