Real-world Engineering Problems Research Articles

Newton-Raphson-based optimizer: A new population-based metaheuristic algorithm for continuous optimization problems

The Newton-Raphson-Based Optimizer (NRBO), a new metaheuristic algorithm, is suggested and developed in this paper. The NRBO is inspired by Newton-Raphson's approach, and it explores the entire search process using two rules: the Newton-Raphson Search Rule (NRSR) and the Trap Avoidance Operator (TAO) and a few groups of matrices to explore the best results further. The NRSR uses a Newton-Raphson method to improve the exploration ability of NRBO and increase the convergence rate to reach improved search space positions. The TAO helps the NRBO to avoid the local optima trap. The performance of NRBO was assessed using 64 benchmark numerical functions, including 23 standard benchmarks, 29 CEC2017 constrained benchmarks, and 12 CEC2022 benchmarks. In addition, the NRBO was employed to optimize 12 CEC2020 real-world constrained engineering optimization problems. The proposed NRBO was compared to seven state-of-the-art optimization algorithms, and the findings showed that the NRBO produced promising results due to its features, such as high exploration and exploitation balance, high convergence rate, and effective avoidance of local optima capabilities. In addition, the NRBO also validated on challenging wireless communication problem called the internet of vehicle problem, and the NRBO was able to find the optimal path for data transmission. Also, the performance of NRBO in training the deep reinforcement learning agents is also studied by considering the mountain car problem. The obtained results also proved the NRBO's excellent performance in handling challenging real-world engineering problems.

A Modified Water Cycle Algorithm: An Opposition Based Meta-Heuristic Optimization to Solve Real World Engineering Problems

This paper proposes the Opposition based learning on a latest recent population based Water Cycle Algorithm on different benchmark constraint optimization techniques. Water cycle is a Hydrological based technique which works on better search location of the stream and river that flows to the sea which works on certain control parameters that will be defined initially and obtain the population matrix. With the help of the application of the opposition learning opposite search will be made to receive the better search location to find the better fitness value and avoid the premature convergence and get best convergence rate. This Proposed Opposition based Water Cycle Algorithm is implemented and tested on fifteen benchmark problems mentioning the fitness value as well as the constraints value. The convergence plot using a comparative study between Water Cycle Algorithm and Opposition based Water Cycle Algorithm, the proposed method had proved to obtain the best result and superior for the problems on to which it had implemented. The ANOVA test result is shown for the statistical analysis of the data obtained.

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.

Application of Diversity-Maintaining Adaptive Rafflesia Optimization Algorithm to Engineering Optimisation Problems

The Diversity-Maintained Adaptive Rafflesia Optimization Algorithm represents an enhanced version of the original Rafflesia Optimization Algorithm. The latter draws inspiration from the unique characteristics displayed by the Rafflesia during its growth, simulating the entire lifecycle from blooming to seed dispersion. The incorporation of the Adaptive Weight Adjustment Strategy and the Diversity Maintenance Strategy assists the algorithm in averting premature convergence to local optima, subsequently bolstering its global search capabilities. When tested on the CEC2013 benchmark functions under a dimension of 30, the new algorithm was compared with ten optimization algorithms, including commonly used classical algorithms, such as PSO, DE, CSO, SCA, and the newly introduced ROA. Evaluation metrics included mean and variance, and the new algorithm outperformed on a majority of the test functions. Concurrently, the new algorithm was applied to six real-world engineering problems: tensile/compressive spring design, pressure vessel design, three-bar truss design, welded beam design, reducer design, and gear system design. In these comparative optimizations against other mainstream algorithms, the objective function’s mean value optimized by the new algorithm consistently surpassed that of other algorithms across all six engineering challenges. Such experimental outcomes validate the efficiency and reliability of the Diversity-Maintained Adaptive Rafflesia Optimization Algorithm in tackling optimization challenges. The Diversity- Maintained Adaptive Rafflesia Optimization Algorithm is capable of tuning the parameter values for the optimization of symmetry and asymmetry functions. As part of our future research endeavors, we aim to deploy this algorithm on an even broader array of diverse and distinct optimization problems, such as the arrangement of wireless sensor nodes, further solidifying its widespread applicability and efficacy.

