Swarm-based Metaheuristic Algorithm Research Articles

Multi-strategy boosted marine predators algorithm for optimizing approximate developable surface

Marine predators algorithm (MPA) is a newly developed swarm-based meta-heuristic algorithm that is inspired by the foraging strategies of marine predators: Lévy, Brownian motions and optimal encounter rate strategies, and has shown competitive performance with other state-of-the-art algorithms. Despite the effectiveness of original MPA and existing improved MPA in many real applications, the diversity of the population and the solution accuracy of MPA still deserve to be improved. To this end, an enhanced marine predators algorithm with the neighborhood-based learning strategy and the adaptive population size strategy is proposed in this paper, which is termed NMPA. Also, the superiority of the proposed NMPA is verified by being compared with the original MPA, other improved MPA and popular nature-inspired optimization algorithms on the well-known CEC 2017 and CEC 2020 test suites as well as three engineering design problems, respectively. Furthermore, the practicability of NMPA is illustrated by solving a real-world application of approximate developable surface modeling. By taking the maximization of developability degree of the developable surface as the evaluation criterion, the model for interpolating two given spatial curves to design an approximate developable surface is established. Then, the proposed NMPA is used to solve the optimization model, and the approximate developable surfaces with the maximum developability degree can be obtained. The experimental results show the superior performance of NMPA over other algorithms in terms of precision, convergence rate and solution quality. To sum up, NMPA is potentially a competitive and excellent meta-heuristic algorithm for constructing approximate developable surface and solving engineering optimization problems.

Inverse Kinematics Analysis of Novel 6-Dof Robotic Arm Manipulator for Oil and Gas Welding Using Grey Wolf Algorithm

his paper presents a grey-wolf algorithm for solving the inverse kinematics of a newly designed 6-degree-of-freedom robotic arm for oil and gas pipeline welding which has not been used in the literature. Consequently, due to the robot’s multiple joints with compounding combinatory possibilities of joint angles, analysis of the inverse kinematics is relatively complex. In this research, grey-wolf algorithm, a swarm-based meta-heuristic algorithm, has been used to solve for the inverse kinematics of the robotic arm with respect to tracking a rectangular trajectory with six sets of waypoints in the 3D [X, Y, Z] space. The results were further analyzed in terms of the accuracy of the position of end effector from the accurate position of the rectangular target trajectory via a mean squared error cost function. Furthermore, results of comparison between the grey-wolf algorithm and the particle swarm optimisation, an alternate swarm algorithm with respect to position error from the inverse kinematics task is also presented. The results obtained via simulation clearly demonstrates the superior performance of the grey-wolf algorithm compared to particle swarm optimisation with respect to the solving an inverse kinematics task

Beluga whale optimization: A novel nature-inspired metaheuristic algorithm

In this paper, a novel swarm-based metaheuristic algorithm inspired from the behaviors of beluga whales, called beluga whale optimization (BWO), is presented to solve optimization problem. Three phases of exploration, exploitation and whale fall are established in BWO, corresponding to the behaviors of pair swim, prey, and whale fall, respectively. The balance factor and probability of whale fall in BWO are self-adaptive which play significant roles to control the ability of exploration and exploitation. Besides, the Levy flight is introduced to enhance the global convergence in the exploitation phase. The effectiveness of the proposed BWO is tested using 30 benchmark functions, with qualitative, quantitative and scalability analysis, and the statistical results are compared with 15 other metaheuristic algorithms. According to the results and discussion, BWO is a competitive algorithm in solving unimodal and multimodal optimization problems, and the overall rank of BWO is the first in the scalability analysis of benchmark functions among compared metaheuristic algorithms through the Friedman ranking test. Finally, four engineering problems demonstrate the merits and potential of BWO in solving complex real-world optimization problems. The source code of BWO is currently available to public: https://ww2.mathworks.cn/matlabcentral/fileexchange/112830-beluga-whale-optimization-bwo/.

