Real-world Engineering Optimization Problems Research Articles

Serial multilevel-learned differential evolution with adaptive guidance of exploration and exploitation

Recent years have witnessed a surge in the development of multilevel variants of differential evolution (DE), significantly enhancing the performance of DE algorithms. However, systematically guiding algorithms to strike a balance between exploration and exploitation within a parallel multilevel structure remains a challenge. In response to this challenge, we propose serial multilevel-learned differential evolution (SMLDE) with adaptive guidance for exploration and exploitation. This algorithm establishes a tightly connected multilevel-learned structure and an adaptive current best level. It also incorporates a combination of strategies including single iterative adaption, Cauchy perturbation, and iterative constraint strategy into each of the adapted levels, thus enhancing inter-component connections and dynamically balancing exploration and exploitation. To validate its effectiveness, we conduct ablation experiments and visualized analyses of exploration and exploitation to demonstrate the reliable strength of the multilevel-learned structure. The experimental results comparing SMLDE with 15 state-of-the-art algorithms using the IEEE Conference on Evolutionary Computation (CEC) 2017 benchmark test sets across various dimensions showcase its superior performance. Additionally, its remarkable results on the CEC2011 benchmark test and two real-world engineering optimization problems underscore the robustness and effectiveness of SMLDE.

Implementation of an Enhanced Crayfish Optimization Algorithm.

This paper presents an enhanced crayfish optimization algorithm (ECOA). The ECOA includes four improvement strategies. Firstly, the Halton sequence was used to improve the population initialization of the crayfish optimization algorithm. Furthermore, the quasi opposition-based learning strategy is introduced to generate the opposite solution of the population, increasing the algorithm's searching ability. Thirdly, the elite factor guides the predation stage to avoid blindness in this stage. Finally, the fish aggregation device effect is introduced to increase the ability of the algorithm to jump out of the local optimal. This paper performed tests on the widely used IEEE CEC2019 test function set to verify the validity of the proposed ECOA method. The experimental results show that the proposed ECOA has a faster convergence speed, greater performance stability, and a stronger ability to jump out of local optimal compared with other popular algorithms. Finally, the ECOA was applied to two real-world engineering optimization problems, verifying its ability to solve practical optimization problems and its superiority compared to other algorithms.

Improved stochastic fractal search algorithm involving design operators for solving parameter extraction problems in real-world engineering optimization problems

The characteristic parameters of renewable energy sources (RESs) are changes over time under changing operating conditions. Therefore, the accuracy of the model is important in order to establish appropriate control and operating plans for the stable operation of such systems. Determining the parameters of RESs and creating an accurate model of them is an inevitable reality and plays an important role in the success of system modeling. Many methods have been used to determine these parameters in the literature. Furthermore, optimization algorithms are now considered to be among the most significant approaches for resolving problems pertaining to system parameter extraction in many scientific areas. In the study, this parameter extraction is done by a new optimization method called stochastic fractal search algorithm (FDB-NSM-SFS-OBLs), which includes natural survivor updating (NSM) and fitness distance balance (FDB) guiding mechanisms, and opposite based learning (OBL) methods. The performance of the proposed FDB-NSM-SFS-OBL algorithm has been tested in two different experimental studies. In the first experimental study, the proposed approach is tested on CEC2020 benchmark test functions and the algorithm structure containing the best OBL approach is determined using nonparametric Wilcoxon and Friedman statistical analysis methods. The second experimental study is carried out with the proposed optimization algorithm to estimate the parameters of the photovoltaic cell used in the modeling, which is the building block of photovoltaic panels used in renewable energy systems, proton-exchange membrane fuel cell (PEMFC) that is another renewable energy source, and Li-Ion battery used as a backup power unit. The FDB-NSM-SFS-OBL algorithm, which is used both in the CEC2020 benchmark test functions and in determining the parameters of photovoltaic (PV) cells, PEMFC and Li-Ion batteries, performed better in searching and finding the global solution point during the optimization process.

Imitation-based Cognitive Learning Optimizer for solving numerical and engineering optimization problems

A novel human cognitive and social interaction-based metaheuristic called Imitation-based Cognitive Learning Optimizer (CLO) is proposed and developed to solve engineering optimization problems effectively. CLO is inspired by humans’ imitation and social learning behavior during the life cycle. The human life cycle consists of various stages. Social and imitating human behavior during the life cycle is incorporated into this algorithm to improve cognitive abilities. The three real-world mechanical engineering optimization problems (Welded beam problem, Tension–Compression String Design Problem, and Speed reducer problem) and 100 challenging benchmark functions including uni-modal, multi-modal and CEC-BC-2017 functions are used for the real-time validation. CLO is compared with 12 state-of-art algorithms from the literature. The experiments along with convergence analysis and Friedman’s Mean Rank (FMR) statistical test show the superiority of CLO over the other chosen algorithms.

