Single-objective Optimization Research Articles

Multi-objective optimization of a bistable curved shell with controllable thickness based on machine learning

Bistable curved shells have become a promising low-cost application in energy absorption fields owing to recent advances in material and technology. Significant research has been conducted to improve their energy absorption effect through forward prediction and single-objective optimization. However, these approaches may not fully explore their functional potential. In this study, we propose a multi-objective optimization framework based on the principle of main objective optimization that combines neural networks and genetic algorithms. The energy absorption effect and backward snapping force of the bistable curved shell are improved synchronously. Meanwhile, a reverse design algorithm is developed to generate the preset load-displacement curve, which further expands the application of machine learning methods in the field of multi-objective optimization. The combination of machine learning and multi-objective optimization is highly effective for building meta-structures with specific performance requirements and has potential applications in solving complex optimization tasks in various fields.

Multi-strategy learning-based particle swarm optimization algorithm for COVID-19 threshold segmentation

With advancements in science and technology, the depth of human research on COVID-19 is increasing, making the investigation of medical images a focal point. Image segmentation, a crucial step preceding image processing, holds significance in the realm of medical image analysis. Traditional threshold image segmentation proves to be less efficient, posing challenges in selecting an appropriate threshold value. In response to these issues, this paper introduces Inner-based multi-strategy particle swarm optimization (IPSOsono) for conducting numerical experiments and enhancing threshold image segmentation in COVID-19 medical images. A novel dynamic oscillatory weight, derived from the PSO variant for single-objective numerical optimization (PSOsono) is incorporated. Simultaneously, the historical optimal positions of individuals in the particle swarm undergo random updates, diminishing the likelihood of algorithm stagnation and local optima. Moreover, an inner selection learning mechanism is proposed in the update of optimal positions, dynamically refining the global optimal solution. In the CEC 2013 benchmark test, PSOsono demonstrates a certain advantage in optimization capability compared to algorithms proposed in recent years, proving the effectiveness and feasibility of PSOsono. In the Minimum Cross Entropy threshold segmentation experiments for COVID-19, PSOsono exhibits a more prominent segmentation capability compared to other algorithms, showing good generalization across 6 CT images and further validating the practicality of the algorithm.

Estimation single output with a hybrid of ANFIS and MOPSO_HS

In the field of soft computing, the Adaptive Neuro-Fuzzy Inference System (ANFIS) has been more well-liked in recent years for its predictive capabilities. Appropriate ANFIS parameter adjusting is critical, which creates a gap in its predictive integration with traditional optimization techniques. Although some academics have concentrated on incorporating single-objective optimization, they frequently encounter issues with reliability and stability when striving to solve problems. In this work, an innovative multi-objective optimization technique that integrates ANFIS with MOPSO_HS is introduced. The model has consistency in problem solving and shows accurate predictions for both odd and even interval input models. In addition, three actual datasets are used to demonstrate the effectiveness of the suggested model's integration. A comparison is made between the suggested integrated model and established algorithms after 20 runs of analysis. The algorithm's accuracy, stability, and dependability in resolving integration problems are demonstrated by the results, which also show how superior it is to alternative approaches.

Operation optimization and performance evaluation of a ventilated heating floor in a nearly-zero-energy building with mixed power

With the proportion of renewable energy in the construction sector increasing and the structure of energy systems becoming increasingly complex, it is crucial to optimize the operation strategy of building energy systems with thermal energy storage for improving multi-performance. However, conventional heuristic optimization algorithm exhibits low searching speed and converges slowly, which is hard for operation optimization of such systems. In this study, with a binary particle swarm optimization (BPSO) algorithm coupled with experience-based searching guiding strategy, the operation of a ventilated floor heating system in a nearly-zero-energy building was optimized . System performance under different optimization objectives and combinations, including reducing operation cost and carbon emission fee, meanwhile increasing wind power consumption and thermal comfort time, was investigated. Results show that with the experience-based accelerating strategy, the BPSO algorithm converged fast and found more reasonable solutions. In contrast, multi-objective optimization yielded better and diverse feasible solutions were found than single-objective optimization. By optimizing operating costs, wind power consumption, and environmental costs, the best comprehensive solution was obtained. The cost range of energy consumption and carbon emissions within 10 days is 19.24–22.17 yuan and 17.45–20.11 yuan, respectively. The proportion of thermal comfort time is 95.39–95.82%. However, due to high thermal insulation level, thermal comfort time under different optimization objectives showed little difference.

