Xin-She Yang

Geethu Joy, Christian Huyck, Xin-She Yang

Almost all optimization algorithms have algorithm-dependent parameters, and the setting of such parameter values can largely influence the behaviour of the algorithm under consideration. Thus, proper parameter tuning should be carried out to ensure the algorithm used for optimization may perform well and can be sufficiently robust for solving different types of optimization problems. This chapter reviews some of the main methods for parameter tuning and then highlights the important issues concerning the latest development in parameter tuning. A few open problems are also discussed with some recommendations for future research.

Kyeong Soo Kim, Sanghyuk Lee, Tiew On Ting et al.

The current formulation of the optimal scheduling of appliance energy consumption uses as optimization variables the vectors of appliances' scheduled energy consumption over equally-divided time slots of a day, which does not take into account the atomicity of appliances' operations (i.e., the unsplittable nature of appliances' operations and resulting energy consumption). In this paper, we provide a new formulation of atomic scheduling of energy consumption based on the optimal routing framework; the flow configurations of users over multiple paths between the common source and destination nodes of a ring network are used as optimization variables, which indicate the starting times of scheduled energy consumption, and optimal scheduling problems are now formulated in terms of the user flow configurations. Because the atomic optimal scheduling results in a Boolean-convex problem for a convex objective function, we propose a successive convex relaxation technique for efficient calculation of an approximate solution, where we iteratively drop fractional-valued elements and apply convex relaxation to the resulting problem until we find a feasible suboptimal solution. Numerical results for the cost and peak-to-average ratio minimization problems demonstrate that the successive convex relaxation technique can provide solutions close to, often identical to, global optimal solutions.

Xin-She Yang

Many problems in science and engineering are optimization problems, which may require sophisticated optimization techniques to solve. Nature-inspired algorithms are a class of metaheuristic algorithms for optimization, and some algorithms or variants are often developed by hybridization. Benchmarking is also important in evaluating the performance of optimization algorithms. This chapter focuses on the overview of optimization, nature-inspired algorithms and the role of hybridization. We will also highlight some issues with hybridization of algorithms.

Xin-She Yang

Benchmarks are used for testing new optimization algorithms and their variants to evaluate their performance. Most existing benchmarks are smooth functions. This chapter introduces ten new benchmarks with different properties, including noise, discontinuity, parameter estimation and unknown paths.

Geethu Joy, Christian Huyck, Xin-She Yang

Almost all optimization algorithms have algorithm-dependent parameters, and the setting of such parameter values can significantly influence the behavior of the algorithm under consideration. Thus, proper parameter tuning should be carried out to ensure that the algorithm used for optimization performs well and is sufficiently robust for solving different types of optimization problems. In this study, the Firefly Algorithm (FA) is used to evaluate the influence of its parameter values on its efficiency. Parameter values are randomly initialized using both the standard Monte Carlo method and the Quasi Monte-Carlo method. The values are then used for tuning the FA. Two benchmark functions and a spring design problem are used to test the robustness of the tuned FA. From the preliminary findings, it can be deduced that both the Monte Carlo method and Quasi-Monte Carlo method produce similar results in terms of optimal fitness values. Numerical experiments using the two different methods on both benchmark functions and the spring design problem showed no major variations in the final fitness values, irrespective of the different sample values selected during the simulations. This insensitivity indicates the robustness of the FA.

Joao Paulo Papa, Gustavo Henrique Rosa, Douglas Rodrigues et al.

Optimization techniques play an important role in several scientific and real-world applications, thus becoming of great interest for the community. As a consequence, a number of open-source libraries are available in the literature, which ends up fostering the research and development of new techniques and applications. In this work, we present a new library for the implementation and fast prototyping of nature-inspired techniques called LibOPT. Currently, the library implements 15 techniques and 112 benchmarking functions, as well as it also supports 11 hypercomplex-based optimization approaches, which makes it one of the first of its kind. We showed how one can easily use and also implement new techniques in LibOPT under the C paradigm. Examples are provided with samples of source-code using benchmarking functions.

Jinyan Li, Yaoyang Wu, Simon Fong et al.