Improved whale optimization algorithm and its application in vehicle structural crashworthiness

Whale optimization algorithm (WOA) is a novel-innovative swarm-based meta-heuristic algorithm with excellent performance, but it may still be trapped into local extremum for troublesome problems. To this end, an improved multi-objective whale optimization algorithm (IMOWOA) is proposed to cover the shortages. Firstly, in the search stage of WOA, individual difference is considered to strengthen the exploration ability, and evolution operators are introduced to regenerate the stagnated population to prevent premature convergence. Next, the performance of IMOWOA is compared with MOWOA and other classical optimization algorithms, and a series of multi-objective test functions are used. The results on the convergence and diversity of Pareto front confirm that IMOWOA has better feasibility and competitiveness. Finally, integrated with the least squares support vector regression (LSSVR) model, IMOWOA is applied to the deterministic optimization of vehicle structural crashworthiness. The conclusion testified the efficiency of IMOWOA in the field of vehicle crashworthiness.

A powerful meta-heuristic search algorithm for solving global optimization and real-world solar photovoltaic parameter estimation problems

The teaching-learning-based artificial bee colony (TLABC) is a new hybrid swarm-based metaheuristic search algorithm. It combines the exploitation of the teaching learning-based optimization (TLBO) with the exploration of the artificial bee colony (ABC). With the hybridization of these two nature-inspired swarm intelligence algorithms, a robust method has been proposed to solve global optimization problems. However, as with swarm-based algorithms, with the TLABC method, it is a great challenge to effectively simulate the selection process. Fitness-distance balance (FDB) is a powerful recently developed method to effectively imitate the selection process in nature. In this study, the three search phases of the TLABC algorithm were redesigned using the FDB method. In this way, the FDB-TLABC algorithm, which imitates nature more effectively and has a robust search performance, was developed. To investigate the exploitation, exploration, and balanced search capabilities of the proposed algorithm, it was tested on standard and complex benchmark suites (Classic, IEEE CEC 2014, IEEE CEC 2017, and IEEE CEC 2020). In order to verify the performance of the proposed FDB-TLABC for global optimization problems and in the photovoltaic parameter estimation problem (a constrained real-world engineering problem) a very comprehensive and qualified experimental study was carried out according to IEEE CEC standards. Statistical analysis results confirmed that the proposed FDB-TLABC provided the best optimum solution and yielded a superior performance compared to other optimization methods.

Evolutionary Computation Based Real-time Robot Arm Path-planning Using Beetle Antennae Search

This paper presents a model-free real-time kinematic tracking controller for a redundant manipulator. Redundant manipulators are common in industrial applications because of the flexibility and dexterity they get from redundant joints. However, at the same time, the modeling of these systems becomes quite challenging, even for simple tasks like trajectory tracking. Some classical approaches are being used to tackle the issue, including a numerical approximation of the Jacobian and pseudo-inverse of the Jacobian matrix. These approaches have their limitations as they require exact parameters for the modeling of the manipulator; they are not immune to position error accumulation with time and put the manipulator way off the target position. Swarm-based meta-heuristic algorithms have given a new direction to the solution of the redundancy resolution problem. However, they are computationally intensive, formulated in discrete-time, and better suited for offline computation rather than real-time. We proposed a novel continuous-time Zeroing Neural Network with Beetle Antennae Search (ZNNBAS). The ZNNBAS algorithm can solve the quadratic optimization problem for redundancy resolution in real-time. To test its performance, we applied it on 7-DOF redundant manipulator with two trajectories to follow: character ``M" and hypotrochoid. The manipulator was able to trace the reference trajectories with minimal tracking errors.

Re-Allocation of Distributed Generations Using Available Renewable Potential Based Multi-Criterion-Multi-Objective Hybrid Technique

