Engineering Optimization Problems Research Articles

Adaptive multi-strategy particle swarm optimization for solving NP-hard optimization problems

Particle Swarm Optimization algorithm (PSO) has been widely utilized for addressing optimization problems due to its straightforward implementation and efficiency in tackling various test functions and engineering optimization problems. Nevertheless, PSO encounters issues like premature convergence and a lack of diversity, particularly when confronted with complex high-dimensional optimization tasks. In this study, we propose an enhanced version of the Island Model Particle Swarm Optimization (IMPSO), where island models are integrated into the PSO algorithm based on several migration strategies. The first contribution consists in applying a new selection and replacement strategies based on tabu search technique, while the second contribution consists in proposing a dynamic migration rate relying on the Biogeography-Based Optimization technique. To assess and validate the effectiveness of the proposed method, several unconstrained benchmark functions are applied. The obtained results confirm that the approach yield better performance than the old version of IMPSO for solving NP-hard optimization problems. Compared to the performance of other well-known evolutionary algorithms, the proposed approach is more efficient and effective.

Symmetry-Enhanced, Improved Pathfinder Algorithm-Based Multi-Strategy Fusion for Engineering Optimization Problems

The pathfinder algorithm (PFA) starts with a random search for the initial population, which is then partitioned into only a pathfinder phase and a follower phase. This approach often results in issues like poor solution accuracy, slow convergence, and susceptibility to local optima in the PFA. To address these challenges, a multi-strategy fusion approach is proposed in the symmetry-enhanced, improved pathfinder algorithm-based multi-strategy fusion for engineering optimization problems (IPFA) for function optimization problems. First, the elite opposition-based learning mechanism is incorporated to improve the population diversity and population quality, to enhance the solution accuracy of the algorithm; second, to enhance the convergence speed of the algorithm, the escape energy factor is embedded into the prey-hunting phase of the GWO and replaces the follower phase in the PFA, which increases the diversity of the algorithm and improves the search efficiency of the algorithm; lastly, to solve the problem of easily falling into the local optimum, the optimal individual position is perturbed using the dimension-by-dimension mutation method of t-distribution, which helps the individual to jump out of the local optimum rapidly and advance toward other regions. The IPFA is used for testing on 16 classical benchmark test functions and 29 complex CEC2017 function sets. The final optimization results of PFA and IPFA in pressure vessels are 5984.8222 and 5948.3597, respectively. The final optimization results in tension springs are 0.012719 and 0.012699, respectively, which are comparable with the original algorithm and other algorithms. A comparison between the original algorithm and other algorithms shows that the IPFA algorithm is significantly enhanced in terms of solution accuracy, and the lower engineering cost further verifies the robustness of the IPFA algorithm.

Fireworks algorithm with elitism-based selection strategy and optimal particle guidance mechanism

With the increasing complexity and difficulty of numerical optimization problems in the real world, many efficient meta-heuristic optimization methods have been proposed to solve these problems. An improved Fireworks Algorithm (FWA) with elitism-based selection and optimal particle guidance strategies (EO-FWA) was proposed to address the limitations of the traditional FWA in terms of optimization accuracy and convergence speed, which not only improves the efficiency of the searching agent but also accelerates its convergence speed. In addition, by adopting boundary-based mapping rules, EO-FWA eliminates the randomness of traditional modulo operation mapping rules, which improves its stability and reliability. Twelve benchmark functions in CEC-BC-2022 are used to test the performance of EO-FWA, and the welded beam design problem is optimized at the end. The results show that EO-FWA exhibits stronger competitiveness than other algorithms in dealing with high-dimensional optimization problems and engineering optimization problem, and it can balance exploitation and exploration effectively so as to prevent the algorithm from falling into local optimal solutions.

