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
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.
This work proposes two novel optimization algorithms called Salp Swarm Algorithm (SSA) and Multi-objective Salp Swarm Algorithm (MSSA) for solving optimization problems with single and multiple objectives. The main inspiration of SSA and MSSA is the swarming behaviour of salps when navigating and foraging in oceans. These two algorithms are tested on several mathematical optimization functions to observe and confirm their effective behaviours in finding the optimal solutions for optimization problems. The results on the mathematical functions show that the SSA algorithm is able to improve the initial random solutions effectively and converge towards the optimum. The results of MSSA show that this algorithm can approximate Pareto optimal solutions with high convergence and coverage. The paper also considers solving several challenging and computationally expensive engineering design problems (e.g. airfoil design and marine propeller design) using SSA and MSSA. The results of the real case studies demonstrate the merits of the algorithms proposed in solving real-world problems with difficult and unknown search spaces.
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 .
This paper proposes an optimisation algorithm called Grasshopper Optimisation Algorithm (GOA) and applies it to challenging problems in structural optimisation. The proposed algorithm mathematically models and mimics the behaviour of grasshopper swarms in nature for solving optimisation problems. The GOA algorithm is first benchmarked on a set of test problems including CEC2005 to test and verify its performance qualitatively and quantitatively. It is then employed to find the optimal shape for a 52-bar truss, 3-bar truss, and cantilever beam to demonstrate its applicability. The results show that the proposed algorithm is able to provide superior results compared to well-known and recent algorithms in the literature. The results of the real applications also prove the merits of GOA in solving real problems with unknown search spaces.
We provide a sensitivity analysis toolbox consisting of a set of Matlab functions that offer utilities for quantifying the influence of uncertain input parameters on uncertain model outputs. It allows the determination of the key input parameters of an output of interest. The results are based on a probability density function (PDF) provided for the input parameters. The toolbox for uncertainty and sensitivity analysis methods consists of three ingredients: (1) sampling method, (2) surrogate models, (3) sensitivity analysis (SA) method. Numerical studies based on analytical functions associated with noise and industrial data are performed to prove the usefulness and effectiveness of this study.
This paper describes jMetal, an object-oriented Java-based framework aimed at the development, experimentation, and study of metaheuristics for solving multi-objective optimization problems. jMetal includes a number of classic and modern state-of-the-art optimizers, a wide set of benchmark problems, and a set of well-known quality indicators to assess the performance of the algorithms. The framework also provides support to carry out full experimental studies, which can be configured and executed by using jMetal’s graphical interface. Other features include the automatic generation of statistical information of the obtained results, and taking advantage of the current availability of multi-core processors to speed-up the running time of the experiments. In this work, we include two case studies to illustrate the use of jMetal in both solving a problem with a metaheuristic and designing and performing an experimental study.
With several characteristics, such as large scale, diverse predictability and timeliness, the city traffic data falls in the range of definition of Big Data. A Virtual Reality GIS based traffic analysis and visualization system is proposed as a promising and inspiring approach to manage and develop traffic big data. In addition to the basic GIS interaction functions, the proposed system also includes some intelligent visual analysis and forecasting functions. The passenger flow forecasting algorithm is introduced in detail.
Nature has provided inspiration for most of the man-made technologies. Scientists believe that dolphins are the second to humans in smartness and intelligence. Echolocation is the biological sonar used by dolphins and several kinds of other animals for navigation and hunting in various environments. This ability of dolphins is mimicked in this paper to develop a new optimization method. There are different meta-heuristic optimization methods, but in most of these algorithms parameter tuning takes a considerable time of the user, persuading the scientists to develop ideas to improve these methods. Studies have shown that meta-heuristic algorithms have certain governing rules and knowing these rules helps to get better results. Dolphin echolocation takes advantages of these rules and outperforms many existing optimization methods, while it has few parameters to be set. The new approach leads to excellent results with low computational efforts.