Improved Finite Element Model Updating of a Highway Viaduct Using Acceleration and Strain Data.

Most finite element model updating (FEMU) studies on bridges are acceleration-based due to their lower cost and ease of use compared to strain- or displacement-based methods, which entail costly experiments and traffic disruptions. This leads to a scarcity of comprehensive studies incorporating strain measurements. This study employed the strain- and acceleration-based FEMU analyses performed on a more than 50-year-old multi-span concrete highway viaduct. Mid-span strains under heavy vehicles were considered for the strain-based FEMU, and frequencies and mode shapes for the acceleration-based FEMU. The analyses were performed separately for up to three variables, representing Young's modulus adjustment factors for different groups of structural elements. FEMU studies considered residual minimisation and the error-domain model falsification (EDMF) methodology. The residual minimisation utilised four different single-objective optimisations focusing on strains, frequencies, and mode shapes. Strain- and frequency-based FEMU analyses resulted in an approximately 20% increase in the overall superstructure's design stiffness. This study shows the benefits of the intuitive EDMF over residual minimisation for FEMU, where information gained from the strain data, in addition to the acceleration data, manifests more sensible updated variables. EDMF finally resulted in a 25-50% overestimated design stiffness of internal main girders.

Research on Multibeam Bathymetric System Based on Greedy Algorithm and Variable Step Size Traversal Algorithm

Multi-beam bathymetry system is an advanced technology to measure the seabed based on single-beam bathymetry. In this paper, the greedy algorithm and variable step traversal method will be used to establish the mathematical models of coverage width and overlapping rate of adjacent strips of multi-beam sounding, and the best scheme of survey line layout will be designed by establishing the optimization model. According to the established mathematical model of overlap rate, the mathematical model of coverage width of multi-beam sounding in three-dimensional rectangular waters is optimized. Finally, according to the real life, with the overlapping rate of adjacent strips within 10% to 20% as the limiting condition and the minimum total length of survey lines as the objective function, a single-objective optimization model is established. Then, Python is used to solve the problem through greedy algorithm and variable step-size traversal algorithm, and it is found that the included angle of survey line direction in the optimal scheme is 90, and the minimum total length of survey line is 68 nautical miles. Stability analysis is carried out by changing the constraint range of overlap rate.

An adaptive differential evolution algorithm with multi-strategy for solving complex optimization problem

In this paper, an adaptive differential evolution algorithm with multi-strategy, namely ESADE is proposed to solve the premature convergence and high time complexity for complex optimization problem. In the ESADE, the population is divided into several sub-populations after the fitness value of each individual is sorted. Then different mutation strategies are proposed for different populations to balance the global exploration and local optimization. Next, a new self-adaptive strategy is designed adjust parameters to avoid falling into local optimum while the convergence accuracy has reached its maximum value. And a complex airport gate allocation multi-objective optimization model with the maximum flight allocation rate, the maximum near gate allocation rate, and the maximum passenger rate at near gate is constructed, which is divided into several single-objective optimization model. Finally, the ESADE is applied solve airport gate allocation optimization model. The experiment results show that the proposed ESADE algorithm can effectively solve the complex airport gate allocation problem and achieve ideal airport gate allocation results by comparing with the current common heuristic optimization algorithms.

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

A review of nature-inspired algorithms on single-objective optimization problems from 2019 to 2023

The field of nature inspired algorithm (NIA) is a vital area of research that consistently aids in solving optimization problems. One of the metaheuristic algorithm classifications that has drawn attention from researchers in recent decades is NIA. It makes a significant contribution by addressing numerous large-scale problems and achieving the best results. This research aims to identify the optimal NIA for solving single-objective optimization problems. The NIA discovered between 2019 and 2023 is presented in this study with a brief description. About 83 distinct NIAs have been studied in this study in order to address the optimization issues. In order to accomplish this goal, we have taken into consideration eight real-world single-objective optimization problems: the 3-bar truss design problem, the rolling element bearing, the pressure vessel, the cantilever beam, the I beam, the design of a welded beam, and the design of a spring. Based on a comparative study and bibliographic analysis, we have determined that two algorithms—the flow direction algorithm, and prairie dog optimization—give us the best results and optimal solutions for all eight of the engineering problems listed. Lastly, some perspectives on the limitations, difficulties, and future course are provided. In addition to providing future research guidelines, this will assist the novice and emerging researcher in providing a more comprehensive perspective on advanced NIA.

