Development of a multi-objective optimization algorithm using surrogate models for coastal aquifer management

In chemical engineering design, process plants are often capable of turndown and flexible operation to maximise profitability depending on demand and price signals, and the optimisation of these processes needs to take into account the variability in the plant operation. By performing the optimisation with flexible operating conditions the overall plant performance can be improved. The optimisation process makes use of two computational modelling techniques: multi-objective optimisation (MOO) and surrogate modelling. Multi-objective optimisation allows for the optimisation of two or more competing variables simultaneously. In the cases studied here, the long individual simulation time coupled with the large number of individual simulations required meant that the total simulation time was prohibitive for dynamic MOO. In order to reduce computation time surrogate models of the processes are developed using artificial neural networks. A statistical dynamic modelling framework within a multi-objective optimisation methodology is developed to optimise a process plant’s performance. Here the dynamic modelling is used to optimise the economic and environmental performance of natural gas combined cycle power plant systems fitted with carbon capture and storage (CCS) and solar thermal energy (STE) in a time-integrated MOO framework. This framework allows for variable process inputs and flexible operation based on external signals, such as product price. By introducing a probabilistic approach to the modelling of flexible operation allows for more data to be included in the analysis. The methodology for dynamic modelling of flexible operation could be applied to other industrial processes that face similar dynamic economic and/or environmental conditions. From a CCS standpoint dynamic MOO was used to show that variable capture can be used to make the CCS plant more profitable over steady state operation. At a capture rate of 80 % the NPV of a gas turbine combined cycle with CCS improved by 38 m$AU by utilising flexible operation of the capture process. This also allows for various economic scenarios to incentivise the reduction of CO₂ emissions from natural gas based power plants, with the use of CCS and STE used to reduce the greenhouse emissions. The economic strategies of a carbon price and governmental grants are investigated to determine the levels of policy help to incentivise implementing CO₂ reduction technologies. In order to achieve a financial incentive for limiting CO₂ emissions from a combined cycle power plants equipped with CCS a government co-investment grant of 50 % of the capital costs and a carbon price of 83 $AU/tCO₂ is required.

A hyperparameter-optimized Kriging surrogate model was developed for the structural collapse behavior framework presented in this paper. The assessment is conducted on a stiffened panel subject to axial load and lateral pressure, typical of the deck structure of a bulk carrier ship. This behavior is characterized using nonlinear finite element analysis to determine the collapse response. The surrogate model’s hyperparameters were optimized using a Genetic Algorithm to achieve the best performance, and the trained framework can predict ultimate strength. By following this approach, the problem can be reformulated as a multi-objective optimization task. This framework involves associating the Kriging surrogate model with a multi-objective evolutionary optimization algorithm based on Genetic Algorithms to balance the trade-off between the weight and ultimate strength of the stiffened panel. The results confirm the applicability of the Kriging surrogate framework to predict the ultimate strength and assess the collapse analysis of the stiffened panels, ensuring accuracy through GA-based hyperparameter optimization.

With the complexity of mechanical manufacturing system design increasing, the traditional single-objective optimization method can no longer meet the needs of multi-objective optimization, such as lightweight, high efficiency, low energy consumption and long life. Multi-objective optimization algorithm is widely used in mechanical design and manufacturing process planning because of its good convergence and diversity. Taking robot motion planning as an example, this paper analyzes the application methods of multi-objective optimization algorithm in mechanical structure design in detail, including problem description, multi-objective optimization model construction, algorithm application and performance analysis. Through the application of Genetic Algorithm (GA), this paper shows how the multi-objective optimization algorithm can balance multiple objectives such as path length, energy consumption and obstacle avoidance effect, and realize more intelligent and efficient solutions in robot motion planning. Performance analysis shows that GA is superior to single-objective optimization and random search algorithm in optimization effect, computational efficiency and stability. In addition, this paper also discusses the influence of the change of target weight and algorithm parameters on the optimization results, which provides valuable reference for future algorithm optimization and practical application. Multi-objective optimization algorithm shows obvious advantages in mechanical manufacturing system, which provides new ideas and methods for realizing more efficient, more environmentally friendly and more intelligent mechanical manufacturing design.