Generating Cheap Representative Functions for Expensive Automotive Crashworthiness Optimization

Solving real-world engineering optimization problems, such as automotive crashworthiness optimization, is extremely challenging, because the problem characteristics are oftentimes not well understood. Furthermore, typical hyperparameter optimization approaches that require a large function evaluation budget are computationally hindered, if the function evaluation is expensive, e.g., requires finite element (FE) simulation runs. In this paper, we propose an approach to characterize real-world expensive black-box optimization problems using the exploratory landscape analysis (ELA). Based on these landscape characteristics, we can identify test functions that are fast-to-evaluate and representative for hyperparameter optimization purposes. Focusing on 20 problem instances from automotive crashworthiness optimization, our results reveal that these 20 crashworthiness problems exhibit landscape features different from classical optimization benchmark test suites, such as the widely-used black-box optimization benchmarking (BBOB) problem set. In fact, these 20 problem instances belong to problem classes that are distinct from the BBOB test functions based on the clustering results. Further analysis indicates that, as far as the ELA features concern, they are most similar to problem classes of tree-based test functions. By analyzing the performance of two optimization algorithms with different hyperparameters, namely the covariance matrix adaptation evolutionary strategy (CMA-ES) and Bayesian optimization (BO), we show that the tree-based test functions are indeed representative in terms of predicting the algorithm performances. Following this, such scalable and fast-to-evaluate tree-based test functions have promising potential for automated design of an optimization algorithm for specific real-world problem classes.

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.

Surrogate-Assisted Differential Evolution With Adaptive Multisubspace Search for Large-Scale Expensive Optimization

Real-world industrial engineering optimization problems often have a large number of decision variables. Most existing large-scale evolutionary algorithms need a large number of function evaluations to achieve high-quality solutions. However, the function evaluations can be computationally intensive for many of these problems, particularly, which makes large-scale expensive optimization challenging. To address this challenge, surrogate-assisted evolutionary algorithms based on the divide-and-conquer strategy have been proposed and shown to be promising. Following this line of research, we propose a surrogate-assisted differential evolution algorithm with adaptive multi-subspace search for large-scale expensive optimization to take full advantage of the population and the surrogate mechanism. The proposed algorithm constructs multi-subspace based on principal component analysis and random decision variable selection, and searches adaptively in the constructed subspaces with three search strategies. The experimental results on a set of large-scale expensive test problems have demonstrated its superiority over three state-of-the-art algorithms on the optimization problems with up to 1000 decision variables.

An Enhanced Hunger Games Search Optimization with Application to Constrained Engineering Optimization Problems.

The Hunger Games Search (HGS) is an innovative optimizer that operates without relying on gradients and utilizes a population-based approach. It draws inspiration from the collaborative foraging activities observed in social animals in their natural habitats. However, despite its notable strengths, HGS is subject to limitations, including inadequate diversity, premature convergence, and susceptibility to local optima. To overcome these challenges, this study introduces two adjusted strategies to enhance the original HGS algorithm. The first adaptive strategy combines the Logarithmic Spiral (LS) technique with Opposition-based Learning (OBL), resulting in the LS-OBL approach. This strategy plays a pivotal role in reducing the search space and maintaining population diversity within HGS, effectively augmenting the algorithm's exploration capabilities. The second adaptive strategy, the dynamic Rosenbrock Method (RM), contributes to HGS by adjusting the search direction and step size. This adjustment enables HGS to escape from suboptimal solutions and enhances its convergence accuracy. Combined, these two strategies form the improved algorithm proposed in this study, referred to as RLHGS. To assess the efficacy of the introduced strategies, specific experiments are designed to evaluate the impact of LS-OBL and RM on enhancing HGS performance. The experimental results unequivocally demonstrate that integrating these two strategies significantly enhances the capabilities of HGS. Furthermore, RLHGS is compared against eight state-of-the-art algorithms using 23 well-established benchmark functions and the CEC2020 test suite. The experimental results consistently indicate that RLHGS outperforms the other algorithms, securing the top rank in both test suites. This compelling evidence substantiates the superior functionality and performance of RLHGS compared to its counterparts. Moreover, RLHGS is applied to address four constrained real-world engineering optimization problems. The final results underscore the effectiveness of RLHGS in tackling such problems, further supporting its value as an efficient optimization method.