An effective and robust genetic algorithm with hybrid multi-strategy and mechanism for airport gate allocation

Gate allocation is a combinatorial scheduling problem with multi-constraint and multi-objective. It is challenging to solve this problem when the size of flights increases continuously. As an adaptive technology with a random search ability, the genetic algorithm (GA) has been widely used for resource scheduling and combinatorial optimization. However, it is prone to slow convergence and falling into local optimal solutions. Therefore, an effective and robust GA based on hybrid multi-strategy of reverse learning, interval probability mutation, and phagocytosis mechanism, called RPIP-GA, is proposed to implement a new airport gate-allocation method. In the RPIP-GA, the population is divided into several subpopulations based on the fitness values of all individuals to prevent population degradation and improve population quality. The reverse learning strategy with elite retention is designed to initialize the population, expand the global search space, improve the quality of the original solution, and increase the population diversity. The phagocytosis mechanism is employed to implement a crossover operation to enhance the convergence rate and local search ability. An interval probability mutation technique is designed to improve the local search ability in the early stage and prevent falling into the local optimum in the later stage. The effectiveness of the RPIP-GA is validated using 45 complex functions selected from the benchmark functions and CEC 2017, 22 real-world engineering problems selected from CEC 2011, and an actual gate allocation problem via comparisons with the GA, PSO, GSA, DNLGSA, WMSDE, PADE, HIRCGA, and other algorithms. The experimental results show that the RPIP-GA can obtain optimal results with improved stability in most cases. The maximum allocation rate of actual airport gates reaches 98%, and the average convergence accuracy increases by 19% compared with that of the GA. The data used in the study is publicly available from the GitHub repository (https://github.com/xiaocangjiu).

Snow Geese Algorithm: A novel migration-inspired meta-heuristic algorithm for constrained engineering optimization problems

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive “Herringbone” and “Straight Line” shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project.

Pattern Matching in Python: Expanding the Horizons of Engineering Applications

Pattern matching is a powerful programming construct that simplifies code, enhances readability, and enables efficient handling of complex data structures. This paper introduces the pattern matching feature newly introduced in Python 3.10 and explores its applications in various engineering domains. The aim of this research is to showcase how Python's pattern matching capability can be leveraged for parsing and analyzing data, structural matching in data analysis, model and system validation, and signal processing. Through illustrative examples and case studies, we demonstrate the versatility and effectiveness of Python pattern matching in solving real-world engineering problems. By introducing pattern matching in Python, this research opens new avenues for engineers and scientists to tackle complex data processing tasks, enhance system validation techniques, and streamline algorithmic implementations. With the integration of pattern matching into Python's ecosystem, the language becomes even more powerful and expressive, empowering practitioners to write cleaner, more concise, and efficient code. This research lays the foundation for the adoption and exploration of pattern matching techniques in Python, highlighting its potential impact on engineering applications and providing a roadmap for future research and development in this field.

Lévy Arithmetic Algorithm: An enhanced metaheuristic algorithm and its application to engineering optimization

Lévy Arithmetic Algorithm is an upgraded metaheuristic optimization approach proposed to enhance the Arithmetic Optimization Algorithm using the Lévy random step. Arithmetic Optimization Algorithm addresses diverse optimization problems by employing arithmetic operators. However, its linear search capability might hinder attaining optimal solutions, which leads to stagnation. In this study, the Lévy Arithmetic Algorithm is introduced by combining the Arithmetic Optimization Algorithm and the Lévy random step to enhance search capabilities and minimize computational demands for improved outcomes. The evaluation encompassed ten CEC2019 benchmark functions, four established real-world engineering problems, and the Economic Load Dispatch of microgrids with renewable energy integration. Using evaluation metrics such as standard deviation and mean, along with hypothesis tests, the study conducts a thorough comparison between the performance of the proposed algorithm and that of the conventional Arithmetic Optimization Algorithm. The results show that the Lévy Arithmetic Algorithm achieves optimization with a minimized number of evaluations in terms of standard deviation and mean, compared to the Arithmetic Optimization Algorithm. Additionally, the proposed method was compared with various well-known and recent metaheuristics algorithms, and the Lévy Arithmetic Algorithm consistently demonstrates superior performance, especially in contrast to the Arithmetic Optimization Algorithm.

