Optimal Design Problem Research Articles

A multi-strategy enhanced reptile search algorithm for global optimization and engineering optimization design problems

The reptile search algorithm (RSA) is a well-known swarm-based metaheuristic algorithm inspired by the hunting behaviors of crocodiles. To overcome the problems of falling into local optima and premature convergence, this paper proposes a multi-strategy enhanced reptile search algorithm (MRSA), which integrates a novel dynamic evolutionary sense, prey approaching strategy and Cauchy mutation strategy. The prey approaching strategy comes from the secretary bird optimization algorithm and is applied to strengthen the exploration capability of RSA. A comparative performance analysis is conducted using the CEC2005, CEC2017 and CEC2022 benchmark functions. And fifteen algorithms are employed for the performance comparison. The results of numerical, convergence curves, boxplots, Wilcoxon rank-sum test and Friedman ranking confirm the efficacy and stability of proposed MRSA, indicating its superior performance compared to other algorithms. Moreover, seven practical engineering design tasks are used to test the performance of MRSA in real-world optimization problems. The results also show that MRSA can efficiently obtain better optimal solution compared to existing methods.

Reliability and Sustainability Integrated Design Optimization for Engineering Structures with Active Machine Learning Technique

Recent strategic plans from many governments share the same emphasis on sustainable development goals. The construction industry is recognized as one of the primary contributors to greenhouse gas emissions. Stimulated by such political and practical requirements, this research aims to develop a reliability and sustainability integrated design optimization (RSIDO) framework for engineering structures. Statistical modelling is conducted which provides probabilistic models for embodied carbon coefficients (ECCs). The proposed RSIDO framework contains three main stages. The first stage solves the classical reliability-based design optimization (RBDO) problem. The second stage conducts the reliability-based embodied carbon quantification to define the sustainable reliability constraint. Lastly, the new sustainable probabilistic design constraint is embedded in the design question. Furthermore, to overcome the computational difficulty, an active-learning extended-support vector regression (AL-X-SVR) technique is proposed to improve the computational efficiency of the proposed framework. The embedded regression algorithm is presented with consolidated theoretical backgrounds. Further, an active learning strategy is implemented to select the learning samples efficiently. The applicability and effectiveness of the proposed AL-X-SVR method are demonstrated using a highly nonlinear-constrained mathematical validation. Additionally, the RSIDO framework is demonstrated through three engineering applications. This research contributes a comprehensive framework that not only addresses reliability and sustainability but also enhances computational efficiency, thereby introducing an innovative approach to design optimization in building engineering.

Topology optimization for 3D fluid diode design considering wall-connected structures

This paper proposes a density-based topology optimization method for the three-dimensional design of fluid diodes considering wall-connected structures based on the fictitious physical modeling approach. The optimum design problem of fluid diodes is formulated as maximizing the energy dissipation in the reverse flow subject to the upper bound constraint of the energy dissipation in the forward flow. A fictitious physical model and a geometric constraint are constructed to detect and restrict the “floating” solid domains, which are not connected to the outer boundaries. The sensitivities of cost functions are derived and computed based on the continuous adjoint method. The finite volume method is employed to discretize the governing and adjoint equations to mitigate the huge computational costs of three-dimensional fluid analysis. Numerical investigations are presented to validate the fictitious physical model and the geometric constraint for excluding “floating” islands. Finally, topology optimization for fluid diodes with and without the geometric constraint is performed, and the result demonstrates that the proposed method is capable of generating fluid diodes with wall connectivity, while maintaining a good functional performance.

Optimized design for integrated sensing and communication in secure MIMO SWIPT systems

This paper investigates a secure multiple-input multiple-output integrated sensing and communication (MIMO ISAC)-enabled untrusted simultaneous wireless information and power transfer (SWIPT) system in which a base station is concurrently responsible for three different functionalities of communicating with users, sensing targets, and powering energy harvesting (EH) devices. These EH devices are assumed to be untrusted and potentially wiretap the information intended for legitimate users. This paper considers three different system design strategies: (i) communication-centric design, (ii) sensing-centric design, and (iii) EH-centric design. In each strategy, we aim to jointly design the transmit communication precoders and sensing precoder (which also acts as both the energy beam for EH and the artificial noise for securing communication) subject to requirements corresponding to the transmit power budget, minimum achievable secrecy rate, minimum amount of harvested energy, and maximum beampattern similarity constraint. The optimization design problems are highly non-convex, and thus it is mathematically challenging to directly find the optimal solutions. To overcome this issue, we first derive convex inner approximations, and then utilize the sequential convex programming (SCP) approach to develop efficient iterative algorithms which converge at least to a locally optimal solution. Extensive numerical results are simulated to verify the optimality of developed algorithms and highlight the impact of sensing on the system secrecy rate and harvested energy.

Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Swarm Intelligence-based metaheuristic algorithms are widely applied to global optimization and engineering design problems. However, these algorithms often suffer from two main drawbacks: susceptibility to the local optima in large search space and slow convergence rate. To address these issues, this paper develops a novel cooperative metaheuristic algorithm (CMA), which is inspired by heterosis theory. Firstly, simulating hybrid rice optimization algorithm (HRO) constucted based on heterosis theory, the population is sorted by fitness and divided into three subpopulations, corresponding to the maintainer, restorer, and sterile line in HRO, respectively, which engage in cooperative evolution. Subsequently, in each subpopulation, a novel three-phase local optima avoidance technique-Search-Escape-Synchronize (SES) is introduced. In the search phase, the well-established Particle Swarm Optimization algorithm (PSO) is used for global exploration. During the escape phase, escape energy is dynamically calculated for each agent. If it exceeds a threshold, a large-scale Lévy flight jump is performed; otherwise, PSO continues to conduct the local search. In the synchronize phase, the best solutions from subpopulations are shared through an elite-based strategy, while the classical Ant Colony Optimization algorithm is employed to perform fine-tuned local optimization near the shared optimal solutions. This process accelerates convergence, maintains population diversity, and ensures a balanced transition between global exploration and local exploitation. To validate the effectiveness of CMA, this study evaluates the algorithm using 26 well-known benchmark functions and 5 real-world engineering problems. Experimental results demonstrate that CMA outperforms the 10 state-of-the-art algorithms evaluated in the study, which is a very promising for engineering optimization problem solving.

Comprehensive Geometric Parameterization and Computationally Efficient 3D Shape Matching Optimization of Realistic Stents

Abstract Flexible and compact shape representation schemes are essential for design optimization problems. Current shape representation schemes for coronary stent designs concern predominantly idealized or independent ring (IR) designs, which are outdated and only consider a small number of core design variables (such as strut width, height, and thickness) and ignore clinically critical design characteristics such as the number of connectors. No reports exist on the geometry parameterization of the latest helical stents (HS) that have more complex geometric designs than IR stents. Here, we present two new shape parameterization schemes to fully capture the 3D designs of contemporary IR and double-helix HS stents. We developed a 3D stent geometry builder based on 17 (IR) and 18 (HS) design variables, including strut width, thickness, height, number of connectors and rings, stent length, and strut centerline shape. The shape of the strut centerline was derived via a combination of NURBS, PARSEC, quarter circle, and straight line segments. Shape matching for complex 3D geometries, such as the contemporary stents within limited function evaluations, is not trivial and requires efficient parameterization and optimization algorithms. We used shape matching optimization with a limited function evaluation budget to test the proposed parameterization and two surrogate-assisted optimization algorithms relying on predictor believer and an expected improvement maximization formulation. The performance of these algorithms is objectively compared with a gradient-based optimization method to highlight their strengths. Our work paves the way for more realistic, full-fledged stent design optimization with structural and hemodynamic objectives in the future.

Application of a novel metaheuristic algorithm inspired by connected banking system in truss size and layout optimum design problems and optimization problems

Optimum design of truss structures can be a challenging and difficult field of study specially if an optimum design problem is comprised of continuous and discrete decision variables such as in truss size and layout optimization problems. Usually metaheuristic approaches are selected to solve these kind of problems and there are many different metaheuristic methods that have been used in dealing with truss optimization problems, which provide optimum solutions for those problems. However, among these various proposed metaheuristics, it is very seldom to face and find a method that is based on technologies such as computer networks. This paper aims to utilize a metaheuristic algorithm which is based on some principals of connected banking systems, which is called the Connected Banking System Optimizer(CBSO) algorithm. The performance of the CBSO is tested against three benchmark truss size/layout optimum design problems namely 15, 18 and 25 bar truss structures. Besides the truss size/layout problems, CEC-BC-2017 test functions with ten dimensions and also three other constrained optimum design problems are also investigated to examine the performance of the CBSO in dealing with these standard unconstrained and constrained test functions. The results of the CBSO optimum designs are presented and compared with some of the available studies in the literature. Statistical analyses are done to have a fair evaluation of the CBSO algorithm’s efficiency and its ability in dealing with the benchmark truss size/layout optimization problems. The CBSO outperforms its rivals and presents lighter weight truss structures. There is no need for configuration of extra parameters in the CBSO algorithm when solving the examined benchmark truss structures, which makes it a robust parameter-free optimization algorithm.