Ensemble technique and under-sampling technique are both effective tools used for imbalanced dataset classification problems. In this paper, a novel ensemble method combining the advantages of both ensemble learning for biasing classifiers and a new under-sampling method is proposed. The under-sampling method is named Binary PSO instance selection; it gathers with ensemble classifiers to find the most suitable length and combination of the majority class samples to build a new dataset with minority class samples. The proposed method adopts multi-objective strategy, and contribution of this method is a notable improvement of the performances of imbalanced classification, and in the meantime guaranteeing a best integrity possible for the original dataset. We experimented the proposed method and compared its performance of processing imbalanced datasets with several other conventional basic ensemble methods. Experiment is also conducted on these imbalanced datasets using an improved version where ensemble classifiers are wrapped in the Binary PSO instance selection. According to experimental results, our proposed methods outperform single ensemble methods, state-of-the-art under-sampling methods, and also combinations of these methods with the traditional PSO instance selection algorithm.

Geethu Joy, Christian Huyck, Xin-She Yang

There are many different nature-inspired algorithms in the literature, and almost all such algorithms have algorithm-dependent parameters that need to be tuned. The proper setting and parameter tuning should be carried out to maximize the performance of the algorithm under consideration. This work is the extension of the recent work on parameter tuning by Joy et al. (2024) presented at the International Conference on Computational Science (ICCS 2024), and the Firefly Algorithm (FA) is tuned using three different methods: the Monte Carlo method, the Quasi-Monte Carlo method and the Latin Hypercube Sampling. The FA with the tuned parameters is then used to solve a set of six different optimization problems, and the possible effect of parameter setting on the quality of the optimal solutions is analyzed. Rigorous statistical hypothesis tests have been carried out, including Student's t-tests, F-tests, non-parametric Friedman tests and ANOVA. Results show that the performance of the FA is not influenced by the tuning methods used. In addition, the tuned parameter values are largely independent of the tuning methods used. This indicates that the FA can be flexible and equally effective in solving optimization problems, and any of the three tuning methods can be used to tune its parameters effectively.

Gustavo H. de Rosa, João Paulo Papa, Xin-She Yang

Feature selection for a given model can be transformed into an optimization task. The essential idea behind it is to find the most suitable subset of features according to some criterion. Nature-inspired optimization can mitigate this problem by producing compelling yet straightforward solutions when dealing with complicated fitness functions. Additionally, new mathematical representations, such as quaternions and octonions, are being used to handle higher-dimensional spaces. In this context, we are introducing a meta-heuristic optimization framework in a hypercomplex-based feature selection, where hypercomplex numbers are mapped to real-valued solutions and then transferred onto a boolean hypercube by a sigmoid function. The intended hypercomplex feature selection is tested for several meta-heuristic algorithms and hypercomplex representations, achieving results comparable to some state-of-the-art approaches. The good results achieved by the proposed approach make it a promising tool amongst feature selection research.

Eneko Osaba, Javier Del Ser, Xin-She Yang et al.

Multitasking optimization is an emerging research field which has attracted lot of attention in the scientific community. The main purpose of this paradigm is how to solve multiple optimization problems or tasks simultaneously by conducting a single search process. The main catalyst for reaching this objective is to exploit possible synergies and complementarities among the tasks to be optimized, helping each other by virtue of the transfer of knowledge among them (thereby being referred to as Transfer Optimization). In this context, Evolutionary Multitasking addresses Transfer Optimization problems by resorting to concepts from Evolutionary Computation for simultaneous solving the tasks at hand. This work contributes to this trend by proposing a novel algorithmic scheme for dealing with multitasking environments. The proposed approach, coined as Coevolutionary Bat Algorithm, finds its inspiration in concepts from both co-evolutionary strategies and the metaheuristic Bat Algorithm. We compare the performance of our proposed method with that of its Multifactorial Evolutionary Algorithm counterpart over 15 different multitasking setups, composed by eight reference instances of the discrete Traveling Salesman Problem. The experimentation and results stemming therefrom support the main hypothesis of this study: the proposed Coevolutionary Bat Algorithm is a promising meta-heuristic for solving Evolutionary Multitasking scenarios.