<div>Continuous rubber track systems for heavy applications are typically designed using multiple iterations of full-scale physical prototypes. This costly and time-consuming approach limits the possibility of exploring the design space and understanding how the design space of that kind of system is governed. A multibody dynamic simulation has recently been developed, but its complexity (due to the number of model’s inputs) makes it difficult to understand and too expensive to be used with multi-objective optimization algorithms (approximately 3 h on a desktop computer).</div> <div>This article aims to propose a first design space exploration of continuous rubber track systems via multi-objective optimization methods. Using an existing expensive multibody dynamic model as original function, surrogate models (artificial neural networks) have been trained to predict the simulation responses. These artificial neural networks are then used to explore the design space efficiently by using optimization algorithms. Sensitivity studies and multi-objective optimization were carried out on surrogate models to identify high-impact design parameters and potential improvements ranging from 2.24% to 17.2% compared to the current design of reference (CTS halftrack system) on wheel load, track pinch, and maximum required torque to cross a bump.</div>

This study presents a method that combines two deep learning models—the surrogate model and the bandgap optimization model—to design 1-D Phononic Crystals. The surrogate model is trained to predict the bandgaps of Phononic Crystals, while the bandgap optimization model is used to determine their geometric parameters. The goal is to leverage deep learning’s ability to capture complex input-output relationships and exploit the inherent optimization capabilities of these models. To improve design accuracy and account for manufacturing constraints, a user-defined activation function is incorporated into the optimization model. Various loss functions are introduced to address different design objectives, such as maximizing the bandgap at a lower frequency or maximizing while aligning the center frequency of the bandgap with a specified value. The 1-D Phononic Crystal designed for bandgap maximization at lower frequencies using this method outperformed results predicted by a Genetic Algorithm. Unlike previous studies that often rely on deep learning only as a predictive tool or require external optimizers, our method uses a deep learning model directly as an optimization engine. The integration of customizable loss functions, user-defined physical constraints, and an unsupervised training approach enables versatile and efficient design without the need for labeled optimization datasets. The approach is readily extensible to 2-D and 3-D configurations, offering a versatile solution for advanced Phononic Crystal design.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

A data-driven optimization framework that integrates machine learning surrogate models, finite element analysis (FEA), and a multi-objective optimization algorithm is used in this study for developing thermoplastic elastomer (TPE) parts for aerospace applications. By using FEA simulations and experiments, a database of input design parameters (e.g., geometry and structural shape modifier) is generated. Afterwards, we train surrogate models (e.g., Gaussian Process Regression, neural networks) to approximate mappings from design space to performance space. Finally, we propose Pareto-optimal TPE designs using the surrogate embedded in a multi-objective optimization loop (such as NSGA-II or gradient-based methods). The novelty of this approach is demonstrated by employing highly simplified surrogate models, including an artificial neural network (ANN) with 10 hidden neurons trained on analytically generated synthetic data. The proposed methodology has been validated using an aerospace-related case study: a vibration-damping plate. Compared with the baseline configuration, Pareto-optimal designs identified by the proposed framework achieved a reduction in maximum deflection of 23%–28% and a reduction in von Mises stress of 18%–24%, depending on the selected trade-off solution, as the number of full FEA simulations required for optimization was reduced from 500 to 50. This framework enables faster design of TPE components for aerospace systems. Validation against high-fidelity ANSYS simulations showed a mean error of ~1.18% and a maximum deviation of ~2.6%.

In order to solve the problem of the multi-objective spectrum allocation on the joint optimization of maximal network utility and fairness of users in cognitive radio network, based on quantum bee colony theory and membrane computing, a novel multi-objective discrete combinatorial optimization algorithm, named membrane-inspired quantum bee optimization, is proposed. The global optimal solution of single objective can be searched in the elementary membranes, and Pareto front solutions which take account of network utility and fairness, can be obtained from skin membrane with the proposed method. The multi-objective optimization algorithm, which can solve both single objective and multi-objective optimization problems at the same time, is designed by the communication rules between membranes, the cooperative evolution of foraging behavior based on quantum state, and non-dominated sorting. Compared with classical color-sensitive graph coloring algorithm, genetic algorithm, quantum genetic algorithm, and particle swarm optimization under different objective functions, the proposed spectrum allocation method can search the global optimal solution of single objective as shown by the simulation results, and it is superior to classical spectrum allocation algorithms and existing intelligence spectrum allocation methods. The optimal Pareto front solutions of multi-objective spectrum allocation are also obtained.

