Constrained Engineering Problems Research Articles

A multi-strategy boosted bald eagle search algorithm for global optimization and constrained engineering problems: case study on MLP classification problems

The Bald Eagle Search (BES) algorithm is an innovative population-based method inspired by the intelligent hunting behavior of bald eagles. While BES shows promise, it faces challenges such as susceptibility to local optima and imbalances between exploration and exploitation phases. To address these limitations, this paper introduces the Multi-Strategy Boosted Bald Eagle Search (MBBES) algorithm. MBBES enhances the original BES by incorporating an adaptive parameter, two distinct mutation strategies, and replacing the swoop stage with a fall stage. We rigorously evaluate MBBES against classic and improved algorithms using the CEC2014 and CEC2017 test sets. The experimental results demonstrate that MBBES significantly improves the ability to escape local optima and achieves superior convergence accuracy. Moreover, MBBES ranks first according to the Friedman test, outperforming its counterparts in solving five practical engineering problems and three MLP classification problems, underscoring its effectiveness in real-world optimization scenarios. These findings indicate that MBBES not only surpasses BES but also sets a new benchmark in optimization performance.

A multi-strategy improved beluga whale optimization algorithm for constrained engineering problems

A multi-strategy improved beluga whale optimization algorithm for constrained engineering problems

A rhinopithecus swarm optimization algorithm for complex optimization problem

This paper introduces a novel meta-heuristic algorithm named Rhinopithecus Swarm Optimization (RSO) to address optimization problems, particularly those involving high dimensions. The proposed algorithm is inspired by the social behaviors of different groups within the rhinopithecus swarm. RSO categorizes the swarm into mature, adolescent, and infancy individuals. Due to this division of labor, each category of individuals employs unique search methods, including vertical migration, concerted search, and mimicry. To evaluate the effectiveness of RSO, we conducted experiments using the CEC2017 test set and three constrained engineering problems. Each function in the test set was independently executed 36 times. Additionally, we used the Wilcoxon signed-rank test and the Friedman test to analyze the performance of RSO compared to eight well-known optimization algorithms: Dung Beetle Optimizer (DBO), Beluga Whale Optimization (BWO), Salp Swarm Algorithm (SSA), African Vultures Optimization Algorithm (AVOA), Whale Optimization Algorithm (WOA), Atomic Retrospective Learning Bare Bone Particle Swarm Optimization (ARBBPSO), Artificial Gorilla Troops Optimizer (GTO), and Harris Hawks Optimization (HHO). The results indicate that RSO exhibited outstanding performance on the CEC2017 test set for both 30 and 100 dimension. Moreover, RSO ranked first in both dimensions, surpassing the mean rank of the second-ranked algorithms by 7.69% and 42.85%, respectively. Across the three classical engineering design problems, RSO consistently achieves the best results. Overall, it can be concluded that RSO is particularly effective for solving high-dimensional optimization problems.

A novel artificial hummingbird algorithm improved by natural survivor method

The artificial hummingbird algorithm (AHA) has been applied in various fields of science and provided promising solutions. Although the algorithm has demonstrated merits in the optimization area, it suffers from local optimum stagnation and poor exploration of the search space. To overcome these drawbacks, this study redesigns the update mechanism of the original AHA algorithm with the natural survivor method (NSM) and proposes a novel metaheuristic called NSM-AHA. The strength of the developed algorithm is that it performs population management not only according to the fitness function value but also according to the NSM score value. The adopted strategy contributes to NSM-AHA exhibiting powerful local optimum avoidance and unique exploration ability. The optimization ability of the proposed NSM-AHA algorithm was compared with 21 state-of-the-art algorithms over CEC 2017 and CEC 2020 benchmark functions with dimensions of 30, 50, and 100, respectively. Based on the Friedman test results, it was observed that NSM-AHA ranked 1st out of 22 competitive algorithms, while the original AHA ranked 8th. This result highlights that the NSM update mechanism provides a remarkable evolution in the convergence performance of the original AHA algorithm. Furthermore, two constrained engineering problems including the optimization of single-diode solar cell model (SDSCM) parameters and the design of a power system stabilizer (PSS) are solved with the proposed algorithm. The NSM-AHA algorithm provided better results compared to other algorithms with a value of 9.86E − 04 root mean square error for SDSCM and 1.43E − 03 integral time square error for PSS. The experimental results showed that the proposed NSM-AHA is a competitive optimizer for solving global and engineering problems.