Integration of Distributed generations (DGs) and capacitor banks (CBs) in distribution systems (DS) have the potential to enhance the system’s overall capabilities. This work demonstrates the application of a hybrid optimization technique the applies an available renewable energy potential (AREP)-based, hybrid-enhanced grey wolf optimizer–particle swarm optimization (AREP-EGWO-PSO) algorithm for the optimum location and sizing of DGs and CBs. EGWO is a metaheuristic optimization technique stimulated by grey wolves, and PSO is a swarm-based metaheuristic optimization algorithm. Hybridization of both algorithms finds the optimal solution to a problem through the movement of the particles. Using this hybrid method, multi-criterion solutions are obtained, such as technical, economic, and environmental, and these are enriched using multi-objective functions (MOF), namely minimizing active power losses, voltage deviation, the total cost of electrical energy, total emissions from generation sources and enhancing the voltage stability index (VSI). Five different operational cases were adapted to validate the efficacy of the proposed scheme and were performed on two standard distribution systems, namely, IEEE 33- and 69-bus radial distribution systems (RDSs). Notably, the proposed AREP-EGWO-PSO algorithm compared the AREP at the candidate locations and re-allocated the DGs with optimal re-sizing when the EGWO-PSO algorithm failed to meet the AREP constraints. Further, the simulated results were compared with existing optimization algorithms considered in recent studies. The obtained results and analysis show that the proposed AREP-EGWO-PSO re-allocates the DGs effectively and optimally, and that these objective functions offer better results, almost similar to EGWO-PSO results, but more significant than other existing optimization techniques.

Rank-driven salp swarm algorithm with orthogonal opposition-based learning for global optimization.

Salp swarm algorithm (SSA) is a relatively new and straightforward swarm-based meta-heuristic optimization algorithm, which is inspired by the flocking behavior of salps when foraging and navigating in oceans. Although SSA is very competitive, it suffers from some limitations including unbalanced exploration and exploitation operation, slow convergence. Therefore, this study presents an improved version of SSA, called OOSSA, to enhance the comprehensive performance of the basic method. In preference, a new opposition-based learning strategy based on optical lens imaging principle is proposed, and combined with the orthogonal experimental design, an orthogonal lens opposition-based learning technique is designed to help the population jump out of a local optimum. Next, the scheme of adaptively adjusting the number of leaders is embraced to boost the global exploration capability and improve the convergence speed. Also, a dynamic learning strategy is applied to the canonical methodology to improve the exploitation capability. To confirm the efficacy of the proposed OOSSA, this paper uses 26 standard mathematical optimization functions with various features to test the method. Alongside, the performance of the proposed methodology is validated by Wilcoxon signed-rank and Friedman statistical tests. Additionally, three well-known engineering optimization problems and unknown parameters extraction issue of photovoltaic model are applied to check the ability of the OOSA algorithm to obtain solutions to intractable real-world problems. The experimental results reveal that the developed OOSSA is significantly superior to the standard SSA, currently popular SSA-based algorithms, and other state-of-the-artmeta-heuristic algorithms for solving numerical optimization, real-world engineering optimization, and photovoltaic model parameter extraction problems. Finally, an OOSSA-based path planning approach is developed for creating the shortest obstacle-free route for autonomous mobile robots. Our introduced method is compared with several successful swarm-based metaheuristic techniques in five maps, and the comparative results indicate that the suggested approach can generate the shortest collision-free trajectory as compared to other peers.

Penyelesaian Container Stowage Problem untuk Kontainer Ukuran 20 Feet menggunakan Whale Optimization Algorithm

This paper has purpose to solve Container Stowage Problem (CSP) for 20 feet container using Whale Optimization Algorithm (WOA). CSP is a problem discussing about how to stowage a container on the ship where the purpose to minimize the unloading time. Moreover, 20 feet container is one of container types. WOA is a recently developed swarm-based metaheuristic algorithm that is based on the bubble net hunting maneuver technique of humpback whales for solving complex optimization problems. WOA had three procedures, first encircling prey, second bubble-net attacking method or exploitation phase, and third search for prey or exploration phase. WOA application program or resolving solve CSP for 20 feet container was made by using Borland C++ programming language which was implemented in three cases types of CSP data, first, the small data taking about nine containers with the number of bays, rows and tiers, respectively, are 4, 4, 4. The second and third data was medium data and big data with 62 containers and 95 containers each data, and had the number of bays, rows and tiers, respectively, are 14, 4, 5. After executing the program can be concluded the unloading time will be better if the number of whales is larger, while the number of iterations and the number of parameter control for shape of a logaritma spiral don’t affect the solution.