Qian Li, San-Yang Liu, Xin-She Yang

Many real-world applications can be modelled as complex networks, and such networks include the Internet, epidemic disease networks, transport networks, power grids, protein-folding structures and others. Network integrity and robustness are important to ensure that crucial networks are protected and undesired harmful networks can be dismantled. Network structure and integrity can be controlled by a set of key nodes, and to find the optimal combination of nodes in a network to ensure network structure and integrity can be an NP-complete problem. Despite extensive studies, existing methods have many limitations and there are still many unresolved problems. This paper presents a probabilistic approach based on neighborhood information and node importance, namely, neighborhood information-based probabilistic algorithm (NIPA). We also define a new centrality-based importance measure (IM), which combines the contribution ratios of the neighbor nodes of each target node and two-hop node information. Our proposed NIPA has been tested for different network benchmarks and compared with three other methods: optimal attack strategy (OAS), high betweenness first (HBF) and high degree first (HDF). Experiments suggest that the proposed NIPA is most effective among all four methods. In general, NIPA can identify the most crucial node combination with higher effectiveness, and the set of optimal key nodes found by our proposed NIPA is much smaller than that by heuristic centrality prediction. In addition, many previously neglected weakly connected nodes are identified, which become a crucial part of the newly identified optimal nodes. Thus, revised strategies for protection are recommended to ensure the safeguard of network integrity. Further key issues and future research topics are also discussed.

Qian Li, San-Yang Liu, Xin-She Yang

All metaheuristic optimization algorithms require some initialization, and the initialization for such optimizers is usually carried out randomly. However, initialization can have some significant influence on the performance of such algorithms. This paper presents a systematic comparison of 22 different initialization methods on the convergence and accuracy of five optimizers: differential evolution (DE), particle swarm optimization (PSO), cuckoo search (CS), artificial bee colony (ABC) algorithm and genetic algorithm (GA). We have used 19 different test functions with different properties and modalities to compare the possible effects of initialization, population sizes and the numbers of iterations. Rigorous statistical ranking tests indicate that 43.37\% of the functions using the DE algorithm show significant differences for different initialization methods, while 73.68\% of the functions using both PSO and CS algorithms are significantly affected by different initialization methods. The simulations show that DE is less sensitive to initialization, while both PSO and CS are more sensitive to initialization. In addition, under the condition of the same maximum number of function evaluations (FEs), the population size can also have a strong effect. Particle swarm optimization usually requires a larger population, while the cuckoo search needs only a small population size. Differential evolution depends more heavily on the number of iterations, a relatively small population with more iterations can lead to better results. Furthermore, ABC is more sensitive to initialization, while such initialization has little effect on GA. Some probability distributions such as the beta distribution, exponential distribution and Rayleigh distribution can usually lead to better performance. The implications of this study and further research topics are also discussed in detail.

Xin-She Yang

Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional algorithms may struggle to deal with such problems. A current trend is to use nature-inspired algorithms due to their flexibility and effectiveness. However, there are some key issues concerning nature-inspired computation and swarm intelligence. This paper provides an in-depth review of some recent nature-inspired algorithms with the emphasis on their search mechanisms and mathematical foundations. Some challenging issues are identified and five open problems are highlighted, concerning the analysis of algorithmic convergence and stability, parameter tuning, mathematical framework, role of benchmarking and scalability. These problems are discussed with the directions for future research.

Nunzia Palmieri, Xin-She Yang, Floriano De Rango et al.

This work addresses the coordination problem of multiple robots with the goal of finding specific hazardous targets in an unknown area and dealing with them cooperatively. The desired behaviour for the robotic system entails multiple requirements, which may also be conflicting. The paper presents the problem as a constrained bi-objective optimization problem in which mobile robots must perform two specific tasks of exploration and at same time cooperation and coordination for disarming the hazardous targets. These objectives are opposed goals, in which one may be favored, but only at the expense of the other. Therefore, a good trade-off must be found. For this purpose, a nature-inspired approach and an analytical mathematical model to solve this problem considering a single equivalent weighted objective function are presented. The results of proposed coordination model, simulated in a two dimensional terrain, are showed in order to assess the behaviour of the proposed solution to tackle this problem. We have analyzed the performance of the approach and the influence of the weights of the objective function under different conditions: static and dynamic. In this latter situation, the robots may fail under the stringent limited budget of energy or for hazardous events. The paper concludes with a critical discussion of the experimental results.

Si Chen, Guo-Hua Peng, Xing-Shi He et al.

The bat algorithm (BA) has been shown to be effective to solve a wider range of optimization problems. However, there is not much theoretical analysis concerning its convergence and stability. In order to prove the convergence of the bat algorithm, we have built a Markov model for the algorithm and proved that the state sequence of the bat population forms a finite homogeneous Markov chain, satisfying the global convergence criteria. Then, we prove that the bat algorithm can have global convergence. In addition, in order to enhance the convergence performance of the algorithm, we have designed an updated model using the dynamical system theory in terms of a dynamic matrix, and the parameter ranges for the algorithm stability are then obtained. We then use some benchmark functions to demonstrate that BA can indeed achieve global optimality efficiently for these functions.

