The Whale Optimization Algorithm

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

The Ant Lion Optimizer

Grasshopper Optimisation Algorithm

Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications

Colliding bodies optimization: A novel meta-heuristic method

Colliding Bodies Optimization method for optimum design of truss structures with continuous variables

Colliding Bodies Optimization method for optimum discrete design of truss structures

This book presents and applies a novel efficient meta-heuristic optimization algorithm called Colliding Bodies Optimization (CBO) for various optimization problems. The first part of the book introduces the concepts and methods involved, while the second is devoted to the applications. Though optimal design of structures is the main topic, two chapters on optimal analysis and applications in constructional management are also included. This algorithm is based on one-dimensional collisions between bodies, with each agent solution being considered as an object or body with mass. After a collision of two moving bodies with specified masses and velocities, these bodies again separate, with new velocities. This collision causes the agents to move toward better positions in the search space. The main algorithm (CBO) is internally parameter independent, setting it apart from previously developed meta-heuristics. This algorithm is enhanced (ECBO) for more efficient applications in the optimal design of structures. The algorithms are implemented in standard computer programming languages (MATLAB and C++) and two main codes are provided for ease of use

Colliding Bodies Optimization: Extensions and Applications

A new hybrid CBO-PSO algorithm is presented by adding positive properties of the PSO algorithm to the CBO.The CBO is a recently developed meta-heuristic algorithm which does not use the internal parameter and memory in its formulation.In the CBO-PSO the memory of the PSO is added to the CBO to improve the performance of the latter algorithm.The new algorithm is compared to other advanced meta-heuristic methods to illustrate the effectiveness. The vibration domain of structures can be reduced by imposing some constraints on their natural frequencies. For this purpose optimal design of structures under frequency constraints is required which involves highly non-linear and non-convex problems. In this paper an efficient hybrid algorithm is developed for solving such optimization problems. This algorithm utilizes the recently developed colliding bodies optimization (CBO) algorithm as the main engine and uses the positive properties of the particle swarm optimization (PSO) algorithm to increase the efficiency of the CBO. The distinct feature of the present hybrid algorithm is that it requires no parameter tuning. The CBO is known for being parameter independent, and avoiding the use of the traditional penalty method to handle the constraints upholds this property. Two mathematical constrained functions taken from the literature are studied to verify the performance of the algorithm. The algorithm is then applied to optimize truss structures with frequency limitations. The numerical results demonstrate the efficiency of the presented algorithm for this class of problems.

V.R. Mahdavi

Papers

Colliding bodies optimization: A novel meta-heuristic method

Colliding Bodies Optimization method for optimum design of truss structures with continuous variables

Colliding Bodies Optimization method for optimum discrete design of truss structures

Colliding Bodies Optimization: Extensions and Applications

A hybrid CBO-PSO algorithm for optimal design of truss structures with dynamic constraints