Actively learning costly reward functions for reinforcement learning

Transfer of recent advances in deep reinforcement learning to real-world applications is hindered by high data demands and thus low efficiency and scalability. Through independent improvements of components such as replay buffers or more stable learning algorithms, and through massively distributed systems, training time could be reduced from several days to several hours for standard benchmark tasks. However, while rewards in simulated environments are well-defined and easy to compute, reward evaluation becomes the bottleneck in many real-world environments, e.g. in molecular optimization tasks, where computationally demanding simulations or even experiments are required to evaluate states and to quantify rewards. When ground-truth evaluations become orders of magnitude more expensive than in research scenarios, direct transfer of recent advances would require massive amounts of scale, just for evaluating rewards rather than training the models. We propose to alleviate this problem by replacing costly ground-truth rewards with rewards modeled by neural networks, counteracting non-stationarity of state and reward distributions during training with an active learning component. We demonstrate that using our proposed method, it is possible to train agents in complex real-world environments orders of magnitudes faster than would be possible when using ground-truth rewards. By enabling the application of RL methods to new domains, we show that we can find interesting and non-trivial solutions to real-world optimization problems in chemistry, materials science and engineering. We demonstrate speed-up factors of 50–3000 when applying our approach to challenges of molecular design and airfoil optimization.

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

Improved honey badger algorithm based on elementary function density factors and mathematical spirals in polar coordinate systema

The Honey Badger Algorithm (HBA) is a new swarm intelligence optimization algorithm by simulating the foraging behavior of honey badgers in nature. To further improve its convergence speed and convergence accuracy, an improved HBA based on the density factors with the elementary functions and the mathematical spirals in the polar coordinate system was proposed. The algorithm proposes six density factors for attenuation states based on elementary functions, and introduces mathematical expressions of the polar diameters and angles of seven mathematical spirals (Fibonacci spiral, Butterfly curve, Rose spiral, Cycloid, Archimedean spiral, Hypotrochoid and Cardioid) in the polar coordinate system based on the density factors with the best synthesized effect to replace the foraging strategy of honey badger digging pattern in HBA. By using 23 benchmark test functions, the above improvements are sequentially compared with the original HBA, and the optimization algorithm with the best improvement, α4CycρHBA, is selected to be compared with SOA, MVO, DOA, CDO, MFO, SCA, BA, GWO and FFA. Finally, four engineering design problems (pressure vessel design, three-bar truss design, cantilever beam design and slotted bulkhead design) were solved. The simulation experiments results show that the proposed improved HBA based on the density factors with the elementary functions and the mathematical spirals of the polar coordinate system has the characteristics of balanced exploration and expiration, fast convergence and high accuracy, and is able to solve the function optimization and engineering optimization problems in a better way.

Multi-strategy-based adaptive sine cosine algorithm for engineering optimization problems

Sine Cosine Algorithm(SCA) is a population-based optimization algorithm, to find the optimal solution. However, SCA has problems such as premature convergence, insufficient solution precision for high-dimensional functions, and slow convergence speed. To solve the problems above, this paper proposes a multi-strategy-based Adaptive Sine Cosine Algorithm (ASCA). Firstly, a more uniform initial population is generated by the Halton sequence so that the initial population covers the entire search space to maintain the diversity of the initial population. Secondly, the adaptive grading strategy is adopted to sort according to the fitness value, and the population dynamics are divided into 4 grades: excellent, good, medium and poor. For the purpose of improving the convergence accuracy of the algorithm and enhancing the ability to jump out of the local optimum, hybrid mutation and elite guidance methods are applied to different levels of populations for perturbing mutations. Finally, in order to improve the convergence speed of the algorithm, a dynamic opposition-based learning global search strategy is proposed. The ASCA is tested on a set of 20 functions in low- dimensional and high-dimensional, and the improved algorithm is compared with Particle Swarm Optimization (PSO), Backtracking Search Algorithm(BSA), Genetic Algorithm(GA)and other improved Sine Cosine Algorithms. The results show the improved convergence accuracy and speed of the ASCA. Moreover, the ASCA proposed in this paper is applied to engineering optimization design. The solution results show that the ASCA is better than other algorithms in superiority-seeking ability, and can effectively solve the optimization problems in engineering.

A New Hybrid Three-Term HS-DY Conjugate Gradient In Solving Unconstrained Optimization Problems

Conjugate Gradient (CG) method is an interesting tool to solve optimization problems in many fields, such design, economics, physics and engineering. Until now, many CG methods have been developed to improve computational performance and have applied in the real-world problems. Combining two CG parameters with distinct denominators may result in non-optimal outcomes and congestion.In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The hybrid threeterm search direction combines Hestenes-Stiefel (HS) and Dai-Yuan (DY) CG parameters which standardized by using a spectral to determine the suitable conjugate parameter choice and it satisfies the sufficient descent condition. Additionally, the global convergence was proved under standard Wolfe conditions and some suitable assumptions. Furthermore, the numerical experiments showed the proposed method is most robust and superior efficiency compared to some existing methods.

