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A novel approach to deal with numerical and engineering constrained optimization problems, which incorporates a hybrid evolutionary
algorithm and an adaptive constraint-handling technique, is presented in this paper. The hybrid evolutionary algorithm simultaneously
uses simplex crossover and two mutation operators to generate the offspring populati...
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... operator for real-code genetic algorithm, which generates offspring based on uniform probability distribution and does not need any fitness informa- tion. In n , n + 1 individuals that are independent of each other form a simplex. For simplicity, in a two- dimensional search space three individuals x 1 , x 2 , and x 3 form a simplex (as shown in Fig. 2). We expand this simplex in each direction ...
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... The ISOA is compared with the algorithms proposed recently, including HWOANM [14], WSOA [24], IDAR-SOA [48], BFOA [54], hHHO-SCA [51], GSA [7], SCA [18], SBO [55], HHO [36], T-cell [56], HEAA [57], Random [58] and Coello [59], and the experimental results are illustrated in Table 8. The optimization result of the ISOA is superior to the others except for HWOANM, with an average improvement of 14.67%. ...
The seagull optimization algorithm (SOA) is a meta-heuristic algorithm proposed in 2019. It has the advantages of structural simplicity, few parameters and easy implementation. However, it also has some defects including the three main drawbacks of slow convergence speed, simple search method and poor ability of balancing global exploration and local exploitation. Besides, most of the improved SOA algorithms in the literature have not considered the drawbacks of the SOA comprehensively enough. This paper proposes a hybrid strategies based algorithm (ISOA) to overcome the three main drawbacks of the SOA. Firstly, a hyperbolic tangent function is used to adjust the spiral radius. The spiral radius can change dynamically with the iteration of the algorithm, so that the algorithm can converge quickly. Secondly, an adaptive weight factor improves the position updating method by adjusting the proportion of the best individual to balance the global and local search abilities. Finally, to overcome the single search mode, an improved chaotic local search strategy is introduced for secondary search. A comprehensive comparison between the ISOA and other related algorithms is presented, considering twelve test functions and four engineering design problems. The comparison results indicate that the ISOA has an outstanding performance and a significant advantage in solving engineering problems, especially with an average improvement of 14.67% in solving welded beam design problem.
... Considering the configuration of the speed reducer, seven decision variables must be defined to meet eleven specified constraints. Table 14 shows the results of WHOFWA and some good algorithms in the literature such as SC [56], PSO-DE [57], DELC [58], DEDS [59], HEAA [60], MDE [61], and ABC [62] on this problem. This table affirms that WHOFWA, in conjunction with DELC and DEDS, achieves the top rank in converging to the optimal solution among the presented approaches. ...
Background and Objectives: This paper explores the realm of optimization by synergistically integrating two unique metaheuristic algorithms: the Wild Horse Optimizer (WHO) and the Fireworks Algorithm (FWA). WHO, inspired by the behaviors of wild horses, demonstrates proficiency in global exploration, while FWA emulates the dynamic behavior of fireworks, thereby enhancing local exploitation. The goal is to harness the complementary strengths of these algorithms, achieving a harmonious balance between exploration and exploitation to enhance overall optimization performance.
Methods: The study introduces a novel hybrid metaheuristic algorithm, WHOFWA, detailing its design and implementation. Emphasis is placed on the algorithm's ability to balance exploration and exploitation. Extensive experiments, featuring a diverse set of benchmark optimization problems, including general test functions and those from CEC 2005, CEC 2019, and 2022, assess WHOFWA's effectiveness. Comparative analyses involve WHO, FWA, and other metaheuristic algorithms such as Reptile Search Algorithm (RSA), Prairie Dog Optimization (PDO), Fick’s Law Optimization (FLA), and Ladybug Beetle Optimization (LBO).
Results: According to the Friedman and Wilcoxon signed-rank tests, for all selected test functions, WHOFWA outperforms WHO, FWA, RSA, PDO, FLA, and LBO by 42%, 55%, 74%, 71%, 48%, and 52%, respectively. Finally, the results derived from addressing real-world constrained optimization problems using the proposed algorithm demonstrate its superior performance when compared to several well-regarded algorithms documented in the literature.