Xin-She Yang, Suash Deb, Sudhanshu K Mishra

Many optimization problems in science and engineering are highly nonlinear, and thus require sophisticated optimization techniques to solve. Traditional techniques such as gradient-based algorithms are mostly local search methods, and often struggle to cope with such challenging optimization problems. Recent trends tend to use nature-inspired optimization algorithms. This work extends the standard cuckoo search (CS) by using the successful features of the cuckoo-host co-evolution with multiple interacting species, and the proposed multi-species cuckoo search (MSCS) intends to mimic the multiple species of cuckoos that compete for the survival of the fittest, and they co-evolve with host species with solution vectors being encoded as position vectors. The proposed algorithm is then validated by 15 benchmark functions as well as five nonlinear, multimodal design case studies in practical applications. Simulation results suggest that the proposed algorithm can be effective for finding optimal solutions and in this case all optimal solutions are achievable. The results for the test benchmarks are also compared with those obtained by other methods such as the standard cuckoo search and genetic algorithm, which demonstrated the efficiency of the present algorithm. Based on numerical experiments and case studies, we can conclude that the proposed algorithm can be more efficient in most cases, leading a potentially very effective tool for solving nonlinear optimization problems.

Xin-She Yang

This article concerns the review of a special class of swarm intelligence based algorithms for solving optimization problems and these algorithms can be referred to as social algorithms. Social algorithms use multiple agents and the social interactions to design rules for algorithms so as to mimic certain successful characteristics of the social/biological systems such as ants, bees, bats, birds and animals.

Xin-She Yang, Xingshi He

Firefly algorithm is a nature-inspired optimization algorithm and there have been significant developments since its appearance about ten years ago. This chapter summarizes the latest developments about the firefly algorithm and its variants as well as their diverse applications. Future research directions are also highlighted.

Asma Chakri, Rabia Khelif, Mohamed Benouaret et al.

Bat algorithm (BA) is a recent optimization algorithm based on swarm intelligence and inspiration from the echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that can occur due to the low exploration ability of the algorithm under some conditions. To overcome this deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and exploitation capabilities. In addition to such directional echolocation, three other improvements have been embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from the CEC2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA variants using non-parametric statistical tests. The statistical test results show the superiority of the directional bat algorithm.

Xin-She Yang, Suash Deb

Since the development of cuckoo search (CS) by Yang and Deb in 2009, CS has been applied in a diverse range of applications. This paper first outlines the key features of the algorithm and its variants, and then briefly summarizes the state-of-the-art developments in many applications. The opportunities for further research are also identified.

Xin-She Yang, Suash Deb, Yuxin Zhao et al.

Many optimization problems in science and engineering are challenging to solve, and the current trend is to use swarm intelligence (SI) and SI-based algorithms to tackle such challenging problems. Some significant developments have been made in recent years, though there are still many open problems in this area. This paper provides a short but timely analysis about SI-based algorithms and their links with self-organization. Different characteristics and properties are analyzed here from both mathematical and qualitative perspectives. Future research directions are outlined and open questions are also highlighted.

Xingshi He, Xin-She Yang, Mehmet Karamanoglu et al.

Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently.

E. Osaba, Xin-She Yang, F. Diaz et al.

A real-world newspaper distribution problem with recycling policy is tackled in this work. In order to meet all the complex restrictions contained in such a problem, it has been modeled as a rich vehicle routing problem, which can be more specifically considered as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP). This is the first study of such a problem in the literature. For this reason, a benchmark composed by 15 instances has been also proposed. In the design of this benchmark, real geographical positions have been used, located in the province of Bizkaia, Spain. For the proper treatment of this AC-VRP-SPDVCFP, a discrete firefly algorithm (DFA) has been developed. This application is the first application of the firefly algorithm to any rich vehicle routing problem. To prove that the proposed DFA is a promising technique, its performance has been compared with two other well-known techniques: an evolutionary algorithm and an evolutionary simulated annealing. Our results have shown that the DFA has outperformed these two classic meta-heuristics.

Eneko Osaba, Xin-She Yang, Fernando Diaz et al.

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases.