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.

SRIME: a strengthened RIME with Latin hypercube sampling and embedded distance-based selection for engineering optimization problems

SRIME: a strengthened RIME with Latin hypercube sampling and embedded distance-based selection for engineering optimization problems

The optimal allocation of thyristor-controlled series compensators for enhancement HVAC transmission lines Iraqi super grid by using seeker optimization algorithm

Abstract Meta-heuristic approaches evaluate the optimum size and position of flexible alternative current transmission systems power systems. The seeker optimization algorithm (SOA) technique was used to solve power engineering optimization problems with better performance than traditional approaches. This article shows the application of SOA for optimal setting and allocation of thyristor-controlled series compensators (TCSCs) in a transmission line. TCSC devices are used to improve transmission systems’ capacity and voltage profile by controlling the transmission line reactance. The IEEE 30 bus system, as well as the Iraqi Super Grid 400 kV system, is used as a test system to illustrate the technique used. Results showed that the installation of TCSC unites the aims to reduce the voltage deviation, reduce the losses of active/reactive power, and increase transmission line reserves over thermal limits. TCSC devices are very effective for the better use of existing installations without sacrificing the stability margin. SOA is intended to identify the best location and size of TCSC devices that resolve the technological difficulties of reducing the TCSC devices’ costs.

Control parameter optimization of underwater gliders with uncertainty using hierarchical optimization method and interval analysis theory

This article attempts to solve the engineering optimization problem for control parameter configuration of underwater gliders with parameter uncertainty. The optimization objectives are maximizing the glider energy utilization rate and average voyage velocity; design variables include the net buoyancy adjustment amount and movable mass block translation amount; and uncertain parameters include the glider control parameter errors, manufacturing errors and sensor measurement errors. First, a dynamic simulation-based performance evaluation model of the glider is established, and interval number order theory is used to quantify the uncertainty. Then, surrogate models of the performance evaluation model are established, and the Sobol’ method-based sensitivity analysis is executed to identify the key uncertain parameters. Thus, a hierarchical optimization framework is introduced, and its system level and sub-level are used for determining optimal control parameter values and performance evaluation parameter intervals, respectively. Finally, optimization calculation is executed under different parameter configurations, and some rules are summarized.

Bayesian-Optimized Riblet Surface Design for Turbulent Drag Reduction via Design-by-Morphing With Large Eddy Simulation

Abstract A computational approach is presented for optimizing new riblet surface designs in turbulent channel flow for drag reduction, utilizing design-by-morphing (DbM), large Eddy simulation (LES), and Bayesian optimization (BO). The design space is generated using DbM to include a variety of novel riblet surface designs, which are then evaluated using LES to determine their drag-reducing capabilities. The riblet surface geometry and configuration are optimized for maximum drag reduction using the mixed-variable Bayesian optimization (MixMOBO) algorithm. A total of 125 optimization epochs are carried out, resulting in the identification of three optimal riblet surface designs that are comparable to or better than the reference drag reduction rate of 8%. The Bayesian-optimized designs commonly suggest riblet sizes of around 15 wall units, relatively large spacing compared to conventional designs, and spiky tips with notches for the riblets. Our overall optimization process is conducted within a reasonable physical time frame with up to 12-core parallel computing and can be practical for fluid engineering optimization problems that require high-fidelity computational design before materialization.

Fast random opposition-based learning Aquila optimization algorithm

Meta-heuristic algorithms are usually employed to address a variety of challenging optimization problems. In recent years, there has been a continuous effort to develop new and efficient meta-heuristic algorithms. The Aquila Optimization (AO) algorithm is a newly established swarm-based method that mimics the hunting strategy of Aquila birds in nature. However, in complex optimization problems, the AO has shown a sluggish convergence rate and gets stuck in the local optimal region throughout the optimization process. To overcome this problem, in this study, a new mechanism named Fast Random Opposition-Based Learning (FROBL) is combined with the AO algorithm to improve the optimization process. The proposed approach is called the FROBLAO algorithm. To validate the performance of the FROBLAO algorithm, the CEC 2005, CEC 2019, and CEC 2020 test functions, along with six real-life engineering optimization problems, are tested. Moreover, statistical analyses such as the Wilcoxon rank-sum test, the t-test, and the Friedman test are performed to analyze the significant difference between the proposed algorithm FROBLAO and other algorithms. The results demonstrate that FROBLAO achieved outstanding performance and effectiveness in solving an extensive variety of optimization problems.