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.

Multi-objective trajectory planning in the multiple strata drilling process:A bi-directional constrained co-evolutionary optimizer with Pareto front learning

Trajectory planning is essential to ensure the safety and efficiency of the drilling process within varying downhole geological conditions. However, numerous constraints and dispersed objectives make this task challenging, resulting in a broken constrained Pareto front (PF) in the objective space. To address this issue, we present a novel multi-objective optimization algorithm (MOEA), the Bi-directional Constrained Co-evolutionary Optimizer (BCCO), for reducing the friction torque of the drilling string system and maintaining the wellbore stability of the directional drilling process in multiple changeable strata. Inspired by dual-population co-evolutionary mechanics, BCCO is thoughtfully developed to enhance complex constraints handling. An ESOINN is introduced to guide the population in exploring the irregular PF and adaptively approximating to it. In addition, a flexible constraint dominance principle is devised to filter out non-inferior infeasible solutions that fully balance feasibility, diversity, and convergence by combining constraint violation, minimum vector angle, and angle-penalized distance. Moreover, we adopt a minimum Manhattan distance (MMD) decision-making method to select the final reference solution for trajectory tracking control. To verify the effectiveness of BCCO, we compared it with seven state-of-the-art constrained MOEAs, four latest published MOEAs used in drilling trajectory planning (DTP) applications, and three ablation MOEAs revised from original BCCO on real-world constrained test instances and four different types of designed standard benchmarks. Extensive testing confirmed adaptability to diverse constrained PFs. BCCO displayed strong convergence and diversity when applied to real-world engineering problems while maintaining feasibility. To evaluate BCCO’s DTP performance, we built a wellbore stability model on actual geological formations and empirically tested it with both composite natural curves and third-order Bézier curves in various drilling trajectory scenarios. We established a comprehensive cloud-based DTP test system with the on-site Programmable Logic Controller (PLC) and the workstation via Data Transfer Unit (DTU) communication. Actual DTP cases confirmed the feasibility of BCCO’s Pareto solutions, with MMD-selected trajectories ensuring a harmonized drilling process.

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.

Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems

An original math-inspired meta-heuristic algorithm, named quadratic interpolation optimization (QIO), is proposed to address numerical optimization and engineering issues. The main inspiration behind QIO is derived from mathematics, specifically the newly proposed generalized quadratic interpolation (GQI) method. This method overcomes the limitations of the traditional quadratic interpolation method to better find the minimizer of the quadratic function formed by any three points. The QIO utilizes the GQI method as a promising searching mechanism for tackling various types of optimization problems. This searching mechanism delivers exploration and exploitation strategies, in which the minimizer provided by the GQI method assists the QIO algorithm in exploring a promising region in unexplored areas and exploit the optimal solutions in promising regions. To evaluate QIO’s effectiveness, it is comprehensively compared with 12 other commonly used optimizers on 23 benchmark test functions and the CEC-2014 test suite. Ten engineering problems are also tested to assess QIO’s practicality. Eventually, a real-world application of QIO is presented in the operation management of a microgrid with an energy storage system. The results demonstrate that QIO is a promising alternative for addressing practical challenges. The source code of QIO is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/135627-quadratic-interpolation-optimization-qio.

