Seyedali Mirjalili

Grey Wolf Optimizer

This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves (Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known test functions, and the results are verified by a comparative study with Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolution Strategy (ES). The results show that the GWO algorithm is able to provide very competitive results compared to these well-known meta-heuristics. The paper also considers solving three classical engineering design problems (tension/compression spring, welded beam, and pressure vessel designs) and presents a real application of the proposed method in the field of optical engineering. The results of the classical engineering design problems and real application prove that the proposed algorithm is applicable to challenging problems with unknown search spaces.

The Whale Optimization Algorithm

The Whale Optimization Algorithm inspired by humpback whales is proposed.The WOA algorithm is benchmarked on 29 well-known test functions.The results on the unimodal functions show the superior exploitation of WOA.The exploration ability of WOA is confirmed by the results on multimodal functions.The results on structural design problems confirm the performance of WOA in practice. This paper proposes a novel nature-inspired meta-heuristic optimization algorithm, called Whale Optimization Algorithm (WOA), which mimics the social behavior of humpback whales. The algorithm is inspired by the bubble-net hunting strategy. WOA is tested with 29 mathematical optimization problems and 6 structural design problems. Optimization results prove that the WOA algorithm is very competitive compared to the state-of-art meta-heuristic algorithms as well as conventional methods. The source codes of the WOA algorithm are publicly available at http://www.alimirjalili.com/WOA.html

The Ant Lion Optimizer

The Ant Lion Optimizer inspired by the hunting mechanism of antlions is proposed.The ALO algorithm is benchmarked on 29 well-known test functions.The results on the unimodal functions show the superior exploitation of ALO.The exploratory ability of ALO is confirmed by the results on multimodal functions.The results on real problems confirm the performance of ALO in practice. This paper proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the hunting mechanism of antlions in nature. Five main steps of hunting prey such as the random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are implemented. The proposed algorithm is benchmarked in three phases. Firstly, a set of 19 mathematical functions is employed to test different characteristics of ALO. Secondly, three classical engineering problems (three-bar truss design, cantilever beam design, and gear train design) are solved by ALO. Finally, the shapes of two ship propellers are optimized by ALO as challenging constrained real problems. In the first two test phases, the ALO algorithm is compared with a variety of algorithms in the literature. The results of the test functions prove that the proposed algorithm is able to provide very competitive results in terms of improved exploration, local optima avoidance, exploitation, and convergence. The ALO algorithm also finds superior optimal designs for the majority of classical engineering problems employed, showing that this algorithm has merits in solving constrained problems with diverse search spaces. The optimal shapes obtained for the ship propellers demonstrate the applicability of the proposed algorithm in solving real problems with unknown search spaces as well. Note that the source codes of the proposed ALO algorithm are publicly available at http://www.alimirjalili.com/ALO.html.

Moth-flame optimization algorithm

In this paper a novel nature-inspired optimization paradigm is proposed called Moth-Flame Optimization (MFO) algorithm. The main inspiration of this optimizer is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a useless/deadly spiral path around artificial lights. This paper mathematically models this behaviour to perform optimization. The MFO algorithm is compared with other well-known nature-inspired algorithms on 29 benchmark and 7 real engineering problems. The statistical results on the benchmark functions show that this algorithm is able to provide very promising and competitive results. Additionally, the results of the real problems demonstrate the merits of this algorithm in solving challenging problems with constrained and unknown search spaces. The paper also considers the application of the proposed algorithm in the field of marine propeller design to further investigate its effectiveness in practice. Note that the source codes of the MFO algorithm are publicly available at http://www.alimirjalili.com/MFO.html.

Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm

The Gravitational Search Algorithm (GSA) is a novel heuristic optimization method based on the law of gravity and mass interactions. It has been proven that this algorithm has good ability to search for the global optimum, but it suffers from slow searching speed in the last iterations. This work proposes a hybrid of Particle Swarm Optimization (PSO) and GSA to resolve the aforementioned problem. In this paper, GSA and PSOGSA are employed as new training methods for Feedforward Neural Networks (FNNs) in order to investigate the efficiencies of these algorithms in reducing the problems of trapping in local minima and the slow convergence rate of current evolutionary learning algorithms. The results are compared with a standard PSO-based learning algorithm for FNNs. The resulting accuracy of FNNs trained with PSO, GSA, and PSOGSA is also investigated. The experimental results show that PSOGSA outperforms both PSO and GSA for training FNNs in terms of converging speed and avoiding local minima. It is also proven that an FNN trained with PSOGSA has better accuracy than one trained with GSA.

Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems

Abstract A novel swarm intelligence optimization technique is proposed called dragonfly algorithm (DA). The main inspiration of the DA algorithm originates from the static and dynamic swarming behaviours of dragonflies in nature. Two essential phases of optimization, exploration and exploitation, are designed by modelling the social interaction of dragonflies in navigating, searching for foods, and avoiding enemies when swarming dynamically or statistically. The paper also considers the proposal of binary and multi-objective versions of DA called binary DA (BDA) and multi-objective DA (MODA), respectively. The proposed algorithms are benchmarked by several mathematical test functions and one real case study qualitatively and quantitatively. The results of DA and BDA prove that the proposed algorithms are able to improve the initial random population for a given problem, converge towards the global optimum, and provide very competitive results compared to other well-known algorithms in the literature. The results of MODA also show that this algorithm tends to find very accurate approximations of Pareto optimal solutions with high uniform distribution for multi-objective problems. The set of designs obtained for the submarine propeller design problem demonstrate the merits of MODA in solving challenging real problems with unknown true Pareto optimal front as well. Note that the source codes of the DA, BDA, and MODA algorithms are publicly available at http://www.alimirjalili.com/DA.html.

S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization

Particle Swarm Optimization (PSO) is one of the most widely used heuristic algorithms. The simplicity and inexpensive computational cost makes this algorithm very popular and powerful in solving a wide range of problems. The binary version of this algorithm has been introduced for solving binary problems. The main part of the binary version is a transfer function which is responsible to map a continuous search space to a discrete search space. Currently there appears to be insufficient focus on the transfer function in the literature despite its apparent importance. In this study six new transfer functions divided into two families, s-shaped and v-shaped, are introduced and evaluated. Twenty-five benchmark optimization functions provided by CEC 2005 special session are employed to evaluate these transfer functions and select the best one in terms of avoiding local minima and convergence speed. In order to validate the performance of the best transfer function, a comparative study with six recent modifications of BPSO is provided as well. The results prove that the new introduced v-shaped family of transfer functions significantly improves the performance of the original binary PSO.

Multi-Verse Optimizer: a nature-inspired algorithm for global optimization

This paper proposes a novel nature-inspired algorithm called Multi-Verse Optimizer (MVO). The main inspirations of this algorithm are based on three concepts in cosmology: white hole, black hole, and wormhole. The mathematical models of these three concepts are developed to perform exploration, exploitation, and local search, respectively. The MVO algorithm is first benchmarked on 19 challenging test problems. It is then applied to five real engineering problems to further confirm its performance. To validate the results, MVO is compared with four well-known algorithms: Grey Wolf Optimizer, Particle Swarm Optimization, Genetic Algorithm, and Gravitational Search Algorithm. The results prove that the proposed algorithm is able to provide very competitive results and outperforms the best algorithms in the literature on the majority of the test beds. The results of the real case studies also demonstrate the potential of MVO in solving real problems with unknown search spaces. Note that the source codes of the proposed MVO algorithm are publicly available at http://www.alimirjalili.com/MVO.html.

SCA: A Sine Cosine Algorithm for solving optimization problems

Abstract 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 aircrafts 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 .

How effective is the Grey Wolf optimizer in training multi-layer perceptrons

This paper employs the recently proposed Grey Wolf Optimizer (GWO) for training Multi-Layer Perceptron (MLP) for the first time. Eight standard datasets including five classification and three function-approximation datasets are utilized to benchmark the performance of the proposed method. For verification, the results are compared with some of the most well-known evolutionary trainers: Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Ant Colony Optimization (ACO), Evolution Strategy (ES), and Population-based Incremental Learning (PBIL). The statistical results prove the GWO algorithm is able to provide very competitive results in terms of improved local optima avoidance. The results also demonstrate a high level of accuracy in classification and approximation of the proposed trainer.