Solving Engineering Optimization Problems Research Articles

Modelling beaches morphodynamic by Hadamard sensitivity analysis

The paper presents a morphodynamic model which can be coupled with any wave model capable of producing time/spectral averaged wave quantities. This model based on a wave energy minimization principle highlights the morphodynamic phenomenology, such as the sandbar creation. Such a model can be used in solving engineering optimization problems. It is also developed to illustrate the idea that beach sand transport can be thought as a non-local phenomenon. We used wave calculations from SWAN and XBeach in our model, and we compared the morphodynamic results to LIP and SANDS hydro-morphodynamic benchmark as well as open-sea simulations. Using supplementary mathematical development, we improved the minimization method using the Hadamard derivative.

An Improved Golden Jackal Optimization Algorithm Based on Multi-strategy Mixing for Solving Engineering Optimization Problems

An Improved Golden Jackal Optimization Algorithm Based on Multi-strategy Mixing for Solving Engineering Optimization Problems

Optical microscope algorithm: A new metaheuristic inspired by microscope magnification for solving engineering optimization problems

A novel optimization algorithm called the optical microscope algorithm (OMA) is developed and applied in this study. Drawing inspiration from the magnification capabilities of an optical microscope on the target object, OMA uses the naked eye for initial observation and simulates the magnification process through an objective lens and an eyepiece. The performance of OMA, which is user friendly and does not require predefined operating parameters, is validated through two experiments: (1) OMA is compared to nine well-known metaheuristic algorithms using constraint handling with 50 benchmark functions involving multiple dimensions. The results indicate that OMA consistently outperforms all other algorithms and requires a short computational time. (2) OMA is applied to solve engineering problems, including structural optimization and multiple resources leveling in the multiple projects scheduling (MRLMP). In those cases, OMA not only demonstrates superiority but also requires the fewest evaluations of objective functions. The novel OMA, which is robust, easy to implement, and uses fewer control parameters, can be deployed to solve for various numerical optimization problems. The source code of OMA is publicly accessible at https://www.mathworks.com/matlabcentral/fileexchange/134541-optical-microscope-algorithm-oma.

An improved rough set strategy-based sine cosine algorithm for engineering optimization problems

In this paper, a hybrid algorithm called rough sine cosine algorithm (RSCA) is introduced for solving engineering optimization problems by merging the sine cosine algorithm (SCA) with the rough set theory concepts (RST). RSCA combines the benefits of SCA and RST to focus the search for a promising region where the global solution can be found. Due to imprecise information on the optimization problems, efficient algorithms roughly identify the optimal solution for this type of uncertain data. The fundamental motive for adding the RST is to deal with the imprecision and roughness of the available information regarding the global optimal, especially for large dimensional problems. The cut concept of RST targeted the more interesting search region so the optimal operation could be sped up, and the global optimum could be reached at a low computational cost. The proposed RSCA algorithm is tested on 23 benchmark functions and 3 design problems. RSCA’s obtained results are mainly compared to the SCA, which is used as a first level of the proposed algorithm in this work and those of other algorithms in the literature. According to the comparisons, the RSCA can provide very competitive performance with different algorithms.

A Subtraction-Average-Based Optimizer for Solving Engineering Problems with Applications on TCSC Allocation in Power Systems.

The present study introduces a subtraction-average-based optimization algorithm (SAOA), a unique enhanced evolutionary technique for solving engineering optimization problems. The typical SAOA works by subtracting the average of searcher agents from the position of population members in the search space. To increase searching capabilities, this study proposes an improved SAO (ISAO) that incorporates a cooperative learning technique based on the leader solution. First, after considering testing on different standard mathematical benchmark functions, the proposed ISAOA is assessed in comparison to the standard SAOA. The simulation results declare that the proposed ISAOA establishes great superiority over the standard SAOA. Additionally, the proposed ISAOA is adopted to handle power system applications for Thyristor Controlled Series Capacitor (TCSC) allocation-based losses reduction in electrical power grids. The SAOA and the proposed ISAOA are employed to optimally size the TCSCs and simultaneously select their installed transmission lines. Both are compared to two recent algorithms, the Artificial Ecosystem Optimizer (AEO) and AQuila Algorithm (AQA), and two other effective and well-known algorithms, the Grey Wolf Optimizer (GWO) and Particle Swarm Optimizer (PSO). In three separate case studies, the standard IEEE-30 bus system is used for this purpose while considering varying numbers of TCSC devices that will be deployed. The suggested ISAOA's simulated implementations claim significant power loss reductions for the three analyzed situations compared to the GWO, AEO, PSO, and AQA.