Triangulation topology aggregation optimizer: A novel mathematics-based meta-heuristic algorithm for continuous optimization and engineering applications

In recent years, numerous meta-heuristic algorithms based on swarm intelligence have been proposed and widely popularized. Although algorithms are designed by some specific behaviors of organisms, their heuristic paradigms and constructed modules are similar, resulting in algorithms still suffer from imbalance between exploration and exploitation for complex optimization problems. Combining mathematical properties with a stochastic search process in meta-heuristic algorithms contributes to breaking the traditional single/dual population-based evolutionary paradigm and facilitating individuals forward optimization. Taking this as motivation, this article proposes a novel mathematics-based meta-heuristic algorithm, named Triangulation Topology Aggregation Optimizer (TTAO), for solving continuous optimization and engineering applications. The core of the proposed algorithm is based on similar triangular topology in mathematics. The TTAO algorithm contains two strategies, i.e., the generic aggregation and the local aggregation, which contributes to iteratively constructing multiple similar triangular topological units to balance the exploration and exploitation. The former generates new vertexes through positive information exchange between different triangular topological units. And the latter constructs new units at promising locations according to the local optimum vertex of each unit. The performance of the TTAO algorithm is evaluated in comparison with some competitive algorithms on CEC2017 functions for different dimensions and 8 real-world engineering problems. Moreover, the Wilcoxon rank sum test is used to verify the effectiveness of the proposed algorithm. The experimental results show that the TTAO algorithm, compared with 10 competitors, obtains 23, 23, and 22 best average results for 29 CEC2017 functions on 30, 50 and 100 dimensions, and its Wilcoxon rank sum test scores still rank first on three different dimensional cases. And more numerical results verify the outstanding optimization performance of the TTAO algorithm effectively. Source codes of TTAO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/136029-triangulation-topology-aggregation-optimizer.

Soft Monte Carlo Simulation for imprecise probability estimation: A dimension reduction-based approach

This paper proposes an efficient solution for solving hybrid reliability problems involving random and interval variables. To meet this aim, using the soft Monte Carlo (SMC) method, a solution is proposed that breaks the random variables space into local 1-D coordinates and then, considers 1-D coordinate as an additional dimension of interval variables. Accordingly, using an optimization in increased interval variables space, the upper and lower bounds of failure probability for each 1-D problem are estimated. In addition, the total failure probabilities are presented as the mathematical expectation of the obtained probability bounds for 1-D coordinates. Then, it is shown that this approach is fit for application of univariate dimension reduction method to reduce the function calls of analysis in the optimization phase. This approach is validated by solving benchmark reliability problems as well as the application of the proposed method for solving real world engineering problems investigated by solving hybrid reliability analysis of reinforced concrete columns. It is shown that the proposed approach efficiently approximates the failure probability bound of problems with moderate nonlinear limit state functions with high accuracy.

An Enhanced Slime Mould Algorithm Combines Multiple Strategies

In recent years, due to the growing complexity of real-world problems, researchers have been favoring stochastic search algorithms as their preferred method for problem solving. The slime mould algorithm is a high-performance, stochastic search algorithm inspired by the foraging behavior of slime moulds. However, it faces challenges such as low population diversity, high randomness, and susceptibility to falling into local optima. Therefore, this paper presents an enhanced slime mould algorithm that combines multiple strategies, called the ESMA. The incorporation of selective average position and Lévy flights with jumps in the global exploration phase improves the flexibility of the search approach. A dynamic lens learning approach is employed to adjust the position of the optimal slime mould individual, guiding the entire population to move towards the correct position within the given search space. In the updating method, an improved crisscross strategy is adopted to reorganize the slime mould individuals, which makes the search method of the slime mould population more refined. Finally, the performance of the ESMA is evaluated using 40 well-known benchmark functions, including those from CEC2017 and CEC2013 test suites. It is also recognized by Friedman’s test as statistically significant. The analysis of the results on two real-world engineering problems demonstrates that the ESMA presents a substantial advantage in terms of search capability.