Airfoil Separation Constraint Formulation for Aerodynamic Shape Optimization

Airfoil design using numerical optimization has addressed the problem of minimizing drag for a given lift constraint for one or more flight conditions. However, designers often want to avoid separation at off-design conditions regardless of the drag. This paper develops a separation constraint formulation for airfoil shape optimization. We perform multipoint optimizations and demonstrate how a separation constraint yields practical airfoil shapes. We compare results from single-point optimizations with and without a leading-edge radius constraint, which is a simple approach used as a surrogate to avoid separation, to an optimization where separation is constrained at a low-speed high-lift off-design point. Constraining the leading-edge edge radius improves the high-lift performance of the airfoil but not as much as constraining separation at the off-design point. We also compare the results of separation-constrained optimizations with optimizations where the drag at an off-design point is included in the objective. The latter formulation also produces optimal designs that are separation-free at the off-design points. However, the separation-constrained formulation produces airfoils with better cruise performance. Finally, we demonstrate the separation constraint efficacy at the off-design point with multiple cruise points. The results help guide parameterization and constraint formulation for airfoil design optimization problems.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

Using of Grasshopper Optimization Algorithm Approach for Optimal Weight Design Problem of the Spur Gear

Gears are undoubtedly the most important parts of motion transmission. One way to increase the motion performance of the system is to reduce the weights of the gears without sacrificing the strength capability. Today, various optimization techniques that rely heavily on analytical and heuristic approaches are used for this problem. In this study, the gear optimization problem in accordance with the minimum weight was solved with Grasshopper Optimization Algorithm (GOA). Introduced in recent years, GOA is a meta-heuristic optimization technique that stands out with its successful performance in engineering applications. This approach was used in a spur gear formation case as per the minimum weight for the first time. Compared to previous studies, the results obtained in this paper show that it is possible to design a lighter gear with GOA.

A semi-definite optimization method for maximizing the shared band gap of topological photonic crystals

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together two photonic crystals with distinct topological invariants, and the corresponding eigenfrequencies are located in the shared band gap of two individual photonic crystals. This work is concerned with maximizing the shared band gap of two photonic crystals with different topological features in order to increase the bandwidth of the edge modes. We develop a semi-definite optimization framework for the underlying optimal design problem, which enables efficient update of dielectric functions at each time step while respecting symmetry constraints and, when necessary, the constraints on topological invariants. At each iteration, we perform sensitivity analysis of the band gap function and the topological invariant constraint function to linearize the optimization problem and solve a convex semi-definite programming (SDP) problem efficiently. Numerical examples show that the proposed algorithm is superior in generating optimized optical structures with robust edge modes.

Enhanced artificial hummingbird algorithm with chaotic traversal flight

Tackling the shortcomings of slow convergence, imprecision, and entrapment in local optima inherent in traditional meta-heuristic algorithms, this study presents the enhanced artificial hummingbird algorithm with chaotic traversal flight (CEAHA), which employs chaotic ergodicity within the foundational framework of the conventional artificial hummingbird algorithm. This approach implements chaotic motion within local regions of the solution space, ensuring a thorough exploration of potential optima and preventing algorithmic stagnation at local maxima by guaranteeing a non-repetitive traversal of all search states. This study also analyzes the intrinsic mechanisms by which eight different chaotic mappings affect optimization performance, from the perspectives of invariant measures and traversal efficiency of ergodic chaotic motion. In comparative tests with 21 meta-heuristic algorithms on the CEC2014, CEC2019, and CEC2022 benchmark suites across various dimensions, CEAHA demonstrates superior optimization performance. Furthermore, the practicability and robustness of CEAHA have been confirmed in mechanical design optimization problems through 4 engineering instances: pressure vessel, gear trains, speed reducers, and piston levers.

