Generalized Firefly Algorithm for Optimal Transmit Beamforming

This paper proposes a generalized Firefly Algorithm (FA) to solve an optimization framework having objective function and constraints as multivariate functions of independent optimization variables. Four representative examples of how the proposed generalized FA can be adopted to solve downlink beamforming problems are shown for a classic transmit beamforming, cognitive beamforming, reconfigurable-intelligent-surfaces-aided (RIS-aided) transmit beamforming, and RIS-aided wireless power transfer (WPT). Complexity analyzes indicate that in large-antenna regimes the proposed FA approaches require less computational complexity than their corresponding interior point methods (IPMs) do, yet demand a higher complexity than the iterative and the successive convex approximation (SCA) approaches do. Simulation results reveal that the proposed FA attains the same global optimal solution as that of the IPM for an optimization problem in cognitive beamforming. On the other hand, the proposed FA approaches outperform the iterative, IPM and SCA in terms of obtaining better solution for optimization problems, respectively, for a classic transmit beamforming, RIS-aided transmit beamforming and RIS-aided WPT.

Review of Parameter Tuning Methods for Nature-Inspired Algorithms

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.

Ten New Benchmarks for Optimization

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.

A Nature-Inspired Feature Selection Approach based on Hypercomplex Information

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.

COEBA: A Coevolutionary Bat Algorithm for Discrete Evolutionary Multitasking

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.

Neighborhood Information-based Probabilistic Algorithm for Network Disintegration

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.

Influence of Initialization on the Performance of Metaheuristic Optimizers

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.

Nature-Inspired Optimization Algorithms: Challenges and Open Problems

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.

Self-adaptive decision-making mechanisms to balance the execution of multiple tasks for a multi-robots team

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.

The Global Convergence Analysis of the Bat Algorithm Using a Markovian Framework and Dynamical System Theory

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.