Improving Wild Horse Optimizer: Integrating Multistrategy for Robust Performance across Multiple Engineering Problems and Evaluation Benchmarks

In recent years, optimization problems have received extensive attention from researchers, and metaheuristic algorithms have been proposed and applied to solve complex optimization problems. The wild horse optimizer (WHO) is a new metaheuristic algorithm based on the social behavior of wild horses. Compared with the popular metaheuristic algorithms, it has excellent performance in solving engineering problems. However, it still suffers from the problem of insufficient convergence accuracy and low exploration ability. This article presents an improved wild horse optimizer (I-WHO) with early warning and competition mechanisms to enhance the performance of the algorithm, which incorporates three strategies. First, the random operator is introduced to improve the adaptive parameters and the search accuracy of the algorithm. Second, an early warning strategy is proposed to improve the position update formula and increase the population diversity during grazing. Third, a competition selection mechanism is added, and the search agent position formula is updated to enhance the search accuracy of the multimodal search at the exploitation stage of the algorithm. In this article, 25 benchmark functions (Dim = 30, 60, 90, and 500) are tested, and the complexity of the I-WHO algorithm is analyzed. Meanwhile, it is compared with six popular metaheuristic algorithms, and it is verified by the Wilcoxon signed-rank test and four real-world engineering problems. The experimental results show that I-WHO has significantly improved search accuracy, showing preferable superiority and stability.

Advanced slime mould algorithm incorporating differential evolution and Powell mechanism for engineering design

The slime mould algorithm (SMA) is a population-based swarm intelligence optimization algorithm that simulates the oscillatory foraging behavior of slime moulds. To overcome its drawbacks of slow convergence speed and premature convergence, this paper proposes an improved algorithm named PSMADE, which integrates the differential evolution algorithm (DE) and the Powell mechanism. PSMADE utilizes crossover and mutation operations of DE to enhance individual diversity and improve global search capability. Additionally, it incorporates the Powell mechanism with a taboo table to strengthen local search and facilitate convergence toward better solutions. The performance of PSMADE is evaluated by comparing it with 14 metaheuristic algorithms (MA) and 15 improved MAs on the CEC 2014 benchmarks, as well as solving four constrained real-world engineering problems. Experimental results demonstrate that PSMADE effectively compensates for the limitations of SMA and exhibits outstanding performance in solving various complex problems, showing potential as an effective problem-solving tool.

A novel chaotic transient search optimization algorithm for global optimization, real-world engineering problems and feature selection.

Metaheuristic optimization algorithms manage the search process to explore search domains efficiently and are used efficiently in large-scale, complex problems. Transient Search Algorithm (TSO) is a recently proposed physics-based metaheuristic method inspired by the transient behavior of switched electrical circuits containing storage elements such as inductance and capacitance. TSO is still a new metaheuristic method; it tends to get stuck with local optimal solutions and offers solutions with low precision and a sluggish convergence rate. In order to improve the performance of metaheuristic methods, different approaches can be integrated and methods can be hybridized to achieve faster convergence with high accuracy by balancing the exploitation and exploration stages. Chaotic maps are effectively used to improve the performance of metaheuristic methods by escaping the local optimum and increasing the convergence rate. In this study, chaotic maps are included in the TSO search process to improve performance and accelerate global convergence. In order to prevent the slow convergence rate and the classical TSO algorithm from getting stuck in local solutions, 10 different chaotic maps that generate chaotic values instead of random values in TSO processes are proposed for the first time. Thus, ergodicity and non-repeatability are improved, and convergence speed and accuracy are increased. The performance of Chaotic Transient Search Algorithm (CTSO) in global optimization was investigated using the IEEE Congress on Evolutionary Computation (CEC)'17 benchmarking functions. Its performance in real-world engineering problems was investigated for speed reducer, tension compression spring, welded beam design, pressure vessel, and three-bar truss design problems. In addition, the performance of CTSO as a feature selection method was evaluated on 10 different University of California, Irvine (UCI) standard datasets. The results of the simulation showed that Gaussian and Sinusoidal maps in most of the comparison functions, Sinusoidal map in most of the real-world engineering problems, and finally the generally proposed CTSOs in feature selection outperform standard TSO and other competitive metaheuristic methods. Real application results demonstrate that the suggested approach is more effective than standard TSO.