Aziz Ouaarab, B. Ahiod, Xin-She Yang

Combinatorial optimization problems are typically NP-hard, and thus very challenging to solve. In this paper, we present the random key cuckoo search (RKCS) algorithm for solving the famous Travelling Salesman Problem (TSP). We used a simplified random-key encoding scheme to pass from a continuous space (real numbers) to a combinatorial space. We also consider the displacement of a solution in both spaces using Levy flights. The performance of the proposed RKCS is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that RKCS is superior to some other metaheuristic algorithms.

Xin-She Yang, Suash Deb, Simon Fong

The efficiency of any metaheuristic algorithm largely depends on the way of balancing local intensive exploitation and global diverse exploration. Studies show that bat algorithm can provide a good balance between these two key components with superior efficiency. In this paper, we first review some commonly used metaheuristic algorithms, and then compare the performance of bat algorithm with the so-called intermittent search strategy. From simulations, we found that bat algorithm is better than the optimal intermittent search strategy. We also analyse the comparison results and their implications for higher dimensional optimization problems. In addition, we also apply bat algorithm in solving business optimization and engineering design problems.

Xin-She Yang, M. Karamanoglu, X. S. He

Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this paper, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis are highlighted and discussed.

Xin-She Yang, M. Karamanoglu, T. O. Ting et al.

All swarm-intelligence-based optimization algorithms use some stochastic components to increase the diversity of solutions during the search process. Such randomization is often represented in terms of random walks. However, it is not yet clear why some randomization techniques (and thus why some algorithms) may perform better than others for a given set of problems. In this work, we analyze these randomization methods in the context of nature-inspired algorithms. We also use eagle strategy to provide basic observations and relate step sizes and search efficiency using Markov theory. Then, we apply our analysis and observations to solve four design benchmarks, including the designs of a pressure vessel, a speed reducer, a PID controller and a heat exchanger. Our results demonstrate that eagle strategy with Lévy flights can perform extremely well in reducing the overall computational efforts.

Xin-She Yang, Suash Deb

Cuckoo search (CS) is a relatively new algorithm, developed by Yang and Deb in 2009, and CS is efficient in solving global optimization problems. In this paper, we review the fundamental ideas of cuckoo search and the latest developments as well as its applications. We analyze the algorithm and gain insight into its search mechanisms and find out why it is efficient. We also discuss the essence of algorithms and its link to self-organizing systems, and finally we propose some important topics for further research.

Xin-She Yang, Slawomir Koziel, Leifur Leifsson

Modelling, simulation and optimization form an integrated part of modern design practice in engineering and industry. Tremendous progress has been observed for all three components over the last few decades. However, many challenging issues remain unresolved, and the current trends tend to use nature-inspired algorithms and surrogate-based techniques for modelling and optimization. This 4th workshop on Computational Optimization, Modelling and Simulation (COMS 2013) at ICCS 2013 will further summarize the latest developments of optimization and modelling and their applications in science, engineering and industry. In this review paper, we will analyse the recent trends in modelling and optimization, and their associated challenges. We will discuss important topics for further research, including parameter-tuning, large-scale problems, and the gaps between theory and applications.

Xin-She Yang, M. Karamanoglu, Xingshi He

Flower pollination algorithm is a new nature-inspired algorithm, based on the characteristics of flowering plants. In this paper, we extend this flower algorithm to solve multi-objective optimization problems in engineering. By using the weighted sum method with random weights, we show that the proposed multi-objective flower algorithm can accurately find the Pareto fronts for a set of test functions. We then solve a bi-objective disc brake design problem, which indeed converges quickly.

Xin-She Yang, Zhihua Cui

It is now five years since the launch of the International Journal of Bio-Inspired Computation (IJBIC). At the same time, significant new progress has been made in the area of bio-inspired computation. This review paper summarizes the success and achievements of IJBIC in the past five years, and also highlights the challenges and key issues for further research.

Xin-She Yang, Christian Huyck, Mehmet Karamanoglu et al.

The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimization algorithms. However, its global optimality is not clear and there has been no mathematical proof put forward. In this paper, a detailed mathematical analysis of this problem is provided that proves that 6059.714335048436 is the global minimum. The Lagrange multiplier method is also used as an alternative proof and this method is extended to find the global optimum of a cantilever beam design problem.