Conclusion: In conclusion, WHOFWA, the hybrid metaheuristic algorithm uniting WHO and FWA, emerges as a powerful optimization tool. Its unique ability to balance exploration and exploitation yields superior performance compared to WHO, FWA, and benchmark algorithms. The study underscores WHOFWA's potential in tackling complex optimization problems, making a valuable contribution to the realm of metaheuristic algorithms.
... Finally, some existing algorithms were selected for comparison with IDPGA. These algorithms performed well in solving all or some of these six problems, including SC (society and civilization) [71], PSO-DE (a novel hybrid algorithm) [72], DEDS (differential evolution with dynamic stochastic selection for constrained optimization) [73], HEAA (constrained optimization based on hybrid evolutionary algorithm and adaptive constrainthandling technique) [74], CS (cuckoo search algorithm) [16], AHA (artificial hummingbird algorithm) [75], GA2 (using co-evolution to adapt the penalty factors of a fitness function incorporated in a genetic algorithm) [76], GA3 (a dominance-based selection scheme to incorporate constraints into the fitness function of a genetic algorithm) [77], CA (a cultural algorithm that uses domain knowledge) [78], CPSO (a co-evolutionary particle swarm optimization approach) [79], ABC (artificial bee colony) [80], GA5 (a new approach to handle constraints using evolutionary algorithms in which the new technique treats constraints as objectives and uses a multiobjective optimization approach to solve the re-stated singleobjective optimization problem) [81], GeneAS I (genetic adaptive search I) [82], GeneAS II (genetic adaptive search II) [76], DMO (dwarf mongoose optimization algorithm) [83], AOA (the arithmetic optimization algorithm) [84], SSA (squirrel search algorithm) [85], SCA (sine cosine algorithm) [86], GWO (grey wolf optimizer) [87], CPSOGSA (hybrid constriction coefficient based PSO with gravitational search algorithm (GSA)) [83], Hsu and Liu's algorithm [88], Rao's algorithm [89], GSA-GA (a new hybrid GSA-GA algorithm) [90], AO (aquila optimizer) [12], GTO (giant trevally optimizer) [13] and TLCO (termite life cycle optimizer) [14]. The best simulation results of IDPGA and other results reported in the current literature are listed in Table 9. ...
Aiming at the current limitations of the dual-population genetic algorithm, an improved dual-population genetic algorithm (IDPGA) for solving multi-constrained optimization problems is proposed by introducing a series of strategies, such as remaining elite individuals, a dynamic immigration operator, separating the objective and constraints, normalized constraints, etc. We selected 14 standard mathematical benchmarks to check the performance of IDPGA, and the results were compared with the theoretical value of CEC 2006. The results show that IDPGA with the current parameters obtains good solutions for most problems. Then 6 well-known engineering optimization problems were solved and compared with other algorithms. The results show that all of the solutions are feasible, the solution precision of IDPGA is better than other algorithms, and IDPGA performs with good efficiency and robustness. Meanwhile, no parameters need to be ignored when IDPGA is applied to solving engineering problems, which is enough to prove that IDPGA is suitable for solving engineering optimization. A Friedman test showed no significant difference between IDPGA and six algorithms, but significant differences between IDPGA and seven other algorithms; thus, a larger number of evaluators will be needed in the future. In addition, further research is still needed about the performance of IDPGA for solving practical large-scale engineering problems.
... In this problem, SSCA has been compared with AVOA (Abdollahzadeh et al. 2021), Belegundu (Belegundu and Arora 1985), GWO (Mirjalili et al. 2014), HEAA (Wang et al. 2009), CPSO (He and Wang 2007a), SFS (Salimi 2015), Arora (Arora 2004), MFO (Mirjalili 2015a), WOA (Mirjalili and Lewis 2016), BA (Gandomi et al. 2013a), GA2 (Deb 1990), GSA (Rashedi et al. 2009), ESs (Mezura-Montes andCoello 2005), Rank-iMMDE (Gong et al. 2014), WCA (Eskandar et al. 2012), WEO (Kaveh and Bakhshpoori 2016), GA3 (Coello Coello and Montes 2002), TEO (Kaveh and Dadras 2017), DELC (Wang and Li 2010), DEDS (Zhang et al. 2008) and SSA . Table 11 illustrates that SSCA can obtain the optimal value. ...