Diffusion Models Beat GANs on Topology Optimization

Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Recently, generative adversarial networks (GANs) have emerged as a popular alternative to traditional iterative topology optimization methods. However, GANs can be challenging to train, have limited generalizability, and often neglect important performance objectives such as mechanical compliance and manufacturability. To address these issues, we propose a new architecture called TopoDiff that uses conditional diffusion models to perform performance-aware and manufacturability-aware topology optimization. Our method introduces a surrogate model-based guidance strategy that actively favors structures with low compliance and good manufacturability. Compared to a state-of-the-art conditional GAN, our approach reduces the average error on physical performance by a factor of eight and produces eleven times fewer infeasible samples. Our work demonstrates the potential of using diffusion models in topology optimization and suggests a general framework for solving engineering optimization problems using external performance with constraint-aware guidance. We provide access to our data, code, and trained models at the following link: https://decode.mit.edu/projects/topodiff/.

Enhanced tunicate swarm algorithm for optimizing shape of C2 RQI-spline curves

The shape optimization of interpolation curves is a crucial and intractable technique in scientific visualization, data analysis, manufacturing and computer-aided design and is potentially used in many engineering fields involving geometric modeling. In this paper, an enhanced hybrid tunicate swarm algorithm (TSA) is used to optimize the shape of complex rational quartic interpolation spline (RQI-spline, for short) curves. Firstly, to modify the shape of the interpolation curve more flexibly, a novel multi-parameter RQI-spline curve with local and global shape parameters is presented. Then the corresponding combined RQI-spline curves with 2th-order parametric continuity denoted C2 are constructed. In addition, considering that the optimization of shape parameters for RQI-spline curves is a complex optimization problem, an enhanced hybrid version of TSA called DQTSA is developed. The introduction of differential evolution and quadratic interpolation strategies enhances the ability of the TSA to jump out of local minima, thus effectively solving the shape parameter optimization of RQI-spline curves. DQTSA and some popular comparison algorithms are used to solve the set of 23 benchmark functions and CEC2019 test functions. The experimental results show that DQTSA performs the best in 7 (30.43%) of the 23 test problems, while DQTSA performs the best in 3 of the 10 CEC2019 suites. Meanwhile, applying DQTSA to three engineering optimization problems, the best value, mean and significantly better than other search algorithms are obtained from 20 optimized designs, which verifies the applicability and stability of DQTSA in solving engineering optimization problems. Finally, the proposed DQTSA is used to solve the shape optimization model for the combined C2 RQI-spline curve. Numerical results find that DQTSA obtains the optimal RQI-spline curve with minimum energy. Some representative numerical examples illustrate that DQTSA is a potentially excellent algorithm for solving curve optimization.

A multi-agent-based symbiotic organism search algorithm for DG coordination in electrical distribution networks

Metaheuristic algorithms have become popular in solving engineering optimization problems due to their advantages of simple implementation and the ability to find near-optimal solutions for complex and large-scale problems. However, most applications of metaheuristic algorithms consider centralized design, assuming that all possible solutions are available in one machine or controller. In some applications, such as power systems, especially DG coordination, centralized design may not be efficient. This work integrates a multi-agent system (MAS) into a metaheuristic algorithm for enhanced performance. In a proposed multi-agent framework, the agent implements a metaheuristic algorithm and uses shared information with neighbours as input to optimize the solutions. In this study, a new distributed Symbiotic Organism Search (SOS) algorithm has been proposed and tested in the proposed multi-agent framework. The proposed algorithm is termed a multi-agent-based symbiotic organism search algorithm (MASOS). The MASOS has been tested and compared with other proficient algorithms through statistical analysis using benchmark functions. The results show that the proposed MASOS solves the considered benchmark functions efficiently. Then MASOS was tested for DGs coordination considering load variations in the Tanzanian electrical distribution network. The results show that the coordination of DG using the proposed algorithm reduces power loss and improves the voltage profiles of the power system.