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.

The corona virus search optimizer for solving global and engineering optimization problems

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.

Evolving Marine Predators Algorithm by dynamic foraging strategy for real-world engineering optimization problems

The Marine Predators Algorithm (MPA) is a novel hunting-based optimizer. The MPA’s central concept is based on the well-known Lévy Flight (LF) and Brownian Motion (BM) strategies as well as a simple transition model between these two strategies. The canonical MPA proposes three static steps to tune the transition behavior between the LF and BM strategies. Although MPA provides exemplary performance in many test functions, the discrete transition between the two mentioned phases causes it to get stuck in local optima when faced with real-world optimization problems. In order to address this shortcoming, this paper proposes a soft dynamic transition between LF and BM to model this encounter naturally, considering the continuous nature of the transition between LF and BM in marine predators’ real life. In order to evaluate the performance of the developed Dynamic Foraging Strategy MPA (DFSMPA), twenty-nine optimization test functions, thirty complex CEC-BC-2017 functions, ten benchmarks of CEC06-2019 test suit, and ten real applicable engineering problems, including power system design, synthesis and process design, industrial chemical producer, power-electronic design, mechanical design, and animal feed ratio, are employed. The DFSMPA is evaluated against four groups of standard optimization approaches, including (1) Arithmetic Optimization Algorithm (AOA), Slime Mould Algorithm (SMA), Equilibrium Optimizer (EO), Niching Chimp Optimization Algorithm (ChOA), Henry Gas Solubility Optimization (HGSO) as recent optimization algorithms, (2) Lévy Flight GWO (LGWO) and Evolutionary Algorithms with Adaptive Lévy Mutations (EALM) as the two best dynamic Lévy-based optimization algorithms, (3) SHADE, CMA-ES, and LSHADESPACMA as the three state-of-the-art optimization algorithms, and jDE100, DISHchain1e+12, CIPDE, and EBOwithCMAR as best performing algorithms in IEEE CEC06-2019 competition. Three non-parametric statistical tests, including the Wilcoxon rank-sum, Bonferroni–Dunn and Holm, and Friedman average rank tests, are utilized to perform a comprehensive assessment. The results show that the DFSMPA achieved the first rank among 46 out of 70 benchmark functions and engineering problems and exhibited similar results compared with SHADE and CMA-ES in other benchmarks. The statistical analysis demonstrated that DFSMPA is a significantly superior optimizer than the three first categories’ benchmark algorithms, while its result is statistically similar to jDE100, DISHchain1e+12.

Batched Data-Driven Evolutionary Multiobjective Optimization Based on Manifold Interpolation

Multiobjective optimization problems are ubiquitous in real-world science, engineering, and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve time-consuming and/or costly physical experiments. Data-driven evolutionary optimization can be used to search for a set of nondominated tradeoff solutions, where the expensive objective functions are approximated as a surrogate model. In this article, we propose a framework for implementing batched data-driven evolutionary multiobjective optimization (EMO). It is so general that any off-the-shelf EMO algorithms can be applied in a plug-in manner. There are two unique components: 1) based on the Karush–Kuhn–Tucker conditions, a manifold interpolation approach that explores more diversified solutions with a convergence guarantee along the manifold of the approximated Pareto-optimal set and 2) a batch recommendation approach that reduces the computational time of the data-driven evolutionary optimization process by evaluating multiple samples at a time in parallel. Comparing against seven state-of-the-art surrogate-assisted evolutionary algorithms, experiments on 168 benchmark test problem instances with various properties and a real-world application on hyper-parameter optimization fully demonstrate the effectiveness and superiority of our proposed framework, which is featured with a faster convergence and a stronger resilience to various Pareto-optimal front shapes.

A novel Human Conception Optimizer for solving optimization problems

Computational techniques are widely used to solve complex optimization problems in different fields such as engineering, finance, biology, and so on. In this paper, the Human Conception Optimizer (HCO) is proposed as a novel metaheuristic algorithm to solve any optimization problems. The idea of this algorithm is based on some biological principles of the human conception process, such as the selective nature of cervical gel in the female reproductive system to allow only healthy sperm cells into the cervix, the guidance nature of mucus gel to help sperm track a genital tracking path towards the egg in the Fallopian tube, the asymmetric nature of flagellar movement which allows sperm cells to move in the reproductive system, the sperm hyperactivation process to make them able to fertilize an egg. Thus, the strategies pursued by the sperm in searching for the egg in the Fallopian tube are modeled mathematically. The best sperm which will meet the position of the egg will be the solution of the algorithm. The performance of the proposed HCO algorithm is examined with a set of basic benchmark test functions called IEEE CEC-2005 and IEEE CEC-2020. A comparative study is also performed between the HCO algorithm and other available algorithms. The significance of the results is verified with statistical test methods. To validate the proposed HCO algorithm, two real-world engineering optimization problems are examined. For this purpose, a complex 14 over-current relay based IEEE 8 bus distribution system is considered. With the proposed algorithm, an improvement of 50% to 60% in total relay operating times is observed comparing with some existing results for the same system. Another engineering problem of designing an optimal proportional integral derivative (PID) controller for a blower driven patient hose mechanical ventilator (MV) is examined. A significant improvement in terms of response time, settling time is observed in the MV system by comparing with existing results.