In this manuscript a concurrent coupling scheme is presented to model three dimensional cracks and dislocations at the atomistic level. The scheme couples molecular dynamics to extended finite element method (XFEM) via the Bridging Domain Method (BDM). This method is based on linear weighting of the strain energy over a region (the bridging domain) which conserves the energy in the entire system. To compute the material behavior in the continuum scale, the Cauchy–Born method is used. Many improvements have been made in the implementation to make the method work for the general case of materials and presence of multi-million degrees of freedom. To show the applicability and productivity of the proposed method, two three dimensional crack examples were modeled. The results show that the method and the corresponding implementation are capable of handling dislocation and crack propagation in the three dimensional space.
Topology optimization is developing rapidly in all kinds of directions; and increasingly more extensions are oriented towards manufacturability of the optimized designs. Therefore, this survey of manufacturing oriented topology optimization methods is intended to provide useful insight classification and expert comments for the community. First, the traditional manufacturing methods of machining and injection molding/casting are reviewed, because the majority of engineering parts are manufactured through these methods and complex design requirements are associated. Next, the challenges and opportunities related to the emerging additive manufacturing (AM) are highlighted. SIMP (Solid Isotropic Material with Penalization) and level set are the concerned topology optimization methods because the majority of manufacturing oriented extensions have been made based on these two methods.
This paper introduces a new optimization algorithm based on Newton's law of cooling, which will be called Thermal Exchange Optimization algorithm. Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. Here, each agent is considered as a cooling object and by associating another agent as environment, a heat transferring and thermal exchange happens between them. The new temperature of the object is considered as its next position in search space. The performance of the algorithm is examined by some mathematical functions and four mechanical benchmark problems.
This paper aims to provide a solution method for a real-world scheduling case from a welding process, which is one of the important processes in modern industry. The unique characteristic of the welding scheduling problem (WSP) is that multiple machines can process one operation at a time. Thus, WSP is a new scheduling problem. We first formulate a new multi-objective mixed integer programming model for this WSP based on a comprehensive investigation. This model involves some realistic constraints, controllable processing times (CPT), sequence dependent setup times (SDST) and job dependent transportation times (JDTT). Then we propose a multi-objective discrete grey wolf optimizer (MODGWO) considering not only production efficiency but also machine load on this real-world scheduling case. The solution is encoded as a two-part representation including a permutation vector and a machine assignment matrix. A reduction machine load strategy is used to adjust the number of machines aiming to minimize the machine load. To evaluate the effectiveness of the proposed MODGWO, we compare it with other well-known multi-objective evolutionary algorithms including NSGA-II and SPEA2 on a set of instances. Experimental results demonstrate that the proposed MODGWO is superior to the compared algorithms in terms of convergence, spread and coverage on most instances. Finally, MODGWO is successfully applied to this real-world WSP. This implies that the proposed model is feasible and the proposed algorithm can solve this real-world scheduling problem very well.
The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack model, especially for complex crack patterns. Due to the involvement of “phased field”, phase-field method can be essentially treated a multifield problem even for pure mechanical problem. Therefore, it is supposed that the implementation of PFM based on a software developer that especially supports the solution of multifield problems should be more effective, simpler and more efficient than PFM implemented on a general finite element software. In this work, the authors aim to devise a simple and efficient implementation of phase-field model for the modelling of quasi-static and dynamic fracture in the general purpose commercial software developer, COMSOL Multiphysics. Notably only the tensile stress induced crack is accounted for crack evolution by using the decomposition of elastic strain energy. The width of the diffusive crack is controlled by a length-scale parameter. Equations that govern body motion and phase-field evolution are written into different modules in COMSOL, which are then coupled to a whole system to be solved. A staggered scheme is adopted to solve the coupled system and each module is solved sequentially during one time step. A number of 2D and 3D examples are tested to investigate the performance of the present implementation. Our simulations show good agreement with previous works, indicating the feasibility and validity of the COMSOL implementation of PFM.