An efficient penalty function method for scenario-based uncertainty quantification problems

This paper proposes an efficient penalty function method to transform constrained optimization problems into unconstrained ones without introducing Lagrange multipliers or slack variables. The method designs new activation and loss penalty functions for inequality and equality functional models and establishes a non-Lagrangian-constrained optimization method. A novel optimality condition independent of any additional variables and equivalent to the Karush–Kuhn–Tucker (KKT) condition is introduced. Additionally, a scenario constraint handling method that does not rely on slack variables is proposed. Compared to soft constraint optimization methods, the proposed method can easily handle numerous scenario constraints. Two examples are used to compare the results with those in the literature, verifying the effectiveness and reliability of the proposed method. Finally, the method is applied to three scenario-based uncertainty quantification problems, including a trigonometric function affected by a noise term, the dynamic performance of a black-box system controller, and the frequency response of a damaged suspension arm. The results demonstrate that the proposed penalty function method can effectively solve scenario-based uncertainty quantification problems with many constraints and improve computational efficiency, providing a new method and means for addressing uncertainty quantification optimization problems in engineering.

Two new single/multi-objective multi-strategy algorithms for the parametric estimation of dual band-notched ultra wideband antennas

This article introduces a novel single objective and a multi-objective multi-hybrid naked mole-rat (moIGDN) algorithm optimization techniques for solving numerical benchmarks and electromagnetic engineering problems. The hybridization was introduced to overcome the basic naked mole-rat algorithm’s (NMRA’s) local optima stagnation and poor exploration problems. The global exploration search equations of INFO, gazelle optimization algorithm (GOA), and dwarf mongoose optimization algorithm (DMO) have been added into the NMRA’s worker phase. Additionally, five mutation operators have been introduced for parametric enhancements and adaptations. For single-objective performance evaluation, three benchmark datasets namely classical benchmark, CEC 2014, CEC 2017, and CEC 2022 have been analysed. A comparison with JADE, SaDE, CMA-ES, success history based DE (SHADE), fractional-order calculus-based FPA (FA-FPO), LSHADE-SPACMA, NL-SHADE-LBC, evolutionary algorithms with eigen crossover (EA4eig), S-LSHADE-DP, L-SHADE-RSP-MID, EBOwithCMAR, LSHADE-EpSin among others. Apart from that, the proposed moIGDN algorithm was utilized to optimize the design of two electromagnetic multi-objective printed monopole antennas categorized as basic ultra-wideband (B-UWB) and dual band-notched ultra-wideband (DBN-UWB) antennas. Simulations have been performed by using the EM-MATLAB optimization interface with two objective functions: trying to minimize pass-band signal reflection and maximizing antenna gain, by mapping solutions to the Pareto-front boundary in the objective space. The best obtained antenna structure had an impedance bandwidth of 2.92–11.96 GHz (fractional bandwidth of 122%), efficient band-rejection characteristics for the WI-MAX (3.3 GHz–3.7 GHz) and WLAN (5.15 GHz–5.85 GHz) bands, and a compact geometry. Based on simulation results, moIGDN is found to be effective and can be utilized to solve complex wireless communication and advanced engineering optimization problems.

Piecewise linear approximation for MILP leveraging piecewise convexity to improve performance

To realize adaptive operation planning with MILP unit commitment, piecewise-linear approximations of the functions that describe the operating behavior of devices in the energy system have to be computed. We present an algorithm to compute a piecewise-linear approximation of a multi-variate non-linear function. The algorithm splits the domain into two regions and approximates each region with a set of hyperplanes that can be translated to a convex set of constraints in MILP. The main advantage of this “piecewise-convex approximation” (PwCA) compared to more general piecewise-linear approximation with simplices is that the MILP representation of PwCA requires only one auxiliary binary variable. For this reason, PwCA yields significantly faster solving times in large MILP problems where the MILP representation of certain functions has to be replicated many times, such as in unit commitment. To quantify the impact on solving time, we compare the performance using PwCA with the performance of simplex approximation with logarithmic formulation and show that PwCA outperforms the latter by a big margin. For this reason, we conclude that PwCA will be a useful tool to set up and solve large MILP problems such as arise in unit commitment and similar engineering optimization problems.