Red-tailed hawk algorithm for numerical optimization and real-world problems

This study suggests a new nature-inspired metaheuristic optimization algorithm called the red-tailed hawk algorithm (RTH). As a predator, the red-tailed hawk has a hunting strategy from detecting the prey until the swoop stage. There are three stages during the hunting process. In the high soaring stage, the red-tailed hawk explores the search space and determines the area with the prey location. In the low soaring stage, the red-tailed moves inside the selected area around the prey to choose the best position for the hunt. Then, the red-tailed swings and hits its target in the stooping and swooping stages. The proposed algorithm mimics the prey-hunting method of the red-tailed hawk for solving real-world optimization problems. The performance of the proposed RTH algorithm has been evaluated on three classes of problems. The first class includes three specific kinds of optimization problems: 22 standard benchmark functions, including unimodal, multimodal, and fixed-dimensional multimodal functions, IEEE Congress on Evolutionary Computation 2020 (CEC2020), and IEEE CEC2022. The proposed algorithm is compared with eight recent algorithms to confirm its contribution to solving these problems. The considered algorithms are Farmland Fertility Optimizer (FO), African Vultures Optimization Algorithm (AVOA), Mountain Gazelle Optimizer (MGO), Gorilla Troops Optimizer (GTO), COOT algorithm, Hunger Games Search (HGS), Aquila Optimizer (AO), and Harris Hawks optimization (HHO). The results are compared regarding the accuracy, robustness, and convergence speed. The second class includes seven real-world engineering problems that will be considered to investigate the RTH performance compared to other published results profoundly. Finally, the proton exchange membrane fuel cell (PEMFC) extraction parameters will be performed to evaluate the algorithm with a complex problem. The proposed algorithm will be compared with several published papers to approve its performance. The ultimate results for each class confirm the ability of the proposed RTH algorithm to provide higher performance for most cases. For the first class, the RTH mostly got the optimal solutions for most functions with faster convergence speed. The RTH provided better performance for the second and third classes when resolving the real word engineering problems or extracting the PEMFC parameters.

Hybridizing interval method with a heuristic for solving real-world constrained engineering optimization problems

Practical issues in real-world engineering problems limit the use of traditional optimization methods in finding solutions to design optimization problems. Although several advanced optimization approaches have been developed recently, a unified way to solve almost every problem effectively is yet to arise. To address this, we present a new method for optimizing several structure engineering design problems using our unique hybrid optimization approach inspired by the integration of branch and bound-like concepts of interval analysis with heuristics, and it differs from other methods in the literature. We hybridize the Split-Detect-Discard-Shrink technique and the Sophisticated ABC (SDDS-SABC) algorithm. The advantage of the SDDS process is that it shrinks the entire search region through recursive breakdown and improves computational effort to focus on subregion covering potential solutions for further decomposition. SABC plays a vital role in extracting the best solutions from subregions whose values help detect the promising subregion. SDDS and SABC are sequentially repeated until global/ close to the global solution(s) is reached. The ranking and selection rules are applied to assist in an optimistic decision-making process. In the SABC algorithm, we introduce Latin Hypercube, a new initialization scheme for food sources. This enhances the computational approach towards the optimal solution. Develop a dual strategy employed bees phase to explore their neighbourhoods better. Introduce a new Dynamic penalty method free from extra parameters/ factors. Here 57 real-world complex constrained optimization benchmark problems (CEC2020) featuring problems with Industrial Chemical Processes, Synthesis and Design, Mechanical Engineering, Power System, Power Electronics, and Livestock Feed Ration Optimization are presented, where our method is applied to optimize the decision parameters. Finally, our optimal results are compared in terms of their statistical significance using Friedman and Wilcoxon rank tests with three well-known optimizer algorithms in the literature. The results show that SDDS-SABC outperforms most tested competitors and demonstrates the practicability of SDDS-SABC in solving challenging real-world problems. Moreover, the SDDS-SABC method is numerically stable and suitable for the illustrated optimization examples. The key novelty of the presented approach is the ability to perform a static and better optimal solution in most runs despite the problem being too complex.