Cost minimization of membrane-based separation systems for H2 recovery: A comparison of two optimization approaches

This paper addresses the optimization of membrane-based processes, with a specific focus on H2 recovery in hydrocarbon processing plants. A comparative analysis of two optimization approaches is conducted for designing H2 recovery systems for a multicomponent gas mixture containing H2/N2/CO2/CO. The main objective is to achieve the desired H2 recovery and product purity levels while minimizing costs. The paper compares two approaches for optimization: the first uses a simulation-based optimization technique with Aspen Custom Modeler/ASPEN Plus, while the second employs a simultaneous optimization method using GAMS (General Algebraic Modeling System). The methods are thoroughly compared, evaluating their strengths and weaknesses through qualitative and numerical assessments. To this end, a reference case was selected from the existing literature. The results obtained indicate that both proposed approaches are suitable for optimizing the design of a two-stage membrane configuration, as evidenced by the similarity of the optimal solutions obtained from both approaches. Subsequently, based on the analysis of numerical values for the optimal design problem for the investigated two-stage membrane configuration, a hybrid strategy for the optimal synthesis and design of multi-stage separation processes is proposed.The study fills a gap in the literature by providing a comprehensive analysis of the advantages and disadvantages of optimization approaches in the context of technology of separation of gases. This research provides valuable insights into the field and offers guidance for selecting appropriate approaches to improve the efficiency and cost-effectiveness of gas separation processes in real-world applications.

A rapid-convergent particle swarm optimization approach for multiscale design of high-permeance seawater reverse osmosis systems

Directly solving sophisticated partial differential equation constrained optimization problems is not only extremely time-consuming, but also very hard to find unique optimal solutions. Here, we propose stable and efficient surrogate models for seawater reverse osmosis desalination processes that enable thorough quantitative description of hydrodynamics and local transport characteristics in narrow flow channels. Without iteratively solving complex multi-physics simulation problem taking several hours, the proposed multi-scale design optimization framework significantly reduces the problem complexity by computing the surrogate models in seconds. Moreover, a fast-converging active subspace particle swarm optimization framework is proposed to address the optimal design problem. Compared to the standard particle swarm optimization algorithm, the proposed method enhances the average optimum by 14% and the standard deviation of optimum results for multiple runs is reduced by no less than ten times. The optimized desalination system achieves 9% reduction on energy consumption and 30% improvement on water production efficiency.

Photoacoustic Waveform Design for Optimal Parameter Estimation Based on Maximum Mutual Information

Waveform design is a potentially significant approach to improve the performance of an imaging or detection system. Photoacoustic imaging is a rapidly developing field in recent years; however, photoacoustic waveform design has not been extensively investigated. This paper considers the problem of photoacoustic waveform design for parameter estimation under constraints on input energy. The use of information theory is exploited to formulate and solve this optimal waveform design problem. The approach yields the optimal waveform power spectral density. Direct inverse Fourier transform of the optimal waveform frequency spectrum amplitude is proposed to obtain a real waveform in the time domain. Absorbers are assumed to be stochastic absorber ensembles with uncertain duration and location parameters. Simulation results show the relationship between absorber parameter distribution and the characteristics of optimal waveforms. Comparison of optimal waveforms for estimation, optimal waveforms for detection (signal-to-noise ratio) and other commonly used waveforms are also discussed. The symmetry properties of the forward and inverse Fourier Transforms are used to analyze the time and frequency properties and provide a heuristic view of how different goals affect the choice of waveform.

Directed interactive topology optimization design for multi-agent affine formation maneuver control

This paper investigates the directed interactive topology optimization design problem for multi-agent affine formation maneuver control. Firstly, considering the optimization indexes such as information interaction cost and information spreading energy consumption, a directed topology optimization model satisfying affine formation maneuver is established, including two sub-models of topology structure construction and weight allocation. Secondly, aiming at the topological structure construction for affine formation maneuver, a directed k-rooted graph detection method is proposed, which can realize the solution of d +1 -rooted constraint for directed information interaction topology, and then an improved NSGA-II topological structure construction optimization algorithm is designed. Finally, a formation of seven agents in twodimensional space is taken as an example for simulation verification. The results show that the improved topology NSGA -II topology construction optimization The algorithm has better optimization effects, can effectively provide a variety of feasible directed interactive topologies for affine formation maneuver control, and the generated interactive topology can meet the requirements of directed d +1 -rooted graph.

