This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http://www.alimirjalili.com/SCA.html .

SCA: A Sine Cosine Algorithm for solving optimization problems

Harris hawks optimization: Algorithm and applications

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior e.g., stable locomotion from a system of coupled oscillators under perceptual guidance. Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

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Dynamical movement primitives: Learning attractor models for motor behaviors

– Nature‐inspired algorithms are among the most powerful algorithms for optimization. The purpose of this paper is to introduce a new nature‐inspired metaheuristic optimization algorithm, called bat algorithm (BA), for solving engineering optimization tasks., – The proposed BA is based on the echolocation behavior of bats. After a detailed formulation and explanation of its implementation, BA is verified using eight nonlinear engineering optimization problems reported in the specialized literature., – BA has been carefully implemented and carried out optimization for eight well‐known optimization tasks; then a comparison has been made between the proposed algorithm and other existing algorithms., – The optimal solutions obtained by the proposed algorithm are better than the best solutions obtained by the existing methods. The unique search features used in BA are analyzed, and their implications for future research are also discussed in detail.

Bat algorithm: a novel approach for global engineering optimization

The Arithmetic Optimization Algorithm

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 article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed.

/pdf/flower-pollination-algorithm-a-novel-approach-for-4yrn41ae49.pdf

Flower pollination algorithm: A novel approach for multiobjective optimization

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.

/pdf/flower-pollination-algorithm-a-novel-approach-for-4igz0940ep.pdf

Flower Pollination Algorithm: A Novel Approach for Multiobjective Optimization

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.

Multi-objective Flower Algorithm for Optimization

Swarm Intelligence and bio-inspired computation have become increasing popular in the last two decades. Bio-inspired algorithms such as ant colony algorithms, bat algorithms, bee algorithms, firefly algorithms, cuckoo search and particle swarm optimization have been applied in almost every area of science and engineering with a dramatic increase of number of relevant publications. This book reviews the latest developments in swarm intelligence and bio-inspired computation from both the theory and application side, providing a complete resource that analyzes and discusses the latest and future trends in research directions. It can help new researchers to carry out timely research and inspire readers to develop new algorithms. With its impressive breadth and depth, this book will be useful for advanced undergraduate students, PhD students and lecturers in computer science, engineering and science as well as researchers and engineers. Focuses on the introduction and analysis of key algorithms Includes case studies for real-world applicationsContains a balance of theory and applications, so readers who are interested in either algorithm or applications will all benefit from this timely book.

Swarm Intelligence and Bio-Inspired Computation: Theory and Applications

Swarm intelligence (SI) and bio-inspired computing in general have attracted great interest in almost every area of science, engineering, and industry over the last two decades. In this chapter, we provide an overview of some of the most widely used bio-inspired algorithms, especially those based on SI such as cuckoo search, firefly algorithm, and particle swarm optimization. We also analyze the essence of algorithms and their connections to self-organization. Furthermore, we highlight the main challenging issues associated with these metaheuristic algorithms with in-depth discussions. Finally, we provide some key, open problems that need to be addressed in the next decade.

Mehmet Karamanoglu

Papers

Flower pollination algorithm: A novel approach for multiobjective optimization

Flower Pollination Algorithm: A Novel Approach for Multiobjective Optimization

Multi-objective Flower Algorithm for Optimization

Swarm Intelligence and Bio-Inspired Computation: Theory and Applications

Swarm Intelligence and Bio-Inspired Computation: An Overview