A novel chaotic artificial rabbits algorithm for optimization of constrained engineering problems

Abstract This study introduces a novel metaheuristic algorithm of optimization named Chaotic Artificial Rabbits Optimization (CARO) algorithm for resolving engineering design problems. In the newly introduced CARO algorithm, ten different chaotic maps are used with the recently presented Artificial Rabbits Optimization (ARO) algorithm to manage its parameters, eventually leading to an improved exploration and exploitation of the search. The CARO algorithm and familiar metaheuristic competitor algorithms were experimented on renowned five mechanical engineering problems of design, in brief; pressure vessel design, rolling element bearing design, tension/compression spring design, cantilever beam design and gear train design. The results indicate that the CARO is an outstanding algorithm compared with the familiar metaheuristic algorithms, and equipped with the best-optimized parameters with the minimal deviation in each case study. Metaheuristic algorithms are utilized to succeed in an optimal design in engineering problems targeting to achieve lightweight designs. In this present study, the optimum design of a vehicle brake pedal piece was achieved through topology and shape optimization methods. The brake pedal optimization problem in terms of the mass minimization is solved properly by using the CARO algorithm in comparison to familiar metaheuristic algorithms in the literature. Consequently, results indicate that the CARO algorithm can be effectively utilized in the optimal design of engineering problems.

Enhanced artificial ecosystem-based optimization for global optimization and constrained engineering problems

Enhanced artificial ecosystem-based optimization for global optimization and constrained engineering problems

Modified crayfish optimization algorithm for solving multiple engineering application problems

Crayfish Optimization Algorithm (COA) is innovative and easy to implement, but the crayfish search efficiency decreases in the later stage of the algorithm, and the algorithm is easy to fall into local optimum. To solve these problems, this paper proposes an modified crayfish optimization algorithm (MCOA). Based on the survival habits of crayfish, MCOA proposes an environmental renewal mechanism that uses water quality factors to guide crayfish to seek a better environment. In addition, integrating a learning strategy based on ghost antagonism into MCOA enhances its ability to evade local optimality. To evaluate the performance of MCOA, tests were performed using the IEEE CEC2020 benchmark function and experiments were conducted using four constraint engineering problems and feature selection problems. For constrained engineering problems, MCOA is improved by 11.16%, 1.46%, 0.08% and 0.24%, respectively, compared with COA. For feature selection problems, the average fitness value and accuracy are improved by 55.23% and 10.85%, respectively. MCOA shows better optimization performance in solving complex spatial and practical application problems. The combination of the environment updating mechanism and the learning strategy based on ghost antagonism significantly improves the performance of MCOA. This discovery has important implications for the development of the field of optimization.Graphical

A novel hippo swarm optimization: for solving high-dimensional problems and engineering design problems

Abstract In recent years, scholars have developed and enhanced optimization algorithms to tackle high-dimensional optimization and engineering challenges. The primary challenge of high-dimensional optimization lies in striking a balance between exploring a wide search space and focusing on specific regions. Meanwhile, engineering design problems are intricate and come with various constraints. This research introduces a novel approach called Hippo Swarm Optimization (HSO), inspired by the behavior of hippos, designed to address high-dimensional optimization problems and real-world engineering challenges. HSO encompasses four distinct search strategies based on the behavior of hippos in different scenarios: starvation search, alpha search, margination, and competition. To assess the effectiveness of HSO, we conducted experiments using the CEC2017 test set, featuring the highest dimensional problems, CEC2022 and four constrained engineering problems. In parallel, we employed 14 established optimization algorithms as a control group. The experimental outcomes reveal that HSO outperforms the 14 well-known optimization algorithms, achieving first average ranking out of them in CEC2017 and CEC2022. Across the four classical engineering design problems, HSO consistently delivers the best results. These results substantiate HSO as a highly effective optimization algorithm for both high-dimensional optimization and engineering challenges.

Multi-strategy improved artificial rabbit optimization algorithm based on fusion centroid and elite guidance mechanisms

The Artificial Rabbit Optimization (ARO) algorithm has been proposed as an effective metaheuristic optimization approach in recent years. However, the ARO algorithm exhibits shortcomings in certain cases, including inefficient search, slow convergence, and vulnerability to local optima. To address these issues, this paper introduces a multi-strategy improved Artificial Rabbit Optimization (IARO) algorithm. Firstly, in the enhanced search strategy, we propose integrating the centroid guidance mechanism and elite guidance mechanism with the greedy strategy to update the position during the exploration phase. Additionally, the Levy flight strategy integrated with self-learning, is employed to update the position during the development phase to improve convergence speed and prevent falling into local optima. Secondly, the algorithm incorporates a per-dimension mirror boundary control strategy to map individuals exceeding the boundary back within the boundary back inside the boundary. This boundary control strategy ensures the algorithm operates within bounds and enhances convergence speed. Finally, within the survival of the fittest strategy, an adaptive factor is introduced to gradually enhance the population's overall adaptability. This factor regulates the balance between exploration and exploitation, allowing the algorithm to fully explore the search space and improve its robustness. To substantiate the effectiveness of the proposed IARO algorithm, a rigorous and systematic verification analysis was undertaken. Comparative experiments for qualitative and quantitative analysis were conducted on three benchmark test sets, namely CEC2017, CEC2020, and CEC2022. The analysis results, including the Wilcoxon rank-sum test, consistently demonstrates that this improved algorithm outperforms ARO and other state-of-the-art optimization algorithms comprehensively. Finally, the feasibility of the IARO algorithm has been verified in seven classical constrained engineering problems.