... The optimal solution obtained by proposed SSCA algorithm is compared with six other optimization algorithms including MBFPA , WCA (Eskandar et al. 2012), PSODE (Liu et al. 2010), MDE (Mezura-Montes et al. 2007, HEAA (Wang et al. 2009), and PVS (Savsani and Savsani 2016). A detailed comparison is given in Table.14. ...
A unique hybrid meta-heuristic combining the salp swarm algorithm and the sine cosine algorithm (SSCA) is established in this study to improve convergence speed while outperforming existing conventional algorithms. The sine cosine position equations are utilized to update the position of the salp leader in search space while a weighting factor updates the position of the salp follower so that the best and possible optimal solutions are obtained using the sine or cosine and weighting function. Particle swarm optimization PSO inspires this weighting factor. Each salp uses the information-sharing approach of sine and cosine functions during this process to strengthen their exploration and exploitation abilities. The goal of incorporating modifications to the salp swarm optimizer algorithm is to help the standard approach avoid premature convergence that leads the search to the most likely search space. The proposed algorithm is tested on classical optimization benchmark functions and eight real engineering applications. The goal is to investigate and validate the SSCA's proper behaviour while finding the optimum solutions. The results of the comparison demonstrated that the SSCA method achieves the best accuracies.
... The structure of this design is shown in Fig. 19 and two parameters should be found to adjust the sectional areas. This case was previously implemented by many algorithms, including MBA [47], RL-BA [84], HEAA [85], CS [86] and SBO [82]. The CVSO is used with 30,000 evaluations number. ...
... In Table 19, the statistical findings are displayed using various techniques. The CVSO may determine the ideal value of the optimization variables while satisfying the limits that are explicitly stated in the references [47,82,[84][85][86] and the minimum objective function value of the pressure vessel design problem. In other words, the variables that have the greatest impact on reducing the problem's objective function constitute the best set of solutions. ...
In this paper, a new and effective meta-heuristic method named corona-virus search optimizer (CVSO) is proposed inspired based on the movement and search of the corona-virus among different societies, prevalence, and death of individuals. The CVSO has local and global search suitable balance due to the use of evolutionary strategies as well as appropriate social learning. This algorithm has desirable optimization power, easy implementation and requires only a control parameter. The CVSO algorithm is implemented on 30 modern and standard test functions of CEC2014 and also 10 test functions of CEC2019. The performance and capability of CVSO is compared with new and well-known meta-heuristics including particle swarm optimization (PSO), artificial bee colony (ABC) tree growth algorithm (TGA), and Lion optimization algorithm (LOA), bat algorithm (BA) and harris hawks optimization (HHO). The results showed that the CVSO can be more effective than other algorithms to solve the test functions and also various complex real-world engineering optimization problems in terms of optimization accuracy and convergence rate. Also, the superiority of CVSO is demonstrated in the designing of a hybrid energy system by achieving a lower cost of M$ 2.7492 compared to TGA, LOA, ABC, PSO, BA, and HHO algorithms, which achieve costs of M$ 2.7878, M$ 2.7556, M$ 2.8521, M$ 2.9503, M$ 3.0942, and M$ 2.9614, respectively. In addition, due to the optimal balance between local and global search and strength, it is able to avoid getting stuck in locally optimal solutions while obtaining global optimal solutions with a higher convergence rate than other algorithms. The source code of CVSO is publicly available at https://github.com/Irajfaraji/CVSO.
... The objective of this problem is to minimize the weight of the truss using the three design variables of the length of the three bars subject to the three constraints of deflection, stress, and buckling (Fig. 6). So far, this challenge has evaluated some algorithms, such as DEDS (Abualigah et al., 2021b), SC (Ray and Liew, 2003), PSO-DE (Liu et al., 2010), HEAA (Wang et al., 2009), CS (Gandomi et al., 2013), FATLBO (Cheng and Prayogo, 2017), ICHIMP-SHO (Kumari et al., 2022), and TLNNABC (Kundu and Garg, 2022). In addition to the mentioned algorithms, to better evaluate the performance of the proposed method, some other recently published algorithms, including RUN (Ahmadianfar et al., 2021), AO (Abualigah et al., 2021a), AHA (Zhao et al., 2022a), ATLBO-DA (Bureerat and Sleesongsom, 2021), SMA (Li et al., 2020), FDB-TLABC (Duman et al., 2022), SPMGTLO (Kommadath et al., 2016), TLSBO (Akbari et al., 2022), TLABC (Chen et al., 2018), MPA (Faramarzi et al., 2020b), QANA (Zamani et al., 2021), and EO (Faramarzi et al., 2020a), are investigated. ...