A constrained multi-objective evolutionary algorithm based on decomposition with improved constrained dominance principle

There are various constraints in many real engineering problems, and the constrained handling methods play a key role in the constrained multi-objective evolutionary algorithms (CMOEAs). Many constraint-handling strategies will struggle to reach optimum results when dealing with constrained multi-objective optimization problems (CMOPs) with large and complex infeasible areas. It brings stiffer challenges to CMOEAs in maintaining the convergence, diversity, and feasibility of the population. To remedy these issues, this paper proposes an improved constrained dominance principle (ICDP) embedded in MOEA/D, named MOEA/D-ICDP. In MOEA/D-ICDP, the original weight vector that a solution matches may not be the best suitable weight vector that this solution corresponds to, then there is a deviation between them. According to the above situation, ICDP is designed in this way. Firstly, a dynamic tolerability value about the deviation is introduced. Then ICDP adjusts the dominance relationship of solutions in light of the relationship between the deviation and tolerability so that it can preserve some valuable infeasible solutions in the early evolutionary stage and help the population to cross the large and complex regions. Three test suites and two real-world engineering optimization problems are used to evaluate the performance of the proposed MOEA/D-ICDP and the other five representative CMOEAs. The experimental results demonstrate that MOEA/D-ICDP has more excellent performance and competitiveness than the other five CMOEAs.

A survey of recently developed metaheuristics and their comparative analysis

The aim of this study was to gather, discuss, and compare recently developed metaheuristics to understand the pace of development in the field of metaheuristics and make some recommendations for the research community and practitioners. By thoroughly and comprehensively searching the literature and narrowing the search results, we created with a list of 57 novel metaheuristic algorithms. Based on the availability of the source code, we reviewed and analysed the optimization capability of 26 of these algorithms through a series of experiments. We also evaluated the exploitation and exploration capabilities of these metaheuristics by using 50 unimodal functions and 50 multimodal functions, respectively. In addition, we assessed the capability of these algorithms to balance exploration and exploitation by using 29 shifted, rotated, composite, and hybrid CEC-BC-2017 benchmark functions. Moreover, we evaluated the applicability of these metaheuristics on four real-world constrained engineering optimization problems. To rank the algorithms, we performed a nonparametric statistical test, the Friedman mean rank test. Based on the statistical results for the unimodal and multimodal functions, we declared that the GBO, PO, and MRFO algorithms have better exploration and exploitation capabilities. Based on the results for the CEC-BC-2017 benchmark functions, we found the MPA, FBI, and HBO algorithms to be the most balanced. Finally, based on the results for the constrained engineering optimization problems, we declared that the HBO, GBO, and MA algorithms are the most suitable. Collectively, we confidently recommend the GBO, MPA, PO, and HBO algorithms for real-world optimization problems.

Disturbance inspired equilibrium optimizer with application to constrained engineering design problems

This work proposes a novel adaptive global optimization algorithm called Disturbance Inspired Equilibrium Optimizer. The purpose of this study is to enhance the exploitation ability of the newly developed Equilibrium Optimizer, and to address the issue of getting trapped in local minima. The proposed algorithm is benefited from the novel disturbance-based hybrid initialization strategy, the new form of time factor, and the new update rule of particle's position. In addition, a novel boundary check strategy and an adaptive global position disturbance mechanism are proposed and installed into our algorithm. Based on the disturbance-inspired modifications, the exploration and exploitation ability of the standard Equilibrium Optimizer are significantly improved. The performance of the proposed algorithm is evaluated using representative different benchmark functions, consisting of three well-known mathematical benchmark functions, six complex composite functions, and four challenge functions proposed on 2017 IEEE Congress on Evolutionary Computation. Also, the proposed algorithm is conducted to optimize three engineering designs to examine its applicability in constrained real-world problems. In all experiments, the developed algorithm is compared with six other state-of-the-art metaheuristics. Experimental results and the average rank of Friedman test show that our algorithm provides promising results in solving mathematical problems and constrained real-world engineering optimization problems. Therefore, the proposed algorithm is competitive compared to the other state-of-the-art metaheuristic algorithms and is an effective solution to real-world engineering problems.