Hybrid evolutionary grey wolf optimizer for constrained engineering problems and multi-unit production planning

Hybrid evolutionary grey wolf optimizer for constrained engineering problems and multi-unit production planning

Enhanced Aquila optimizer based on tent chaotic mapping and new rules

Metaheuristic algorithms, widely applied across various domains due to their simplicity and strong optimization capabilities, play a crucial role in problem-solving. While the Aquila Optimizer is recognized for its effectiveness, it often exhibits slow convergence rates and susceptibility to local optima in certain scenarios. To address these concerns, this paper introduces an enhanced version, termed Tent-enhanced Aquila Optimizer (TEAO). TEAO incorporates the Tent chaotic map to initialize the Aquila population, promoting a more uniform distribution within the solution space. To balance exploration and exploitation, novel formulas are proposed, accelerating convergence while ensuring precision. The effectiveness of the TEAO algorithm is validated through a comprehensive comparison with 14 state-of-the-art algorithms using 23 classical benchmark test functions. Additionally, to assess the practical feasibility of the approach, TEAO is applied to six constrained engineering problems and benchmarked against the performance of the same 14 algorithms. All experimental results consistently demonstrate that TEAO outperforms other advanced algorithms in terms of solution quality and stability, establishing it as a more competitive choice for optimization tasks.

Optimizing constrained engineering problem nH-WDEOA: using hybrid nature-inspired algorithm

Optimizing constrained engineering problem nH-WDEOA: using hybrid nature-inspired algorithm

Guided learning strategy: A novel update mechanism for metaheuristic algorithms design and improvement

Meta-heuristic algorithms (MH) are naturally inspired global optimization algorithms. They are often relatively simple and can solve problems in a short period of time, with certain benefits. However, as the problem becomes more complex, the solution that the algorithm can obtain is often not the optimal solution to the problem, which limits its application scenarios. Therefore, improving the performance and solving accuracy of existing algorithms is crucial for expanding their application ability. In traditional optimization algorithms, there are often two concepts, namely exploration and exploitation. Exploration refers to a wide range of discrete search, used to avoid falling into local optima, and exploitation refers to a small range of focused exploration, used to improve algorithm accuracy. How to balance exploration and exploitation is the key to enhancing algorithm performance and problem adaptability. This paper proposes a brand new strategy named Guided Learning Strategy (GLS) to solve above problem. GLS obtains the dispersion degree of the population by calculating the standard deviation of the historical locations of individuals in recent generations, and infers what guidance the algorithm currently needs. When the algorithm is biased towards exploration, it will guide the algorithm to exploit. Otherwise, it will guide the algorithm to explore. It is precisely because this strategy can identify the current needs of the algorithm and provide assistance that it can improve the performance of most algorithms. This article improves three types of algorithms based on evolution (LSHADE_SPACMA), Stochastic Fractal Search (SFS), and Marine Predators Algorithm (MPA) with better performance, and tests their performance on 57 constrained engineering problems and CEC2020. The effectiveness of this strategy has been confirmed and proved for optimization problem. The source codes of the proposed GLS (GLS_MPA) can be accessed by https://github.com/luchenghao2022/Guided-Learning-Strategy

Slime Mould Reproduction: A New Optimization Algorithm for Constrained Engineering Problems

Slime Mould Reproduction: A New Optimization Algorithm for Constrained Engineering Problems

An Improved Heterogeneous Comprehensive Learning Symbiotic Organism Search for Optimization Problems

The Symbiotic Organism Search (SOS) algorithm, and most of its variants, exhibit the same search behaviour. That is, each organism or individual in the ecosystem applies the same update rules according to 3 phases: mutualism, commensalism, and parasitism. By applying this strategy, an organism is capable of crippling the search effort of another organism. To overcome this problem, this paper proposes a Heterogeneous Comprehensive Learning SOS (HCLSOS) which divides the population into two distinct subpopulations namely: the exploration and exploitation subpopulations. HCLSOS allows each organism to follow one of two search behaviour according to into its subpopulation: whether to explore or exploit. This addresses the problem of balancing exploration and exploitation in SOS. The proposed algorithm employs a comprehensive learning strategy for the exploration group to generate a new type of mutual vector called the multispecies mutual vector capable of preserving organisms' diversity and discouraging premature convergence. Information exchange between the two groups is unidirectional and managed through a random elite learning strategy. Through this collaboration, HCLSOS can effectively evolve organisms to explore the search space and properly exploit the discovered optimal regions. The study tested HCLSOS on 23 benchmark functions, CEC2014, CEC2017, and the recent CEC 2022 test suites. The outcome of HCLSOS is compared with 15 state-of-the-art algorithms, and the results obtained showed that HCLSOS can attain competitive or even better results. Furthermore, we applied HCLSOS to solve 3 constrained engineering problems and to design an efficient frequency control of a two-area islanded microgrid system.