This research proposes a novel approach for the robust optimization of the design of hydrogen peroxide propulsion control systems using the efficient and advanced Teaching-Learning-Based Optimization (TLBO) method. This study adopts a robust design optimization (RDO) formulation that considers both epistemic and aleatory uncertainties, including sparse points and interval data, and uses the Johnson distribution family for uncertainty representation. The maximum likelihood estimation method is applied to determine the distribution parameters, also considering interval data with a nested optimization technique. A novel advanced TLBO method with high accuracy and convergence rate is employed to optimization of this robust design approach. The method's originality and advancement come from two categories of modifications to the original framework: the structure of the teaching and learning phases and the initialization and search approach. The efficacy and applicability of the proposed Ad-TLBO, respectively, were evaluated using benchmark problems from the CEC2020 competition and three real-world engineering problems, with a comparison to some recently published and the CEC competition's top-ranked algorithms. The results and statistical analyses of the Quade test, Wilcoxon signed-rank test, and Friedman test show that the proposed Ad-TLBO method outperforms the other algorithms. The proposed optimization method is eventually applied to design a monopropellant propulsion system as the control actuator of a satellite orbital transfer system. It is found that the proposed advanced TLBO is effective in handling uncertainty in real design problems and improves both the convergence rate and accuracy of the optimization process.
... In this paper, all the algorithm parameters were selected based on the basic FDA literature. The LSFDA search results were compared with different algorithms by considering 10 random runs [28][29][30][31][32][33]. The results of the highest and lowest values, the means, and the standard deviation are given in Table 6. ...
... To solve the tensile/compression spring problem, the population size, number of neighbors, and number of iterations determined via sensitivity analysis are equal to 50, 1, and 200 in the basic FDA literature. In this paper, all the algorithm parameters were selected based on the basic FDA literature [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The LSRFDA search results were compared with different algorithms by considering 10 random runs. ...
... In this paper, all the algorithm parameters were selected based on the basic FDA literature, and the different results are shown in Table 8. In Table 8, NO means that the literature does give the value of the algorithm [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. The LSRFDA search's highest value, lowest value, mean value, and standard deviation are higher than those of the FDA search result. ...
Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm’s diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm.
... The optimization problem described in Appendix A.2 has been previously tackled by various optimization algorithms, such as SR (Runarsson & Yao, 2000), CULDE (Landa Becerra & Coello, 2006), ASCHEA (Hamida & Schoenauer, 2002), SAPF (Tessema & Yen, 2006), HS (Lee & Geem, 2005a), HM (Koziel & Michalewicz, 1999), DE (Lampinen, 2002), DEDS (Zhang et al., 2008), ISR (Runarsson & Yao, 2005), SMES (Mezura-Montes & Coello, 2005), HEAA (Y. Wang et al., 2009), PSO (Liu et al., 2010a), a Simplex method (Takahama & Sakai, 2005), cultural algorithms with evolutionary programming (CAEP) (Coello Coello & Becerra, 2004), hybrid particle swarm optimization (HPSO) , changing range genetic algorithm (CRGA) (Amirjanov, 2006), particle swarm optimization with differential evolution (PSO-DE) (Liu, Cai, & Wang, 2010b), and differential evolution with level comparison (DELC) (L. Wang & Li, 2010). ...
The utilization of meta-heuristics has been widespread in resolving optimization problems, with constant development of new and effective algorithms. Thisresearch presents the Garter Snake Optimization Algorithm (GSO), which ismotivated by the mating behavior of garter snakes and leverages various techniques such as screening, grafting, and annual growth to conduct a productive andthorough search of the exploration space. The algorithm incorporates both socialand personal behaviors to accomplish a balance between exploration and exploitation of the best solutions. To assess the performance of the proposed algorithm,it is tested on four restricted benchmark problems and a frequently utilized realengineering problem, and the optimization results are compared with other algorithms. In many respects, the GSO outperforms other algorithms, demonstratingits superiority and potential in addressing constrained optimization problems.
