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Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology | Mirjalili S.M.,Zharfa Pajohesh System ZPS Co. | Hatamlou A.,Islamic Azad University at Khoy
Neural Computing and Applications | Year: 2016

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. © 2015, The Natural Computing Applications Forum.


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology
Structural and Multidisciplinary Optimization | Year: 2015

In 2013 Gaspar-Cunha et al. proposed a set of novel robust multi-objective benchmark functions to increase the difficulty of the current test problems and effectively mimic the characteristics of real search spaces. Despite the merits of the proposed benchmark problems, it is observed that the robust Pareto optimal fronts are located on the boundaries of the search space, which may result in the infeasibility of solutions obtained in case of perturbations along the negative side of the second parameter. This paper modifies the proposed test functions by Gaspar-Cunha et al. to mimic real problems better and allow the parameters to be fluctuated by any degree of perturbations. In fact, the robust fronts are shifted to the centre of the search space, so that any degree of uncertainties can be considered. The paper considers theoretical and experimental analysis of both set of test functions as well. © 2015, Springer-Verlag Berlin Heidelberg.


Saremi S.,Griffith University | Saremi S.,Queensland Institute of Business and Technology | Mirjalili S.Z.,Zharfa Pajohesh System ZPS Co. | Mirjalili S.M.,Zharfa Pajohesh System ZPS Co.
Neural Computing and Applications | Year: 2015

Evolutionary population dynamics (EPD) deal with the removal of poor individuals in nature. It has been proven that this operator is able to improve the median fitness of the whole population, a very effective and cheap method for improving the performance of meta-heuristics. This paper proposes the use of EPD in the grey wolf optimizer (GWO). In fact, EPD removes the poor search agents of GWO and repositions them around alpha, beta, or delta wolves to enhance exploitation. The GWO is also required to randomly reinitialize its worst search agents around the search space by EPD to promote exploration. The proposed GWO–EPD algorithm is benchmarked on six unimodal and seven multi-modal test functions. The results are compared to the original GWO algorithm for verification. It is demonstrated that the proposed operator is able to significantly improve the performance of the GWO algorithm in terms of exploration, local optima avoidance, exploitation, local search, and convergence rate. © 2014, The Natural Computing Applications Forum.


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology
Applied Intelligence | Year: 2015

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. © 2015, Springer Science+Business Media New York.


Mirjalili S.Z.,Zharfa Pajohesh System ZPS Co. | Saremi S.,Griffith University | Saremi S.,Queensland Institute of Business and Technology | Mirjalili S.M.,Zharfa Pajohesh System ZPS Co.
Neural Computing and Applications | Year: 2015

Training feedforward neural networks (FNNs) is considered as a challenging task due to the nonlinear nature of this problem and the presence of large number of local solutions. The literature shows that heuristic optimization algorithms are able to tackle these problems much better than the mathematical and deterministic methods. In this paper, we propose a new trainer using the recently proposed heuristic algorithm called social spider optimization (SSO) algorithm. The trained FNN by SSO (FNNSSO) is benchmarked on five standard classification data sets: XOR, balloon, Iris, breast cancer, and heart. The results are verified by the comparison with five other well-known heuristics. The results prove that the proposed FNNSSO is able to provide very promising results compared with other algorithms. © 2015, The Natural Computing Applications Forum.


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology
Neural Computing and Applications | Year: 2015

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. © 2015 The Natural Computing Applications Forum


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology
Knowledge-Based Systems | Year: 2015

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. © 2015 Elsevier B.V. All rights reserved.


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology
Advances in Engineering Software | Year: 2015

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. © 2015 Elsevier Ltd. All rights reserved.


Mirjalili S.,Griffith University | Mirjalili S.,Queensland Institute of Business and Technology | Lewis A.,Griffith University
Swarm and Evolutionary Computation | Year: 2015

Performance metrics are essential for quantifying the performance of optimization algorithms in the field of evolutionary multi-objective optimization. Such metrics allow researchers to compare different algorithms quantitatively. In the field of robust multi-objective optimization, however, there is currently no performance metric despite its significant importance. This motivates our proposal of three novel specific metrics for measuring the convergence, coverage, and success rate of robust Pareto optimal solutions obtained by robust multi-objective algorithms. The proposed metrics are employed to quantitatively evaluate and compare Robust Multi-objective Particle Swarm Optimization (RMOPSO) and Robust Non-dominated Sorting Genetic Algorithm (RNSGA-II) on seven selected benchmark problems. The results show that the proposed metrics are effective in quantifying the performance of robust multi-objective algorithms in terms of convergence, coverage, and the ratio of the robust/non-robust Pareto optimal solutions obtained. © 2014 Elsevier B.V.

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