Power allocation scheme for sum rate and fairness trade-off in downlink NOMA networks

Non-orthogonal multiple access (NOMA) is an essential enabler technology that is expected to help satisfy the key requirements of increased system throughput in future wireless networks. However, another equally important aspect that should go hand-in-hand with system throughput is user fairness for any network. But, to the best of our knowledge, even though there have been works that look at system throughput or user fairness maximization for NOMA-based networks, they looked at these as a single objective optimization problem, where one is the objective and the other is one of the constraints. However, quite often, joint optimization of both system throughput and user fairness is required to make optimized decisions in the face of trade-offs between these two equally important but conflicting objectives. In this regard, this paper formulates a multi-objective optimization problem to jointly maximize the sum rate and user fairness in a downlink transmission NOMA system, through optimize power allocation (PA), under system-imposed constraints. A weighted sum approach is used to turn the multi-objective optimization problem into a single-objective optimization problem to make it analytically tractable. The optimized PA is then obtained using Lagrange dual decomposition method and Karush–Kuhn–Tucker (KKT) conditions. Using our derived expressions, we propose an iterative PA algorithm that converges fast enough to be employed in practical NOMA networks. We also present simulation results to highlight the effectiveness of the proposed solution. Further, the performance of the proposed method is compared with that of the benchmark methods.

Route and charging planning for electric vehicles: a multi-objective approach

ABSTRACT Electric vehicle (EV) travel planning is a complex task that involves optimizing both the routes and the charging sessions for EVs. Existing algorithms rely on single-objective optimization, which limits their ability to consider EV users’ multiple, often conflicting objectives. In this paper, we introduce a new, genuinely multi-objective approach to EV travel planning, which can find Pareto sets containing multiple EV travel plans optimized simultaneously for multiple objectives. We focus on the bi-objective optimization for travel time and cost. To our knowledge, our algorithm is the first to perform such a genuine multi-objective optimization on realistically large country-scale problem instances involving 12,000 charging stations. We implemented our approach into a fully operational prototype application and extensively evaluated it on real-world data. Our results show that our approach can achieve practically usable planning times with only a minor loss of solution quality despite the very high computational complexity of the problem.

Augmenting bi-objective branch and bound by scalarization-based information

While branch and bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective branch and bound methods are only rarely applied compared to the predominant objective space methods. In this paper we propose modifications to increase the performance of multi-objective branch and bound algorithms by utilizing scalarization-based information. We use the hypervolume indicator as a measure for the gap between lower and upper bound set to implement a multi-objective best-first strategy. By adaptively solving scalarizations in the root node to integer optimality we improve both, upper and lower bound set. The obtained lower bound can then be integrated into the lower bounds of all active nodes, while the determined solution is added to the upper bound set. Numerical experiments show that the number of investigated nodes can be significantly reduced by up to 83% and the total computation time can be reduced by up to 80%.

The Multiobjective Control Based on Tolerance Optimization in a Multienergy System

To address the issue of multiobjective control in multienergy systems with diverse operational objectives, a two-stage optimization framework based on expected point tolerance has been proposed in this paper. In the first stage, a single objective function is used for optimization control to obtain the expected point of the multiobjective optimization problem. Then, in the second stage, by defining the allowable deviation between each optimization objective and the expected point, the original multiobjective optimization problem is transformed into a single objective optimization problem solution with tolerance measurement. Finally, in the simulation scene of a multienergy system, it is demonstrated that compared with the optimal results under each single objective method, the proposed method increases power line loss, maximum voltage deviation, new energy consumption, and economy by 2.22, 2.30, 1.02, and 2.45 times, respectively. Compared with the suboptimal results, the proposed method reduces power line loss by 22.26, 1.74, 1.09, and 0.97 times, respectively. Combining the shape of the Pareto frontier, it is demonstrated that the proposed method can comprehensively consider the needs of multiple power optimization objectives for forming a more reasonable and effective system optimization scheduling and also provide a new approach for solving multiobjective optimization problems.

Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm

This paper presents a comprehensive investigation into the application of the Improved Stochastic Ranking Evolution Strategy (ISRES) algorithm for the sizing and layout optimization of truss benchmark structures. Truss structures play a crucial role in engineering and architecture, and optimizing their designs can lead to more efficient and cost-effective solutions. The ISRES algorithm, known for its effectiveness in multi-objective optimization, is adapted for the single-objective optimization of truss designs with multiple design constraints. This study encompasses a wide range of truss benchmark structures, including 10-bar, 15-bar, 18-bar, 25-bar, and 72-bar configurations, each subjected to distinct loading conditions and stress constraints. The objective is to minimize the truss weight while ensuring stress and displacement limits are met. Through extensive experimentation, the ISRES algorithm demonstrates its ability to efficiently explore the solution space and converge to optimal solutions for each truss benchmark structure. The algorithm effectively handles the complexity of the problems, which involve numerous design variables, stress constraints, and nodal displacement limits. A comparative analysis is conducted to assess the performance of the ISRES algorithm against other state-of-the-art optimization methods reported in the literature. The comparison evaluates the quality of the solutions and the computational efficiency of each method. Furthermore, the optimized truss designs are subjected to finite element analysis to validate their structural integrity and stability. The verification process confirms that the designs adhere to the imposed constraints, ensuring the safety and reliability of the final truss configurations. The results of this study demonstrate the efficacy of the ISRES algorithm in providing practical and reliable solutions for the sizing and layout optimization of truss benchmark structures. The algorithm’s competitive performance and robustness make it a valuable tool for structural engineers and designers, offering a versatile and powerful approach for complex engineering optimization tasks. Overall, the findings contribute to the advancement of optimization techniques in structural engineering, promoting the development of more efficient and cost-effective truss designs for a wide range of engineering and architectural applications. The study’s insights empower practitioners to make informed decisions in selecting appropriate optimization strategies for complex truss-design scenarios, fostering advancements in structural engineering and sustainable design practices.

Global Opposition Learning and Diversity ENhancement based Differential Evolution with exponential crossover for numerical optimization

Since the inception of Differential Evolution (DE), the vast majority of studies on it indicate that exponential crossover does not solve the real-parameter optimization in continuous spaces very well. However, we find that once the appropriate crossover rate CR and its corresponding parameter control are found, the DE variants with exponential crossover can achieve comparable performance with the ones employing binomial crossover. In this paper, a new DE algorithm, called Global Opposition Learning and Diversity ENhancement based DE with exponential crossover (GOLDEN-DE), is proposed to fill the gap in this field. The GOLDEN-DE algorithm has the following highlights: First, a novel global opposition learning mechanism is proposed in our GOLDEN-DE algorithm; Second, a Novel Parameter Control, namely NPC technique, with fitness-independent characteristic is incorporated in the GOLDEN-DE algorithm. Third, a novel population Diversity ENhancement (DEN) mechanism is proposed, and individuals in the stagnation status can be re-calculated in order to enhance population diversity. Fourth, a time stamp mechanism for handling too old inferior solutions in the external archive is also put forward. We evaluate the GOLDEN-DE algorithm for real-parameter single-objective global optimization on 88 benchmarks from the three universal test sets, including CEC2013, CEC2014, and CEC2017 test suites, and experiment results show that our GOLDEN-DE algorithm is competitive with several state-of-the-art DE variants.

A cross-benchmark examination of feature-based algorithm selector generalization in single-objective numerical optimization

The task of selecting the best optimization algorithm for a particular problem is known as algorithm selection (AS). This involves training a model using landscape characteristics to predict algorithm performance, but a key challenge remains: making AS models generalize effectively to new, untrained benchmark suites. This study assesses AS models’ generalizability in single-objective numerical optimization across diverse benchmark suites. Using Exploratory Landscape Analysis (ELA) and transformer-based (TransOpt) features, the research investigates their individual and combined effectiveness in AS across four benchmarks: BBOB, AFFINE, RANDOM, and ZIGZAG. AS models perform differently based on benchmark suite similarities in algorithm performance distributions and single-best solvers. When suites align, these models underperform against a baseline predicting mean algorithm performance; yet, they outperform the baseline when suites differ in performance distributions and solvers. The AS models trained using the ELA landscape features are better than the models trained using the TransOpt features on the BBOB and AFFINE benchmark suites, while the opposite is true for the RANDOM benchmark suite. Ultimately, the study reveals challenges in accurately capturing algorithm performance through problem landscape features (ELA or TransOpt), impacting AS model applicability.

