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

Salp Swarm Algorithm

Harris hawks optimization: Algorithm and applications

A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm

A new efficient optimization method, called 'Teaching-Learning-Based Optimization (TLBO)', is proposed in this paper for the optimization of mechanical design problems. This method works on the effect of influence of a teacher on learners. Like other nature-inspired algorithms, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. The population is considered as a group of learners or a class of learners. The process of TLBO is divided into two parts: the first part consists of the 'Teacher Phase' and the second part consists of the 'Learner Phase'. 'Teacher Phase' means learning from the teacher and 'Learner Phase' means learning by the interaction between learners. The basic philosophy of the TLBO method is explained in detail. To check the effectiveness of the method it is tested on five different constrained benchmark test functions with different characteristics, four different benchmark mechanical design problems and six mechanical design optimization problems which have real world applications. The effectiveness of the TLBO method is compared with the other population-based optimization algorithms based on the best solution, average solution, convergence rate and computational effort. Results show that TLBO is more effective and efficient than the other optimization methods for the mechanical design optimization problems considered. This novel optimization method can be easily extended to other engineering design optimization problems.

Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems

Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems

In this paper, a new global optimisation algorithm, biogeography based optimisation (BBO), for solving discrete optimisation of a gear train is presented. The efficiency and ease of application of the proposed optimisation algorithm is demonstrated by solving a discrete optimisation problem of a four stage gear train from the literature. The objective considered is minimisation of weight. Eighty six inequality constraints are considered which include, bending fatigue strength, contact strength, contact ratio, pinion/gear size, housing size, pitch for gears and kinematic constraints. Twenty two discrete design variables are considered in the optimisation. Design modification is done to reduce the design variables which include two different designs with 18 and 14 design variables. The results of the proposed method are compared with the results obtained by using other optimisation methods such as genetic algorithm, particle swarm optimisation (PSO), and differential evolution (DE). The solution obtained by using BBO is superior to those obtained by using other optimisation techniques.

Discrete optimisation of a gear train using biogeography based optimisation technique

In this paper a new optimisation algorithm, harmony elements algorithm (HEA), for solving mechanical engineering design optimisation problems is presented. This algorithm is inspired by an ancient Chinese philosophy, called as theory of five elements. The basic harmony element algorithm proposed by Cui and Guo (2008) is modified in this paper to reduce the computational effort by dividing the population into equal parts and by incorporating the mutation operator. The efficiency and ease of application of the proposed optimisation algorithm is demonstrated by solving five different mechanical components design problems such as pressure vessel, tension/compression spring, Belleville spring, welded beam and gear train. The results of the proposed method are compared with the results given by other optimisation techniques such as genetic algorithm (GA), particle swarm optimisation (PSO), ant colony algorithm (ACA), Lagrangian multiplier approach and branch and bound approach. In all the cases, the solutions obtained using the proposed modified HEA are superior to those obtained by other optimisation techniques.

Mechanical engineering design optimisation using modified harmony elements algorithm

Ball bearings are widely used as important components in most of mechanical engineering applications. These bearings find wide applications in automotive, manufacturing and aeronautical industries. The problem associated with ball bearings is that the design and selection are based on different operating conditions to reach their excellent performance, long life and high reliability. This leads to the requirement of optimal design of ball bearings. Optimisation aspects of a ball bearing are presented in this paper considering three different objectives namely, dynamic capacity, static capacity and elastohydrodynamic minimum film thickness. The design parameters include mean diameter of rolling, ball diameter, number of balls and inner and outer race groove curvature radii. Different constants associated with the constraints are given some ranges and are included as design variables. The constraints considered are pertaining to the assembly angle, ball size, bearing width size, ensuring running mobility, thickness of bearing rings and curvature radii. The optimisation procedure is carried out using a modified particle swarm optimisation (PSO) technique. Both single and multi-objective optimisation aspects are considered. The results of the proposed technique are compared with the previously published results. The proposed technique has given much better results in comparison to the previously tried approaches.

R.V. Rao

Papers

Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems

Teaching-Learning-Based Optimization: An optimization method for continuous non-linear large scale problems

Discrete optimisation of a gear train using biogeography based optimisation technique

Mechanical engineering design optimisation using modified harmony elements algorithm

Multi-objective design optimisation of ball bearings using a modified particle swarm optimisation technique