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

It is hard to simultaneously improve the peak efficiency (η *) and the width of the high-efficiency region ( Gη) for a hydrodynamic torque converter. A combination of comprehensive CFD simulation and multi-objective optimization was pretested. The elaborate CFD simulation calculation included a reasonable mesh layout, a robust algorithm and a correct turbulence model, whose results were also experimentally verified. In our study, the Kriging surrogate model was first used to construct a nonlinear relationship between the inlet and outlet angle and the economic performance index of the hydrodynamic torque converter. To ensure that the accuracy of the surrogate model meet the requirements, we also used 10 sets of sample points to verify the accuracy of our surrogate model. The accuracy is found to meet the requirements, which shows that the accuracy of the constructed surrogate model is relatively high. We choose to apply the second-generation non-dominant sorting genetic algorithm (NSGA-II) to solve our problem. After solving the Pareto frontier solution set, we obtain a set of global optimal solutions on the Pareto frontier solution set. The optimization results show that the η * is increased by 2.49% and that the Gη is increased by 14.23%. We extracted the flow field structure near the turbine region, characterized the difference between original and optimal model from the flow field perspective, and demonstrated the accuracy of our optimization results. Finally, we used CFD to verify our optimization results, further illustrating the accuracy of the optimization results prediction. Literature research indicates that a large amount of experiments to optimize the η * and the Gη of the hydrodynamic torque converter will bring huge trial cost and time cost. We conclude from our research that the proposed calculation method can solve such problems well.

An integrated optimization strategy based on Kriging model and multi-objective particle swarm optimization (PSO) algorithm was constructed. As a new surrogate model technology, Kriging model has better fitting precision for nonlinear problem. The Kriging model was adopted to replace computer aided engineering (CAE) simulation as fitness function of multi-objective PSO algorithm, and the computation cost can be reduced greatly. By introducing multi-objective handling mechanism of crowding distance and mutation operator to multi-objective PSO algorithm, the entire Pareto front can be approximated better. It is shown that the multi-objective optimization strategy can get higher solving accuracy and computation efficiency under small sample.

Multiobjective optimization on cooperative control of autonomous emergency steering and occupant restraint system for enhancing occupant safety

Battle Royale Optimizer (BRO) is a recently proposed optimization algorithm that has added a new category named game-based optimization algorithms to the existing categorization of optimization algorithms. Both continuous and binary versions of this algorithm have already been proposed. Generally, optimization problems can be divided into single-objective and multi-objective problems. Although BRO has successfully solved single-objective optimization problems, no multi-objective version has been proposed for it yet. This gap motivated us to design and implement the multi-objective version of BRO (MOBRO). Although there are some multi-objective optimization algorithms in the literature, according to the no-free-lunch theorem, no optimization algorithm can efficiently solve all optimization problems. We applied the proposed algorithm to four benchmark datasets: CEC 2009, CEC 2018, ZDT, and DTLZ. We measured the performance of MOBRO based on three aspects: convergence, spread, and distribution, using three performance criteria: inverted generational distance, maximum spread, and spacing. We also compared its obtained results with those of three state-of-the-art optimization algorithms: the multi-objective Gray Wolf optimization algorithm (MOGWO), the multi-objective particle swarm optimization algorithm (MOPSO), the multi-objective artificial vulture's optimization algorithm (MOAVAO), the optimization algorithm for multi-objective problems (MAOA), and the multi-objective non-dominated sorting genetic algorithm III (NSGA-III). The obtained results approve that MOBRO outperforms the existing optimization algorithms in most of the benchmark suites and operates competitively with them in the others.

Relevant with some important subjects like target recognition, sensor fusion systems can be considered as one of the main issues highlighting here. Environmental condition, target characteristic and sensor efficiency are three parameters which can impress on sensor value in target recognition so for recognizing targets, a group of sensors which have more recognition rates, must be selected intelligently. Utilizing many sensors to acquire the highest object recognition rate would have extra cost and decrease energy of mobile sensors rapidly. Therefore make a tradeoff between sensor numbers and object recognition rate would be imperatively. This paper attempts to design a multi objective optimization service by using optimization algorithm and neural network. This service specifies highest recognition rate for each distinct sensor numbers. We propose multi objective optimization algorithm to help accessing the best sensory configuration for a definite environment regarding to the environmental conditions, sensors performance, and object features. Our multi objective optimization algorithm has two functions. Genetic algorithm is used to perform as one of functions to specify object recognition rates of each sensor group. Neural network is used to perform as fitness function of each genetic algorithm chromosomes. Another function is sensor numbers determinant. Highest recognition rate and lowest sensor numbers are two objects which multi objective optimization algorithm wants to make a balance between them. We define 500 different scenarios for 6 different sensors in different conditions. Object recognition rate of each sensor is collected. These rates are used for neural networks training process. By defining new scenario and run multi objective optimization algorithm in this scenario, this algorithm makes a Pareto front between sensor numbers and object recognition rate. Finally this algorithm finds, by distinct numbers of sensor, which sensors by which recognition ability must be used to reach the highest recognition rate.