Multi-objective Approach Research Articles

A multi-objective clustering approach based on different clustering measures combinations

Clustering methods aim to categorize the elements of a dataset into groups according to the similarities and dissimilarities of the elements. This paper proposes the Multi-objective Clustering Algorithm (MCA), which combines clustering methods with the Nondominated Sorting Genetic Algorithm II. In this way, the proposed algorithm can automatically define the optimal number of clusters and partition the elements based on clustering measures. For this, 6 intra-clustering and 7 inter-clustering measures are explored, combining them 2-to-2, to define the most appropriate pair of measures to be used in a bi-objective approach. Out of the 42 possible combinations, 6 of them were considered the most appropriate, since they showed an explicitly conflicting behavior among the measures. The results of these 6 Pareto fronts were combined into two Pareto fronts, according to the measure of intra-clustering that the combination has in common. The elements of these Pareto fronts were analyzed in terms of dominance, so the nondominanted ones were kept, generating a hybrid Pareto front composed of solutions provided by different combinations of measures. The presented approach was validated on three benchmark datasets and also on a real dataset. The results were satisfactory since the proposed algorithm could estimate the optimal number of clusters and suitable dataset partitions. The obtained results were compared with the classical k-means and DBSCAN algorithms, and also two hybrid approaches, the Clustering Differential Evolution, and the Game-Based k-means algorithms. The MCA results demonstrated that they are competitive, mainly for the advancement of providing a set of optimum solutions for the decision-maker.

Construction and Evaluation of Urban Green Infrastructure in Ecologically Vulnerable Areas Based on Multi-Scale and Multi-Objective Approaches: Taking the Four-Lake Hydrographic Network in the Upper Yellow River Basin as an Example

The construction and optimization of urban green infrastructure (UGI) are regarded as effective strategies for harmonizing the natural landscape with human activities, particularly in ecologically vulnerable areas in the Upper Yellow River Basin, China. However, there is little attention paid to the scale effects and object effects as well as an absence of comprehensive assessments regarding landscape stability. Taking the Four-Lake Hydrographic Network (FLHN) in Shizuishan, a prefecture-level city, as an example, this study focuses on identifying the important sources of UGI by integrating both regional and interregional perspectives utilizing morphological spatial pattern analysis (MSPA). UGI networks were constructed and optimized based on trade-offs and synergizing relationships between individual objects using the minimum cumulative resistance (MCR) model, and the UGI network’s stability combined centrality and connectivity aspects, which were subsequently assessed. The results showed that a total of 19 important sources covering an area of 105.07 km2 were identified in the FLHN, integrating both regional and interregional levels. It was deemed unnecessary to maintain lengths of 7.79 km key corridors, 9.42 km general corridors, and 29.89 km fragile corridors; furthermore, there was no longer a requirement to upgrade an additional 5.51 km of general corridors and 25.78 km of any corridor, as UGI corridors were extracted based on a trade-off and synthesized objective methodology. The overall connectivity index value (OG) of UGI stability with respect to the multi-objective model demonstrated superior performance compared to the same index in scenarios involving the use of a single-objective approach and the straightforward overlay of each object. This study reveals the multifaceted requirements of urban landscape security and sustainability, indicating that multi-scale and multi-objective approaches in territorial space planning not only ensure the integrity of the landscape patterns but also reduce the costs associated with landscape construction. This model can be utilized to implement urban landscape entity protection and restoration for landscapes with various geographical characteristics, and it can provide valuable guidance for similar areas.

AoI and Energy Tradeoff for Aerial-Ground Collaborative MEC: A Multi-Objective Learning Approach

AoI and Energy Tradeoff for Aerial-Ground Collaborative MEC: A Multi-Objective Learning Approach

A bi-level multi-objective optimization approach for carbon policy formulation towards food waste resource treatment from environmental, energy and economic perspectives

Excessive food waste contributes to the greenhouse effect. Although low-carbon technology has the potential to reduce carbon emissions and generate renewable energy, the high costs may deter the adoption. To promote low-carbon food waste treatment, local authorities could develop carbon reduction policies targeted at the food waste treatment industry, which could lead to a game between local authorities and food waste treatment enterprises. Hence, a bi-level multi-objective optimization model is put forward to balance the decisions of local authorities and those of food waste treatment enterprises. Enterprises can choose which carbon reduction policies to implement, and local authorities determine the intensity of specific policies. After testing this model on Shenzhen’s food waste treatment system, the model’s validity and feasibility were confirmed. It was discovered that by identifying suitable carbon reduction policies, the model can help enterprises achieve more than 50% carbon reduction. Moreover, different enterprises may choose different carbon reduction policies to implement. Optimal food waste disposal arrangements need flexible adjustments. The constructed model can serve as a decision-making tool for city managers to reduce carbon emissions in food waste treatment.

AC energy islands for the optimal integration of offshore wind energy resources: Operation strategies using multi-objective nonlinear programming

The increasing need for integrating offshore wind generation into power systems has highlighted energy islands as a promising solution. Such islands also could incorporate responsive infrastructure for improving grid flexibility such as energy storage and hydrogen production. AC energy islands could be particularly cost–benefit effective for short and medium distances between wind power parks and onshore grids. However, the implementation of AC energy islands presents challenges from the viewpoints of voltage stability, power dispatch and reliable operation. This paper develops optimal operation strategies for AC energy islands including: i) a nonlinear optimal power flow approach for controlling the reactive power compensation systems; ii) a finite horizon mathematical programming approach for the management of BESS and hydrogen production systems; and iii) a multi-objective programming approach for maximizing the active power delivered to the onshore power grid while minimizing the nodal voltage deviations simultaneously. Results show that the single-objective approach for real and reactive power dispatch reduces voltage deviations by around 20 % and line currents by over 70 % in the evaluated test system, compared to the non-optimal scenario. Moreover, the incorporation of energy storage in AC energy island test system increased the capacity for power dispatch over 10 %. Additionally, the multi-objective approach is effective in aligning the nodal voltages with nominal values and maximizing the power delivered to the onshore grid. Results show that with a small 1% reduction in power delivery, the proposed multi-objective approach achieved an approximate 50 % decrease in nodal voltage compared to the single-objective approach.