Quantum particle swarm optimization algorithm based on diversity migration strategy

Particle swarm optimization algorithm has been successfully applied to solve practical optimization problems due to its simplicity and efficiency. However, the traditional particle swarm optimization algorithm has inferior search performance in complicated high-dimensional optimization issues and is prone to falling into local optima. To address these problems, a new migration mechanism is introduced and a quantum particle swarm optimization method based on diversity migration is proposed. The strategy can capture different ranges of particles in the population, and the selection of migrating individuals depends not only on their fitness values but is also influenced by the positions within the population. The individual with the minimal average Hamming distance in the population can indicate the direction of iterative population optimization. After comparing the fitness values and the average Hamming distance between particles, the particles deviating from the central range of the population are replaced. The performance of the proposed algorithm is investigated under seven different sets of benchmark function optimization problems in the CEC2020 single-objective boundary-constrained optimization competition, and is compared with those of several other representative optimization algorithms. The quantum particle swarm optimization algorithm based on diversity migration strategy outperforms other typical optimization algorithms. Moreover, the proposed algorithm is convergent and stable.

A Bi-level optimization dispatch for hybrid shipboard microgrid considering electricity-gas-heat coupling

With the increasingly severe problem of air pollution and energy crisis, new energy power generation technology in ship has quickly become the focus of attention. Compared with traditional ships, hybrid shipboard microgrid systems can achieve pollution-free, renewable and high use value. However, the integration of electricity-gas-heat in hybrid energy shipboard microgrid system also poses challenges to current optimization methods. Therefore, this paper develops a bi-level optimization dispatch model for hybrid shipboard microgrid system based on multi-objective particle swarm optimization algorithm. Taking the diesel generators, photovoltaic generation system, energy storage system (ESS) and thermal energy storage equipment into account, a hybrid shipboard microgrid system model considering electricity-gas-heat coupling is constructed. Based on this, a bi-level optimization dispatch model is established to reduce total cost, GHG (GHG) emissions and lifespan loss of ESS. The upper-level model achieves the optimization dispatch of power generation equipment and loads; a lower-level optimization model with the goal of reducing the lifespan loss of ESS is constructed. The improved multi-objective and single-objective particle swarm optimization algorithms are introduced to find the optimal dispatch solutions for bi-level optimization dispatch model. Finally, simulation results show that the proposed optimization method can not only reduce the cost and GHG emissions by 8.7% and 10.9%, but also improve the cycle life of ESS by 9.2%.

Swarm-based multi-objective optimization of double-layered microchannel heat sink with hybrid solid-porous ribs

The current article focuses on the thermal and hydraulic optimization of a double-layered microchannel with hybrid solid-porous ribs. Therefore, for both upper and lower layers, solid-porous ribs, having different thickness ratios of porous and solid, are considered. The ratio of solid-porous thickness in the upper and lower layers and Reynolds number variations are taken into account as design variables. The present study is conducted to find an optimum design by which not only thermal performance improves, but also power consumption reduces. At the initial step, the double-layer microchannel is simulated using artificial neural network. The second step involves the application of the optimum network and the microchannel inputs for minimizing the thermal resistance and the power consumption single-objective and multi-objective type’s optimization problems are solved. The two mentioned optimization problems in the proposed strategy are targeted using four swarm-based algorithms. Results indicated that the designed neural network has a maximum error of 4% for producing the desired outputs. Moreover, the single-objective optimization of the second stage showed that by the porous ratios of 0.19 and 1 for the upper and lower layers, respectively, and Reynolds number of 578.7, the minimum values of pressure drop and overall thermal resistance are achieved.

Optimization design of heliostat field based on high-dimensional particle swarm and multiple population genetic algorithms

INTRODUCTION: Tower-type heliostat field is a new type of energy conversion, which has the advantages of high energy efficiency, flexibility and sustainability and environmental friendliness.
 OBJECTIVES: Through the research and improvement of the tower heliostat field to promote the development of solar energy utilization technology.
 METHODS: In this paper, we calculate and optimize the tower heliostat field by using single objective optimization, high-dimensional particle swarm algorithm and multiple group genetic algorithm.
 RESULTS: In this case of question setting, average annual optical efficiency is 0.6696; average annual cosine efficiency is 0.7564; annual average shadow occlusion efficiency is 0.9766; average annual truncation efficiency is 0.9975; average annual output thermal power is 35539.1747W; mean annual output thermal power per unit area is 0.5657W.The optimal solution after the initial optimization of the algorithm is that the total number of mirror fields is 6,384 pieces, and the average annual output power per unit area is 530.6W.
 CONCLUSION: The model of this paper can reasonably solve the problem and has strong practicability and high efficiency, but high dimensional particle swarm algorithm due to easily get local optimal solution, so can introduce the chaotic mapping to increase the randomness of the search space, improve the global search ability of the algorithm.