Self-adaptive classification learning hybrid JAYA and Rao-1 algorithm for large-scale numerical and engineering problems

In this paper, a self-adaptive classification learning hybrid JAYA and Rao-1 algorithm, which is called EHRJAYA, is proposed for solving large-scale numerical problems and real-world complex engineering optimization problems. JAYA algorithm and Rao-1 algorithm are two kinds of algorithms with simple structure and superior performance, which have the characteristics of no particular controlling parameters. In EHRJAYA the evolution strategies of the two algorithms are selected through a random selection mechanism. Then, a novel self-adaptive classification learning strategy is proposed, which fully utilizes information from different individuals. On this basis, two different adaptive coefficients are introduced to guide the population towards the optimal individual and away from the worst individual. Finally, combining the linear population reduction strategy and the dynamic lens opposition-based learning strategy, the convergence speed and ability to jump out of local optimum of the algorithm are greatly improved. To verify the performance of the proposed EHRJAYA, 59 complex functions from the CEC2014 and CEC2017 competitions are solved by EHRJAYA. Then, EHRJAYA and more than 20 algorithms with superior performance jointly solve ten challenging real-world engineering optimization problems. Experimental results show that the proposed EHRJAYA can obtain optimal results with the least computational resources in most cases. Therefore, in the face of these problems, effective solutions can be provided by EHRJAYA.

A modified fireworks algorithm with dynamic search interval based on closed-loop control

Fireworks algorithm performs better in solving some complex real-world engineering optimization problems, but it like other swarm intelligent algorithms, which also have the problems of slow search speed, has low efficiency and easy to fall into local optimum. Therefore, a modified fireworks algorithm is proposed for amending these weaknesses in this paper. Firstly, a closed-loop dynamic search interval adjustment strategy based on feedback control is proposed to improve search effective. Reference selection, controller design and center determination method are designed to obtain a reasonable dynamic search interval. Then we analyze the effective key parameters and design an explosion radius adjustment method related to iteration stage. Inspired by the scale law of foraging behavior of marine predators, Lévy flight and Brownian movement are applied to generate mutation sparks to enhance the algorithm local search capability. To make high-quality fireworks produce denser sparks, an explosion intensity operator based on the ranking of each firework is presented. Finally, a large number of experiments are used to verify the performance of the proposed algorithm, compared to other well-known algorithms, results confirm the superiority of this algorithm in terms of convergence rate and global search capability.

Solving Many-objective Constraint Real-World Optimization Problems with Multi-objective Optimization Algorithms

In real world engineering optimization problems many constraints must be considered due to the imperfect conditions of the systems or process. Therefore, constraint handling methods are integrated into optimization algorithms. However, since the constraints are succeeded by the algorithm, their value is not considered or watched. Alternatively, it is possible to convert constraints to objectives and these many-objective constraint real-world optimization problems are changed to many-objective optimization problems. In this research for this purpose five real world engineering design problems are converted into many-objective optimization problem which are Gear Train Design, Pressure Vessel Design, Two Bar Truss Design, Disc Brake Design and Vibrating Platform Design problems. The problems are solved by using multi-objective optimization algorithms (NSGA-II, MOEA/D, MOEA/D-DE, MPSO/D and MOPSO) and their performance is compared by using the hypervolume metric.

Multi-objective learner performance-based behavior algorithm with five multi-objective real-world engineering problems

In this work, a new multiobjective optimization algorithm called multiobjective learner performance-based behavior algorithm is proposed. The proposed algorithm is based on the process of transferring students from high school to college. The proposed technique produces a set of non-dominated solutions. To judge the ability and efficacy of the proposed multiobjective algorithm, it is evaluated against a group of benchmarks and five real-world engineering optimization problems. Additionally, to evaluate the proposed technique quantitatively, several most widely used metrics are applied. Moreover, the results are confirmed statistically. The proposed work is then compared with three multiobjective algorithms, which are MOWCA, NSGA-II, and MODA. Similar to the proposed technique, the other algorithms in the literature were run against the benchmarks, and the real-world engineering problems utilized in the paper. The algorithms are compared with each other employing descriptive, tabular, and graphical demonstrations. The results proved the ability of the proposed work in providing a set of non-dominated solutions, and that the algorithm outperformed the other participated algorithms in most of the cases.