Non-linear static and dynamic buckling analysis of laminated composite cylindrical shell embedded in non-linear elastic foundation using the swarm-based metaheuristic algorithms

In this paper, by determining the optimal fiber's angles for maximum critical buckling load, the non-linear static and dynamic buckling analyses of laminated composite cylindrical shells resting on non-linear elastic foundation subjected to external loading are investigated. The laminated composite cylindrical with three, four, and five layers is considered. In the present study, first, the optimal fiber's angles are found using the swarm-based metaheuristic algorithms, then, the non-linear static and dynamic buckling analyses are carried out at optimum fiber directions. According to classical shell theory, von-Kármán equation, and Hooke's law, the stress-strain relations are derived for the laminated composite cylindrical shell. Then, based on the Galerkin's method, the discretized motion equation is obtained. For the optimization problem, the design variables are ply angles, and the objective function is maximizing the critical buckling load. Four recently developed swarm-based metaheuristic algorithms including, grey wolf optimizer (GWO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and salp swarm algorithm (SSA), are utilized to solve these optimization problems. Based on the results, the optimization algorithms have improved the value of the critical buckling load significantly. Also, the WOA algorithm had better results than the others, while the GOA was the weakest.

Minimizing the Total Cost of Inventory by Using Artificial Bee Colony Algorithm

Inventory denotes the assets and important resources utilised in an organisation or industry in which it offers various benefits for firm cash flow and persistent viability. If the production inventory of a company faces shortage or other problems such as greater operating cost due to interest payments on loan cash, the management will be in a critical situation, thereby leading to loss of customers and profits. This encourages organisations to implement inventory control, which aims for the lowest total cost of inventory, among others. Therefore, this study employed the Artificial Bee Colony (ABC) algorithm to ascertain the minimum total cost of inventory. The algorithm characterised a swarm-based meta-heuristic algorithm comprised of three divisions of bee troops in the ABC model, namely employed, onlooker, and scout bees. The resulting outcomes revealed a minimum total cost of inventory obtainable of RM45.38, with an optimal order quantity of 37 units.

A comparison of swarm-based optimization algorithms in linear antenna array synthesis

Today, the design of antenna arrays is very important in providing effective and efficient wireless communication. The purpose of antenna array synthesis is to obtain a radiation pattern with a low side lobe level (SLL) at a desired half power beam width in far-field. The amplitude and position values of the array elements can be optimized to obtain a radiation pattern with suppressed SLLs. In this paper, swarm-based metaheuristic algorithms including particle swarm optimization (PSO), artificial bee colony (ABC), mayfly algorithm (MA) and jellyfish search (JS) are compared to determine the optimal design of linear antenna arrays. Extensive experiments are conducted on designing 10-, 16-, 24- and 32-element linear arrays by determining the amplitude and positions. Experiments are repeated 30 times due to the random nature of swarm-based optimizers, and statistical results show that the performance of the novel algorithms, MA and JS, is better than that of the well-known PSO and ABC methods.

A Novel Multiobjective Hybrid Technique for Siting and Sizing of Distributed Generation and Capacitor Banks in Radial Distribution Systems

Distributed generation (DG) and capacitor bank (CB) allocation in distribution systems (DS) has the potential to enhance the overall system performance of radial distribution systems (RDS) using a multiobjective optimization technique. The benefits of CB and DG injection in the RDS greatly depend on selecting a suitable number of CBs/DGs and their volume along with the finest location. This work proposes applying a hybrid enhanced grey wolf optimizer and particle swarm optimization (EGWO-PSO) algorithm for optimal placement and sizing of DGs and CBs. EGWO is a metaheuristic optimization technique stimulated by grey wolves. On the other hand, PSO is a swarm-based metaheuristic optimization algorithm that finds the optimal solution to a problem through the movement of the particles. The advantages of both techniques are utilized to acquire mutual benefits, i.e., the exploration ability of the EGWO and the exploitation ability of the PSO. The proposed hybrid method has a high convergence speed and is not trapped in local optimal. Using this hybrid method, technical, economic, and environmental advantages are enhanced using multiobjective functions (MOF) such as minimizing active power losses, voltage deviation index (VDI), the total cost of electrical energy, and total emissions from generation sources and enhancing the voltage stability index (VSI). Six different operational cases are considered and carried out on two standard distribution systems, namely, IEEE 33- and 69-bus RDSs, to demonstrate the proposed scheme’s effectiveness extensively. The simulated results are compared with existing optimization algorithms. From the obtained results, it is observed that the proposed EGWO-PSO gives distinguished enhancements in multiobjective optimization of different conflicting objective functions and high-level performance with global optimal values.