Osprey optimization algorithm: A new bio-inspired metaheuristic algorithm for solving engineering optimization problems

This paper introduces a new metaheuristic algorithm named the Osprey Optimization Algorithm (OOA), which imitates the behavior of osprey in nature. The fundamental inspiration of OOA is the strategy of ospreys when hunting fish from the seas. In this hunting strategy, the osprey hunts the prey after detecting its position, then carries it to a suitable position to eat it. The proposed approach of OOA in two phases of exploration and exploitation is mathematically modeled based on the simulation of the natural behavior of ospreys during the hunting process. The performance of OOA has been evaluated in the optimization of twenty-nine standard benchmark functions from the CEC 2017 test suite. Furthermore, the performance of OOA is compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that the proposed OOA has provided superior performance compared to competitor algorithms by maintaining the balance between exploration and exploitation. In addition, the implementation of OOA on twenty-two real-world constrained optimization problems from the CEC 2011 test suite shows the high capability of the proposed approach in optimizing real-world applications.

A Parallel Compact Gannet Optimization Algorithm for Solving Engineering Optimization Problems

The Gannet Optimization Algorithm (GOA) has good performance, but there is still room for improvement in memory consumption and convergence. In this paper, an improved Gannet Optimization Algorithm is proposed to solve five engineering optimization problems. The compact strategy enables the GOA to save a large amount of memory, and the parallel communication strategy allows the algorithm to avoid falling into local optimal solutions. We improve the GOA through the combination of parallel strategy and compact strategy, and we name the improved algorithm Parallel Compact Gannet Optimization Algorithm (PCGOA). The performance study of the PCGOA on the CEC2013 benchmark demonstrates the advantages of our new method in various aspects. Finally, the results of the PCGOA on solving five engineering optimization problems show that the improved algorithm can find the global optimal solution more accurately.

Red Panda Optimization Algorithm: An Effective Bio-Inspired Metaheuristic Algorithm for Solving Engineering Optimization Problems

This paper presents a new bio-inspired metaheuristic algorithm called Red Panda Optimization (RPO) that imitates the natural behaviors of red pandas in nature. The main design idea of RPO is derived from two characteristic natural behaviors of red pandas: (i) foraging strategy, and (ii) climbing trees to rest. The proposed RPO approach is mathematically modeled in two phases of exploration based on the simulation of red pandas’ foraging strategy and exploitation based on the simulation of red pandas’ movement in climbing trees. The main advantage of the proposed approach is that there is no control parameter in its mathematical modeling, and for this reason, it does not need a parameter adjustment process. The performance of RPO is evaluated on fifty-two standard benchmark functions including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types as well as CEC 2017 test suite. The optimization results obtained by the proposed RPO approach are compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that RPO, by maintaining the balance between exploration and exploitation, is effective in solving optimization problems and its performance is superior over competitor algorithms. Based on the analysis of the optimization results, RPO has provided more successful performance compared to the competitor algorithms in 100% of unimodal functions, 100% of high-dimensional multimodal functions, 100% of fixed-dimensional multimodal functions, and 86.2% of CEC 2017 test suite benchmark functions. Also, the statistical analysis of the Wilcoxon rank sum test shows that the superiority of RPO in the competition with the compared algorithms is significant from a statistical point of view. In addition, the results of implementing RPO on four engineering design problems confirms the ability of the proposed approach to handle real-world optimization applications.

Hybrid Sine Cosine Algorithm for Solving Engineering Optimization Problems

Engineering design optimization problems are difficult to solve because the objective function is often complex, with a mix of continuous and discrete design variables and various design constraints. Our research presents a novel hybrid algorithm that integrates the benefits of the sine cosine algorithm (SCA) and artificial bee colony (ABC) to address engineering design optimization problems. The SCA is a recently developed metaheuristic algorithm with many advantages, such as good search ability and reasonable execution time, but it may suffer from premature convergence. The enhanced SCA search equation is proposed to avoid this drawback and reach a preferable balance between exploitation and exploration abilities. In the proposed hybrid method, named HSCA, the SCA with improved search strategy and the ABC algorithm with two distinct search equations are run alternately during working on the same population. The ABC with multiple search equations can provide proper diversity in the population so that both algorithms complement each other to create beneficial cooperation from their merger. Certain feasibility rules are incorporated in the HSCA to steer the search towards feasible areas of the search space. The HSCA is applied to fifteen demanding engineering design problems to investigate its performance. The presented experimental results indicate that the developed method performs better than the basic SCA and ABC. The HSCA accomplishes pretty competitive results compared to other recent state-of-the-art methods.