Xin-She Yang

Many optimization algorithms have been developed by drawing inspiration from swarm intelligence (SI). These SI-based algorithms can have some advantages over traditional algorithms. In this paper, we carry out a critical analysis of these SI-based algorithms by analyzing their ways to mimic evolutionary operators. We also analyze the ways of achieving exploration and exploitation in algorithms by using mutation, crossover and selection. In addition, we also look at algorithms using dynamic systems, self-organization and Markov chain framework. Finally, we provide some discussions and topics for further research.

Xiaoge Zhang, Andrew Adamatzky, Xin-She Yang et al.

A supply chain is a system which moves products from a supplier to customers. The supply chains are ubiquitous. They play a key role in all economic activities. Inspired by biological principles of nutrients' distribution in protoplasmic networks of slime mould Physarum polycephalum we propose a novel algorithm for a supply chain design. The algorithm handles the supply networks where capacity investments and product flows are variables. The networks are constrained by a need to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of a flux during the iterative process, which is used in real-time update of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Practicality and flexibility of our algorithm is illustrated on numerical examples.

Iztok Fister, Iztok Fister, Xin-She Yang et al.

The firefly algorithm has become an increasingly important tool of Swarm Intelligence that has been applied in almost all areas of optimization, as well as engineering practice. Many problems from various areas have been successfully solved using the firefly algorithm and its variants. In order to use the algorithm to solve diverse problems, the original firefly algorithm needs to be modified or hybridized. This paper carries out a comprehensive review of this living and evolving discipline of Swarm Intelligence, in order to show that the firefly algorithm could be applied to every problem arising in practice. On the other hand, it encourages new researchers and algorithm developers to use this simple and yet very efficient algorithm for problem solving. It often guarantees that the obtained results will meet the expectations.

Xin-She Yang

Flower pollination is an intriguing process in the natural world. Its evolutionary characteristics can be used to design new optimization algorithms. In this paper, we propose a new algorithm, namely, flower pollination algorithm, inspired by the pollination process of flowers. We first use ten test functions to validate the new algorithm, and compare its performance with genetic algorithms and particle swarm optimization. Our simulation results show the flower algorithm is more efficient than both GA and PSO. We also use the flower algorithm to solve a nonlinear design benchmark, which shows the convergence rate is almost exponential.

Momin Jamil, Xin-She Yang

Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties so that can be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimization problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and tt can be expected this complete set of functions can be used for validation of new optimization in the future.

Xin-She Yang

Bat algorithm (BA) is a bio-inspired algorithm developed by Yang in 2010 and BA has been found to be very efficient. As a result, the literature has expanded significantly in the last 3 years. This paper provides a timely review of the bat algorithm and its new variants. A wide range of diverse applications and case studies are also reviewed and summarized briefly here. Further research topics are also discussed.

Xin-She Yang, Xingshi He

Nature-inspired metaheuristic algorithms, especially those based on swarm intelligence, have attracted much attention in the last ten years. Firefly algorithm appeared in about five years ago, its literature has expanded dramatically with diverse applications. In this paper, we will briefly review the fundamentals of firefly algorithm together with a selection of recent publications. Then, we discuss the optimality associated with balancing exploration and exploitation, which is essential for all metaheuristic algorithms. By comparing with intermittent search strategy, we conclude that metaheuristics such as firefly algorithm are better than the optimal intermittent search strategy. We also analyse algorithms and their implications for higher-dimensional optimization problems.

Iztok Fister, Xin-She Yang, Iztok Fister et al.

Swarm intelligence and bio-inspired algorithms form a hot topic in the developments of new algorithms inspired by nature. These nature-inspired metaheuristic algorithms can be based on swarm intelligence, biological systems, physical and chemical systems. Therefore, these algorithms can be called swarm-intelligence-based, bio-inspired, physics-based and chemistry-based, depending on the sources of inspiration. Though not all of them are efficient, a few algorithms have proved to be very efficient and thus have become popular tools for solving real-world problems. Some algorithms are insufficiently studied. The purpose of this review is to present a relatively comprehensive list of all the algorithms in the literature, so as to inspire further research.

Iztok Fister, Dušan Fister, Xin-She Yang

Swarm intelligence is a very powerful technique to be used for optimization purposes. In this paper we present a new swarm intelligence algorithm, based on the bat algorithm. The Bat algorithm is hybridized with differential evolution strategies. Besides showing very promising results of the standard benchmark functions, this hybridization also significantly improves the original bat algorithm.