Modified Kalman particle swarm optimization: Application for trim problem of very flexible aircraft

Particle swarm optimization (PSO) is one of the most popular stochastic swarm-based metaheuristic algorithms. Kalman filter principle is introduced to predict the global optimum more accurately to enhance convergence. However, the evolution of particles in current Kalman PSO merely depends on the adjustment based on observation. In this paper, a modified Kalman particle swarm optimization (MKPSO) algorithm is proposed. The population is extended with the estimated optimum based on Kalman filtering, in which the prediction model is formulated as the weighted central optimum. Benchmark functions in the CEC14 test suite are adopted to verify the effectiveness of MKPSO. Numerical results show that MKPSO is more effective in mining capability for high-dimensional problems. Besides, the superiority of MKPSO lies in solving hybrid optimization problems. At last, MKPSO is applied to maximize the attainable moments subset of very flexible aircraft (VFA) on account for redundancy of control surfaces. Simulation results reveal that there is a trade-off between flight and control performance for VFA.

Lévy-flight moth-flame optimisation algorithm-based micro-grid equipment sizing: An integrated investment and operational planning approach

Bridging the gap between simulation and reality for successful micro-grid (MG) implementation requires accurate mathematical modelling of the underlying energy infrastructure and extensive optimisation of the design space defined by all possible combinations of the size of the equipment. While exact mathematical optimisation approaches to the MG capacity planning are highly computationally efficient, they often fail to preserve the associated problem nonlinearities and non-convexities. This translates into the fact that the available MG sizing tools potentially return a sub-optimal (inferior) MG design. This brings to light the importance of nature-inspired, swarm-based meta-heuristic optimisation algorithms that are able to effectively handle the nonlinear and non-convex nature of the MG design optimisation problem – and better approximate the globally optimum solution – though at the expense of increased computational complexity. Accordingly, this paper introduces a robust MG capacity planning optimisation framework based on a state-of-the-art meta-heuristic, namely the Lévy-flight moth-flame optimisation algorithm (MFOA). An intelligent linear programming-based day-ahead energy scheduling design is, additionally, integrated into the proposed model. A case study is presented for a real grid-tied community MG in rural New Zealand. A comparison of the modelling results with those of the most popular tool in the literature and industry, HOMER Pro, verifies the superiority of the proposed meta-heuristic-based MG sizing model. Additionally, the efficiency of the Lévy-flight MFOA is compared to nine well-established meta-heuristics in the MG capacity planning literature. The comparative analyses have revealed the statistically significant outperformance of the Lévy-flight MFOA to the examined meta-heuristics. Notably, its superiority to the original MFOA, the hybrid genetic algorithm-particle swarm optimisation, and the ant colony optimiser, by at least ~6.5%, ~8.4%, and ~12.8%, is demonstrated. Moreover, comprehensive capital budgeting analyses have confirmed the financial viability of the test-case system optimised by the proposed model.

Modified salp swarm algorithm for global optimisation

Salp swarm algorithm (SSA) is a newly swarm-based metaheuristic algorithm that simulate the swimming and foraging behaviour of salps in oceans so to search for global optimum solution. Similarly to other metaheuristic algorithms, SSA suffers from poor convergence rate and stagnation in local optima. In this paper, three different improvements to the original population update process are proposed in order to enhance its exploitation and exploration capabilities. The first modification (MSSA1) introduces the concept of local best information to the followers salps update process allowing a better exploration of local search neighbourhood. The second improvement (MSSA2) provide two followers update process. The first is based on a differential evolution combined with a randomly selected local best position, and the second uses a local search in the global best neighbourhood which is triggered by a non-improvement in the corresponding local best. A third modification to the SSA algorithm (MSSA3) penalises a non-improvement of the local best solution by computing a new corresponding follower’s position based on a local jump in the local best neighbourhood for better exploitation. The performances of the proposed algorithms are tested on 27 CEC’15 test suite, and two real-world optimisation problems. A comparative study using nonparametric statistical tests of the obtained results is conducted against those of eight well-known metaheuristics, including the original SSA. The results indicate an overall distinctive performance of all three modification compared to the remaining algorithms, while MSSA1 scored generally better than MSSA2 and MSSA3.