Parameter estimation in single-phase transformers via the generalized normal distribution optimizer while considering voltage and current measurements

This research addresses, from a perspective of metaheuristic optimization, the problem regarding parametric estimation in single-phase transformers while considering voltage and current measures at the terminals of the transformer and weighing linear loads. Transformer parametric estimation is modeled as a nonlinear problem in order to minimize the mean square error between the calculated voltage and current variables and the measurements taken. The nonlinearities are associated with Kirchhoff's first and second laws applied to the equivalent electrical circuit of the single-phase transformer. The nonlinear optimization problem is solved by applying a metaheuristic optimization algorithm known as the generalized normal distribution optimizer (GNDO), which uses evolution rules that allow exploring and exploiting the solution space via the classical probability function based on normal distributions. Numerical results in three test transformers of 20, 45, and 112.5 kVA demonstrate the effectiveness and robustness of the proposed GNDO approach when compared to other optimizers reported in the literature, such as the crow search algorithm, the coyote optimization algorithm, and the exact solution of the nonlinear optimization model using the fmincon solver of the MATLAB software. All numerical simulations confirm the potential of the GNDO approach to deal with complex optimization problems in engineering and science with promising results and low computational effort.

An enhanced Equilibrium Optimizer for solving complex optimization problems

Equilibrium Optimizer (EO), despite its acceptable performance in several complex problems, suffers from low exploitation ability with unbalanced exploration, stagnation in local optima and poor convergence rate. To enhance the performance of the EO, the authors infused the intelligence of quasi-opposite numbers and chaotic-maps into the EO and proposed a Quasi-Oppositional Chaotic Equilibrium Optimizer (QOCEO) that consists of Quasi-Opposition based learning for improving the scalability, Chaotic Time Parameter for ensuring a proper balance between exploration and exploitation, and Chaotic Local Search for reducing the local stagnation. The performance of QOCEO and several contemporary metaheuristics have been evaluated on 96 benchmark functions (including classical benchmark, CEC-2017, CEC-2019, CEC-2020 and CEC-2022) and six constrained engineering optimization problems employing several statistical tests. The average rank Friedman test confirms that for all 96 benchmark functions, QOCEO outperforms CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA, SPS_L_SHADE_EIG, SHADE by 88%, 83%, 49%, 35%, 27%, 18% and 5%, respectively. Comparing the results of Bonferroni-Dunn and Holm’s tests, QOCEO outperforms PSO, GWO, EO, HGSO, SSA, and GSA for classical benchmark functions with 30, 100, 300, and 500 dimensions. Further, QOCEO outperform CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA for all 96 benchmark functions and statistically similar to SPS_L_SHADE_EIG, SHADE and EBOwithCMAR.

Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Beluga Whale Optimization (BWO) is a new metaheuristic algorithm that simulates the social behaviors of beluga whales swimming, foraging, and whale falling. Compared with other optimization algorithms, BWO shows certain advantages in solving unimodal and multimodal optimization problems. However, the convergence speed and optimization performance of BWO still have some performance deficiencies when solving complex multidimensional problems. Therefore, this paper proposes a hybrid BWO method called HBWO combining Quasi-oppositional based learning (QOBL), adaptive and spiral predation strategy, and Nelder-Mead simplex search method (NM). Firstly, in the initialization phase, the QOBL strategy is introduced. This strategy reconstructs the initial spatial position of the population by pairwise comparisons to obtain a more prosperous and higher quality initial population. Subsequently, an adaptive and spiral predation strategy is designed in the exploration and exploitation phases. The strategy first learns the optimal individual positions in some dimensions through adaptive learning to avoid the loss of local optimality. At the same time, a spiral movement method motivated by a cosine factor is introduced to maintain some balance between exploration and exploitation. Finally, the NM simplex search method is added. It corrects individual positions through multiple scaling methods to improve the optimal search speed more accurately and efficiently. The performance of HBWO is verified utilizing the CEC2017 and CEC2019 test functions. Meanwhile, the superiority of HBWO is verified by utilizing six engineering design examples. The experimental results show that HBWO has higher feasibility and effectiveness in solving practical problems than BWO and other optimization methods.