Boosting Engineering Optimization With a Novel Recursive Transfer Bifidelity Surrogate Modeling

Abstract In the engineering optimization, there often exist the multiple sources of information with different fidelity levels. In general, low-fidelity (LF) information is usually more accessible than high-fidelity (HF) information, while the latter is usually more accurate than the former. Thus, to capitalize on the advantages of this information, this study proposes a novel recursive transfer bifidelity surrogate modeling to fuse information from HF and LF levels. First, the selection method of optimal scale factor is proposed for constructing bifidelity surrogate model. Then, a recursive method is developed to further improve its performance. The efficacy of the proposed model is comprehensively evaluated using numerical problems and an engineering example. Comparative analysis with some surrogate models (five multifidelity and a single-fidelity surrogate models) demonstrates the superior prediction accuracy and robustness of the proposed model. Additionally, the impact of varying cost ratios and combinations of HF and LF samples on the performance of the proposed model is also investigated, yielding consistent results. Overall, the proposed model has superior performance and holds potential for practical applications in engineering design optimization problems.

Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm

Abstract Electric vehicles have become a standard means of transportation in the last 10 years. This paper aims to formalize design optimization problems for electric vehicle components. It presents a tool conceptual design technique with a hunger games search optimizer that incorporates dynamic adversary-based learning and diversity leader (referred to as HGS-DOL-DIL) to overcome the local optimum trap and low convergence rate limitations of the Hunger Games search algorithm to improve the convergence rate. The performance of the proposed algorithms is studied on six widely used engineering design problems, complex constraints, and discrete variables. For the HGS-DOL-DIL practical feasibility analysis, a case study of shape optimization of an electric car suspension arm from the industry is carried out. Overall, the inclusion of the OL strategy has proven its superiority in solving real-world problems, especially in solving real-world problems such as shape optimization of an electric vehicle automobile suspension arm, showing that the algorithm improves the search space improves the solution quality, and reflects its potential to find global optimum solutions in a well-balanced exploration and exploitation phase.

Centroid opposition-based backtracking search algorithm for global optimization and engineering problems

Evolutionary algorithms (EAs) have a lot of potential to handle nonlinear and non-convex objective functions. Particularly, the backtracking search algorithm (BSA) is a popular nature-based evolutionary optimization method that has attracted many researchers due to its simple structure and efficiency in problem-solving across diverse fields. However, like other optimization algorithms, BSA is also prone to reduced diversity, local optima, and inadequate intensification capabilities. To overcome the flaws and increase the performance of BSA, this research proposes a centroid opposition-based backtracking search algorithm (CoBSA) for global optimization and engineering design problems. In CoBSA, specific individuals simultaneously acquire current and historical population knowledge to preserve population variety and improve exploration capability. On the other hand, other individuals execute the position from the current population's centroid opposition to progress convergence speed and exploitation potential. In addition, an elite process based on logistic chaotic local search was developed to improve the superiority of the current individuals. The suggested CoBSA was validated on a set of benchmark functions and then employed in a set of application examples. According to extensive numerical results and assessments, CoBSA outperformed the other state-of-the-art methods in terms of accurateness, reliability, and execution capability.

Truss sizing optimum design using a metaheuristic approach: Connected banking system

Several methods have been used to solve structural optimum design problems since the creation of a need for light weight design of structures and there is still no single method for solving the optimum design problems in structural engineering field that is capable of providing efficient solutions to all of the structural optimum design problems. Therefore, there are several proposed and utilized methods to deal with optimum design issues and problems, that sometimes give promising results and sometimes the solutions are quite unacceptable. This issue with metaheuristic algorithms, which are suitable approaches to solve these set of problems, is quite usual and is supported by the “No Free Lunch theorem”. Researchers try harder than the past to propose methods capable of presenting robust and optimal solutions in a wider range of structural optimum design problems, so that to find an algorithm that can cover a wider range of structural optimization problems and obtain a better optimum design. Truss structures are one of these problems which have extremely complex search spaces to conduct search procedures by metaheuristic algorithms. This paper proposes a method for optimum design of truss sizing problems. The presented method is used against 6 well-known benchmark truss structures (10 bar, 17 bar, 18 bar, 25 bar, 72 bar and 120 bar) and its results are compared with some of the available studies in the literature. The performance of the presented algorithm can be considered as very acceptable.