... Table 7 illustrates the proposed GQPSO-OPS algorithm performed better than other algorithms used by various researchers for designing pressure vessel problems. However, the proposed algorithm showed similar results for the tension/compression spring problem (refer to Table 8) when it was compared with other algorithms (Zhang et al. (2008); Wang et al. (2009);Zahara and Kao (2009);Li (2010);Eskandar et al. (2012); Kashan (2011);Sadollah et al. (2012); Yang (2014); Ben (2016)). ...
Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm that falls under the category of nature-inspired algorithms and is similar to evolutionary computing in various ways. Rather than the survival of the fittest, the PSO is driven by a representation of a social psychological model inspired by the group behaviors of birds and other social species. The particle's position is modified in PSO based on its position as well as velocity, while in quantum mechanics, the trajectory idea is absurd; however, the uncertainty principle suggests that a particle's position, as well as velocity, cannot be determined simultaneously. As a result, an advanced version of the quantum mechanics-based PSO method is proposed. The study in this paper is focused on an investigation of a new quantum-behaved PSO (QPSO) method called Gaussian quantum-behaved particle swarm optimization (GQPSO), which uses a mutation operator with a Gaussian distribution and is inspired by classical PSO methods and quantum mechanics concepts. In GQPSO, inadequate control parameter tuning results in poor solutions. To better understand the effect of different control parameters and their implications on GQPSO results, this paper used a full parametric sensitivity analysis on five different problems (the Design of a pressure vessel, Tension/Spring Compression, Rastrigin function, Ackley function, and Constrained Box Volume Problem). By adjusting each parameter one at a time, different optimization problems were used to investigate GQPSO. As a result, to allow particles to change their earliest best solution based on viability, a constraint-handling mechanism was developed. The optimal parameter set for GQPSO is provided based on the analysis of the results. With the help of the proposed optimal parameter set (contraction–expansion coefficient values as (1 = 1.6,2 = 1.3), swarm size as ‘350’, and number of Iterations as ‘500’), GQPSO returned an optimized solution for Rastrigin and Ackley functions. It also performed better in the case of the design of a pressure vessel and tension/spring compression problems in comparison to the existing solution available in related literature. As per the findings of the sensitivity analysis, GQPSO is the most sensitive to the contraction-expansion coefficient in comparison to the maximum number of iterations (itermax) and swarm size (‘n’).
... In this problem, ODMPA is compared with other algorithms, including WCA [65], HEAA [66], MDE [67], m--HHO [68], EHHO, GLF-GWO [69], and m-SSA [70]. The results displayed in Table 7 demonstrate that ODMPA per-forms more excellent than other algorithms, and the optimal cost is 2753.9866. ...
Marine Predators Algorithm (MPA) is a recent efficient metaheuristic algorithm that is enlightened by the biological behavior of ocean predators and prey. This algorithm simulates the Levy and Brownian movements of prevalent foraging strategy and has been applied to many complex optimization problems. However, the algorithm has defects such as a low diversity of the solutions, ease into the local optimal solutions, and decreasing convergence speed in dealing with complex problems. A modified version of this algorithm called ODMPA is proposed based on the tent map, the outpost mechanism, and the differential evolution mutation with simulated annealing (DE-SA) mechanism. The tent map and DE-SA mechanism are added to enhance the exploration capability of MPA by increasing the diversity of the search agents, and the outpost mechanism is mainly used to improve the convergence speed of MPA. To validate the outstanding performance of the ODMPA, a series of global optimization problems are selected as the test sets, including the standard IEEE CEC2014 benchmark functions, which are the authoritative test set, three well-known engineering problems, and photovoltaic model parameters tasks. Compared with some famous algorithms, the results reveal that ODMPA has achieved better performance than its counterparts in CEC2014 benchmark functions. And in solving real-world optimization problems, ODMPA could get higher accuracy than other metaheuristic algorithms. These practical results demonstrate that the mechanisms introduced positively affect the original MPA, and the proposed ODMPA can be a widely effective tool in tackling many optimization problems.