Tuna Swarm Optimization: A Novel Swarm-Based Metaheuristic Algorithm for Global Optimization.

In this paper, a novel swarm-based metaheuristic algorithm is proposed, which is called tuna swarm optimization (TSO). The main inspiration for TSO is based on the cooperative foraging behavior of tuna swarm. The work mimics two foraging behaviors of tuna swarm, including spiral foraging and parabolic foraging, for developing an effective metaheuristic algorithm. The performance of TSO is evaluated by comparison with other metaheuristics on a set of benchmark functions and several real engineering problems. Sensitivity, scalability, robustness, and convergence analyses were used and combined with the Wilcoxon rank-sum test and Friedman test. The simulation results show that TSO performs better compared to other comparative algorithms.

A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems.

The butterfly optimization algorithm (BOA) is a swarm-based metaheuristic algorithm inspired by the foraging behaviour and information sharing of butterflies. BOA has been applied to various fields of optimization problems due to its performance. However, BOA also suffers from drawbacks such as diminished population diversity and the tendency to get trapped in local optimum. In this paper, a hybrid butterfly optimization algorithm based on a Gaussian distribution estimation strategy, called GDEBOA, is proposed. A Gaussian distribution estimation strategy is used to sample dominant population information and thus modify the evolutionary direction of butterfly populations, improving the exploitation and exploration capabilities of the algorithm. To evaluate the superiority of the proposed algorithm, GDEBOA was compared with six state-of-the-art algorithms in CEC2017. In addition, GDEBOA was employed to solve the UAV path planning problem. The simulation results show that GDEBOA is highly competitive.

Evaluation of EHO Algorithm’s in solving various real-life problems

Abstract: This paper, presents a new swarm-based metaheuristic search algorithm, known as Elephant Herding Optimization (EHO), which is proposed for solving various daily real-life problems such as benchmark problems, Service Selection in QoS-Aware Web Service Composition, Energy-Based Localization, PID controller tuning, Appliance Scheduling in Smart Grid identification and other problems. The EHO method is inspired by the herding behavior of elephant group. In nature, elephants live in clans under the leadership of a matriarch (female elephant), while the male elephants separate from their family when they grow up. These two behaviors are used by EHO as two operators: clan updating operator and separating operator, which will be used in the optimizing process. Elephant Herding Optimization (EHO) is used to solve NP-Hard problems.

Modified Harris Hawks Optimization Algorithm for Global Optimization Problems

The Harris hawks optimization algorithm (HHO) is a novel swarm-based meta-heuristic algorithm. In this study, a modified Harris hawks optimization algorithm (MHHO) is proposed to enhance the searching performance of the conventional HHO. Past studies have revealed that different adjustment strategies of important variables in meta-heuristic algorithm will evidently affect the performance of the algorithm. Therefore, this study focuses on the escaping energy (E) of prey is an extremely, which is a critical concept that determines the balance between the exploration and exploitation phases of the HHO. In nature, the Harris hawks will take different the perch strategy and the chasing pattern according to E. For E, six different update strategies are designed to model the real situation. To explore the differences between the six strategies mentioned above, a comparative study through twenty representative benchmark functions is carried out by Experiment 1 (Sect. 4.2). The results show that strategy 6 (the exponential decreasing strategy) outperforms other rivals; therefore, it is deployed into the MHHO. To further demonstrate the superior search performance of MHHO, a similar comparative study between MHHO and several well-established optimization technologies is carried out by Experiment 2 (Sect. 4.3). The results clearly exhibit MHHO outperforms its rivals in most benchmark functions. In addition, compared with other well-known optimizers and the conventional HHO, the competitive results obtained by MHHO on two engineering optimization problems also prove the effectiveness and superiority of the proposed MHHO in solving constrained optimization problems.