MCSA: Multi-strategy boosted chameleon-inspired optimization algorithm for engineering applications

Chameleon swarm algorithm (CSA) is a newly proposed swarm intelligence algorithm inspired by the chameleon’s foraging strategies of tracking, searching and attacking targets, and has shown well competitive performance with other state-of-the-art algorithms. Interestingly, CSA mathematically models and implements the steps of chameleon’s unique food-seeking behavior. Nevertheless, the original CSA suffers from the challenges of insufficient exploitation ability, ease of falling into local optima, and low convergence accuracy in complex large-scale applications. Aiming at these challenges, an efficient enhanced chameleon swarm algorithm termed MCSA, combined with fractional-order calculus, sinusoidal adjustment of parameters and crossover-based comprehensive learning (CCL) strategy, is developed in this paper. Firstly, a good fractional-order calculus strategy is added to update the chameleon’s attack velocity, which heightens the local search ability of CSA and accelerates the convergence speed of the algorithm; meanwhile, the sinusoidal adjustment of parameters is adopted to provide a better balance between exploration and exploitation of CSA. Secondly, the CCL strategy is used for the mutation to increase the diversity of the population and avoid becoming trapped in local optima. Three strategies enhance the overall performance and efficiency of the native CSA. Finally, the superiority of the presented MCSA is verified in detail by comparing it with native CSA and several state-of-the-art algorithms on the well-known 23 benchmark test functions, CEC2017 and CEC2019 test suites, respectively. Furthermore, the practicability of MCSA is also highlighted by six real-world engineering designs and two truss topology optimization problems. Simulation results demonstrate that MCSA has strong competitive capabilities and promising prospects. MCSA is potentially an excellent meta-heuristic algorithm for solving engineering optimization problems.

A new firefly algorithm with improved global exploration and convergence with application to engineering optimization

Firefly algorithm (FA) is a powerful and efficient meta-heuristic algorithm which has shown effective performance in the recent literature when applied to solving engineering optimization problems. FA imitates the flashing behavior of fireflies. FA generates solutions randomly and assumes them as fireflies. However, these algorithms may suffer from premature convergence and poor global exploration when used to optimize complex and high dimension engineering problems. Therefore, this study has proposed a novel FA, called firefly algorithm 1 to 3 (FA1→3), via different types of movements of fireflies in an attempt to improve the global exploration and convergence characteristics of FA. A comprehensive study has been carried out on the CEC2014 test functions to compare FA1→3 with the standard FA and several modern improved FA algorithms to validate its performance. The experimental results demonstrate that FA1→3 has achieved acceptable performance. In addition, it has been applied to six real-world engineering problems to show the optimization capability, robustness, and efficacy of FA1→3 in comparison with modern algorithms As per simulations, FA1→3 has provided suitable performance and higher accuracy than traditional and modified algorithms introduced in the last years. According to simulations, FA1→3 is significantly powerful and robust when dealing with various complex engineering problems and finds the design variables straightforwardly. Note that the source code of the proposed FA1→3 algorithm is publicly available at https://www.optim-app.com/projects/FA.

CQFFA: A Chaotic Quasi-oppositional Farmland Fertility Algorithm for Solving Engineering Optimization Problems

CQFFA: A Chaotic Quasi-oppositional Farmland Fertility Algorithm for Solving Engineering Optimization Problems

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

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

Elite Chaotic Manta Ray Algorithm Integrated with Chaotic Initialization and Opposition-Based Learning

The manta ray foraging optimizer (MRFO) is a novel nature-inspired optimization algorithm that simulates the foraging strategy and behavior of manta ray groups, i.e., chain, spiral, and somersault foraging. Although the native MRFO has revealed good competitive capability with popular meta-heuristic algorithms, it still falls into local optima and slows the convergence rate in dealing with some complex problems. In order to ameliorate these deficiencies of the MRFO, a new elite chaotic MRFO, termed the CMRFO algorithm, integrated with chaotic initialization of population and an opposition-based learning strategy, is developed in this paper. Fourteen kinds of chaotic maps with different properties are used to initialize the population. Thereby, the chaotic map with the best effect is selected; meanwhile, the sensitivity analysis of an elite selection ratio in an elite chaotic searching strategy to the CMRFO is discussed. These strategies collaborate to enhance the MRFO in accelerating overall performance. In addition, the superiority of the presented CMRFO is comprehensively demonstrated by comparing it with a native MRFO, a modified MRFO, and several state-of-the-art algorithms using (1) 23 benchmark test functions, (2) the well-known IEEE CEC 2020 test suite, and (3) three optimization problems in the engineering field, respectively. Furthermore, the practicability of the CMRFO is illustrated by solving a real-world application of shape optimization of cubic generalized Ball (CG-Ball) curves. By minimizing the curvature variation in these curves, the shape optimization model of CG-Ball ones is established. Then, the CMRFO algorithm is applied to handle the established model compared with some advanced meta-heuristic algorithms. The experimental results demonstrate that the CMRFO is a powerful and attractive alternative for solving engineering optimization problems.