A multi-objective cooperation search algorithm for cascade reservoirs operation optimization considering power generation and ecological flows

With growing attention focused on energy generation and environmental conservation, the operation of cascade reservoirs that considers power generation benefits and ecological flow requirements plays an increasingly important role in water resource and power systems. However, the traditional optimization methods may fail to solve complex cascade reservoirs operation models with strong spatial-temporal coupling physical constraints. To effectively address this problem, this study proposes an efficient multi-objective cooperation search algorithm (MOCSA) that utilizes the modified team communication, reflective learning operator and internal competition operators to enhance global exploration and local exploitation. MOCSA is tested on a group of multi-objective benchmark functions and real-world constrained engineering problems. The results demonstrate that MOCSA can provide better results for most benchmark test functions in comparison with the competitive algorithms. Besides, MOCSA exhibits excellent search ability to find feasible solutions of constrained engineering problems. The proposed method is then applied to resolve a real-world reservoir system under different operation scenarios. Simulations indicate that MOCSA provides diversified decision options for the operation of cascade reservoir system and find a more diverse set of non-dominated solutions within the feasible solution space. Overall, this research presents MOCSA as an effective multi-objective optimization tool for complex cascade reservoir operation problems.

Meerkat optimization algorithm: A new meta-heuristic optimization algorithm for solving constrained engineering problems

In this paper, we proposed a meerkat optimization algorithm(MOA) by simulating the behavior pattern of meerkats in nature. MOA is mainly inspired by the survival strategies of meerkat populations, whose sentinel mechanism controls meerkats to switch between different behavior patterns. Some mathematical properties of meerkat optimization algorithm are proved, and the advantages of MOA are verified with classical optimization test functions. MOA is applied to solve real-world engineering problems with constraints, which proves the effectiveness and superiority of MOA in solving such problems.

A Modified Quantum-Inspired Genetic Algorithm Using Lengthening Chromosome Size and an Adaptive Look-Up Table to Avoid Local Optima

The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems.

Modified prairie dog optimization algorithm for global optimization and constrained engineering problems.

The prairie dog optimization (PDO) algorithm is a metaheuristic optimization algorithm that simulates the daily behavior of prairie dogs. The prairie dog groups have a unique mode of information exchange. They divide into several small groups to search for food based on special signals and build caves around the food sources. When encountering natural enemies, they emit different sound signals to remind their companions of the dangers. According to this unique information exchange mode, we propose a randomized audio signal factor to simulate the specific sounds of prairie dogs when encountering different foods or natural enemies. This strategy restores the prairie dog habitat and improves the algorithm's merit-seeking ability. In the initial stage of the algorithm, chaotic tent mapping is also added to initialize the population of prairie dogs and increase population diversity, even use lens opposition-based learning strategy to enhance the algorithm's global exploration ability. To verify the optimization performance of the modified prairie dog optimization algorithm, we applied it to 23 benchmark test functions, IEEE CEC2014 test functions, and six engineering design problems for testing. The experimental results illustrated that the modified prairie dog optimization algorithm has good optimization performance.

A multi-strategy enhanced northern goshawk optimization algorithm for global optimization and engineering design problems

Metaheuristic algorithms are widely utilized in various fields owing to their ability to produce a variety of solutions. The Northern Goshawk Optimization (NGO) is an effective optimization algorithm, however, its convergence rate is slow and it tends to fall into local optima in some cases. Therefore, this paper proposes a Multi-strategy Enhanced Northern Goshawk Optimization (MENGO) algorithm, which introduces a novel exploration strategy based on Levy flights to mitigate the risk of getting trapped in local optima. To balance exploration and exploitation, a new nonlinear reduction strategy based on the sine function is proposed. Additionally, a novel exploitation strategy is employed to accelerate the convergence speed while ensuring accuracy. The effectiveness of MENGO is demonstrated by comparing it with 13 advanced algorithms using 23 classical benchmark and 12 CEC2022 test functions in different dimensions. To evaluate the feasibility of the proposed approach in real-world applications, it is studied for nine constrained engineering problems, and the performance is compared with other contender algorithms extracted from the literature. The all experimental results show that MENGO outperforms other state-of-the-art algorithms in terms of solution quality and stability, making it a more competitive option.