Nature is the principal source for proposing new optimization methods such as genetic algorithms (GA) and simulated annealing (SA) methods. All traditional evolutionary algorithms are heuristic population-based search procedures that incorporate random variation and selection. The main contribution of this study is that it proposes a novel optimization method that relies on one of the theories of the evolution of the universe; namely, the Big Bang and Big Crunch Theory. In the Big Bang phase, energy dissipation produces disorder and randomness is the main feature of this phase; whereas, in the Big Crunch phase, randomly distributed particles are drawn into an order. Inspired by this theory, an optimization algorithm is constructed, which will be called the Big Bang–Big Crunch (BB–BC) method that generates random points in the Big Bang phase and shrinks those points to a single representative point via a center of mass or minimal cost approach in the Big Crunch phase. It is shown that the performance of the new (BB–BC) method demonstrates superiority over an improved and enhanced genetic search algorithm also developed by the authors of this study, and outperforms the classical genetic algorithm (GA) for many benchmark test functions.
Colliding Bodies Optimization (CBO) is a new multi-agent algorithm inspired by a collision between two objects in one-dimension. Each agent is modeled as a body with a specified mass and velocity. A collision occurs between pairs of objects and the new positions of the colliding bodies are updated based on the collision laws. In this paper, Enhanced Colliding Bodies Optimization (ECBO) which uses memory to save some best solutions is developed. In addition, a mechanism is utilized to escape from local optima. The performance of the proposed algorithm is compared to those of standard CBO and some optimization techniques on some benchmark mathematical functions and three standard discrete and continuous structural design problems. Optimization results confirm the validity of the proposed approach.
This paper presents a novel metaheuristic algorithm named as Spotted Hyena Optimizer (SHO) inspired by the behavior of spotted hyenas. The main concept behind this algorithm is the social relationship between spotted hyenas and their collaborative behavior. The three basic steps of SHO are searching for prey, encircling, and attacking prey and all three are mathematically modeled and implemented. The proposed algorithm is compared with eight recently developed metaheuristic algorithms on 29 well-known benchmark test functions. The convergence and computational complexity is also analyzed. The proposed algorithm is applied to five real-life constraint and one unconstrained engineering design problems to demonstrate their applicability. The experimental results reveal that the proposed algorithm performs better than the other competitive metaheuristic algorithms.
A suitable piece of software is presented to connect Abaqus, a sophisticated finite element package, with Matlab, the most comprehensive program for mathematical analysis. This interface between these well-known codes not only benefits from the image processing and the integrated graph-plotting features of Matlab but also opens up new opportunities in results post-processing, statistical analysis and mathematical optimization, among many other possibilities. The software architecture and usage are appropriately described and two problems of particular engineering significance are addressed to demonstrate its capabilities. Firstly, the software is employed to assess cleavage fracture through a novel 3-parameter Weibull probabilistic framework. Then, its potential to create and train neural networks is used to identify damage parameters through a hybrid experimental–numerical scheme, and model crack propagation in structural materials by means of a cohesive zone approach. The source code, detailed documentation and a large number of tutorials can be freely downloaded from .
Unmanned combat aerial vehicle (UCAV) path planning is a fairly complicated global optimum problem, which aims to obtain an optimal or near-optimal flight route with the threats and constraints in the combat field well considered. A new meta-heuristic grey wolf optimizer (GWO) is proposed to solve the UCAV two-dimension path planning problem. Then, the UCAV can find the safe path by connecting the chosen nodes of the two-dimensional coordinates while avoiding the threats areas and costing minimum fuel. Conducted simulations show that the proposed method is more competent for the UCAV path planning scheme than other state-of-the-art evolutionary algorithms considering the quality, speed, and stability of final solutions.
Welding input parameters play a very significant role in determining the quality of a weld joint. The joint quality can be defined in terms of properties such as weld-bead geometry, mechanical properties, and distortion. Generally, all welding processes are used with the aim of obtaining a welded joint with the desired weld-bead parameters, excellent mechanical properties with minimum distortion. Nowadays, application of design of experiment (DoE), evolutionary algorithms and computational network are widely used to develop a mathematical relationship between the welding process input parameters and the output variables of the weld joint in order to determine the welding input parameters that lead to the desired weld quality. A comprehensive literature review of the application of these methods in the area of welding has been introduced herein. This review was classified according to the output features of the weld, i.e. bead geometry and mechanical properties of the welds.