Artificial rabbits optimization: A new bio-inspired meta-heuristic algorithm for solving engineering optimization problems

In this paper, a new bio-inspired meta-heuristic algorithm, named artificial rabbits optimization (ARO), is proposed and tested comprehensively. The inspiration of the ARO algorithm is the survival strategies of rabbits in nature, including detour foraging and random hiding. The detour foraging strategy enforces a rabbit to eat the grass near other rabbits’ nests, which can prevent its nest from being discovered by predators. The random hiding strategy enables a rabbit to randomly choose one burrow from its own burrows for hiding, which can decrease the possibility of being captured by its enemies. Besides, the energy shrink of rabbits will result in the transition from the detour foraging strategy to the random hiding strategy. This study mathematically models such survival strategies to develop a new optimizer. The effectiveness of ARO is tested by comparison with other well-known optimizers by solving a suite of 31 benchmark functions and five engineering problems. The results show that ARO generally outperforms the tested competitors for solving the benchmark functions and engineering problems. ARO is applied to the fault diagnosis of a rolling bearing, in which the back-propagation (BP) network optimized by ARO is developed. The case study results demonstrate the practicability of the ARO optimizer in solving challenging real-world problems. The source code of ARO is publicly available at https://seyedalimirjalili.com/aro and https://ww2.mathworks.cn/matlabcentral/fileexchange/110250-artificial-rabbits-optimization-aro.

Gannet optimization algorithm : A new metaheuristic algorithm for solving engineering optimization problems

Engineering design problems are usually large-scale constrained optimization problems, and metaheuristic algorithms are vital for solving such complex problems. Therefore, this paper introduces a new nature-inspired metaheuristic algorithm: the gannet optimization algorithm (GOA). The GOA mathematizes the various unique behaviors of gannets during foraging and is used to enable exploration and exploitation. GOA’s U-shaped and V-shaped diving patterns are responsible for exploring the optimal region within the search space, with sudden turns and random walks ensuring better solutions are found in this region. In order to verify the ability of the GOA to find the optimal solution, we compared it with other comparison algorithms in multiple dimensions of 28 benchmark functions. We found that the GOA has a shorter running time in high dimensions and can provide a better solution. Finally, we apply the GOA to five engineering optimization problems. The experimental results show that the GOA is suitable for many constrained engineering design problems and can provide better solutions in most cases.

Information-decision searching algorithm: Theory and applications for solving engineering optimization problems

The nature of the real-world problem is multi-modal and multidimensional. This paper proposes a novel metaheuristic algorithm based on social behaviors of people acquiring favorable information, which is the society-based metaheuristic optimization mechanism, called the Information-Decision Search Algorithm(IDSE), aiming to provide a new optimization technology for solving real-world optimization problems. This optimization technology proposes special searching mechanisms of delivery behavior, approaching behavior, inheritance behavior, mutation behavior, interaction, and learning behavior, establishing corresponding mathematical models to develop an efficient optimization framework for solving constrained optimization. The performance of the proposed algorithm and 10 state-of-the-art optimizers is evaluated on 46 benchmarks, including convergence, solution accuracy, robustness, diversity, significance, and the dimensional-scalability on CEC 2017 benchmarks (50 Dim and 100 Dim). The statistical results suggest, with the dimensionality of the problem variable increasing, the computing efficiency of the proposed optimization technology keeps on the highest level at all times. The low-rank feature for IDSE on 46 benchmarks emphasizes the selective priority in solving the same optimization problem. In addition, IDSE also considers 7 real-world engineering problems. The comparison results suggest that IDSE is superior to competitive algorithms in improving solution accuracy and reducing optimization costs, indicating the significant performance for solving constraint optimization.