Multi-objective optimization approach for permanent magnet machine via improved soft actor–critic based on deep reinforcement learning

As awareness of environmental protection grows, the development of electric vehicles has emerged as a prominent area of research. Naturally, optimizing Permanent Magnet (PM) machines is critical for enhancing the power performance of electric vehicles, as they are essential components of these vehicles. Benefitting from the advantage of Deep Neural Network (DNN), optimizing the PM machine by leveraging DNN has drawn great attention from industry and academia. To increase the torque of the PM machine and reduce torque ripple from a structural design perspective, this paper proposes a Multi-objective Optimization approach for PM machine via improved Soft Actor Critic (called MOPM-SAC) based on Deep Reinforcement Learning (DRL). MOPM-SAC consists of two core components: a surrogate model based on DNN and a SAC algorithm. Specifically, the SAC algorithm based on DNN is used to optimize the PM machine. The surrogate model is established by training the DNN to use Finite Element (FE) simulation samples, which possesses higher accuracy than other methods, such as Support Vector Machine (SVM), Random Forest (RF), and so on. Moreover, the SAC algorithm integrates a trained DNN as the state transition function within the DRL environment, which enhances the optimization algorithm’s generalization ability in the context of PM machines. In addition, the reward function is designed based on optimization requirements to guide the agent in the SAC algorithm toward learning the optimal strategy. Finally, a 75 kW prototype is manufactured and tested. The effectiveness of the proposed method is validated through FE simulations and prototype experiments.

Sensor placement optimization for composite aircraft structures: A multi-objective Kriging-based approach

Efficient sensor placement is critical for optimizing structural health monitoring (SHM) systems, particularly for composite aircraft structures. The challenge lies in determining the optimal number and positions of sensors to balance monitoring accuracy with resource efficiency. This study proposes a novel multi-objective optimization methodology that integrates Kriging interpolation for mode shape reconstruction with the Lichtenberg algorithm for sensor placement optimization. The approach minimizes the number of sensors while maximizing signal quality and minimizing interpolation error. The methodology is validated on both composite plates and the main rotor blade of an AS-350 helicopter using finite element modal analysis data. The results demonstrate significant reductions in the number of sensors required while maintaining high accuracy in capturing the structure’s dynamic response, showing the effectiveness of the proposed method for SHM applications in complex composite structures.

Multi-condition and multi-objective conceptual optimization design of automotive front subframe

The lightweight design of the automotive front subframe was performed by combining multi-condition topology optimization and multi-objective optimization approaches. Firstly, to avoid the singularity of the research condition, a rigid-flexible coupled multibody dynamic model of the front suspension was established to extract the loads at articulation points of the subframe under typical working conditions. Then, a finite element model of the front subframe was constructed for strength and modal analysis. Multi-condition topology optimization of the front subframe envelope was performed utilizing the compromise programming approach. The subframe was redesigned according to the optimization results to establish an explicit parametric model, which avoided the blindness of optimization. Three approximate models were established through the optimal Latin hypercube test method to improve the efficiency of subsequent optimization. Furthermore, three algorithms were employed for multi-objective optimization based on the approximate model with the highest accuracy. To enhance the reliability of the optimization results, a comparison of the lightweighting effect of the three algorithms was performed, and the NSGA-II algorithm was determined as the final algorithm due to its greater effectiveness in lightweighting. The optimized front subframe has met various performance specifications while increasing the first-order frequency by 10 Hz and reducing weight by 3.27 kg.

A multi-objective window placement approach using BIM and surrogate model

Conventional expertise-based approaches yield less-than-optimal window placement schemes (WPSs). The simulation-based window placement approaches (e.g., EnergyPlus) also suffer from being time-consuming. This study newly proposes a multi-objective window placement approach that can optimize WPSs under multiple objectives with high efficiency. It includes (i) transforming WPS-related building information from BIM’s IFC to EnergyPlus’s IDF, (ii) developing a surrogate model for WPS performance assessment, and (iii) optimizing WPSs under multiple objectives. The proposed approach is demonstrated using a dormitory building in Beijing, showcasing its ability to rapidly derive Pareto frontiers of optimized WPSs assuming different objective weightings. Compared to expertise-based methods, it shows a 30.66% and 16.47% performance enhancement for flexible-sized and fixed-sized window placements. Compared to simulation-based methods, it reduces time consumption by 98.10% while maintaining 94.3% accuracy in the case study. This study provides a well-performing and highly efficient window placement approach, making large-scale WPS optimizations feasible for designers.

An optimal multi-objective dynamic traffic guidance approach based on dynamic traffic assignment

Based on dynamic traffic assignment (DTA), this paper proposes a system-optimal multi-objective model for dynamic traffic guidance. Firstly, the physical road network is extended into a spatiotemporal network. By considering the impact of traffic congestion, a multi-objective linear programming model is formulated with the objectives of minimizing total travel time, total travel distance, total number of vehicles in the system, and total infrastructure maintenance cost. Subsequently, a solution method is devised, combining multiple objectives into a single composite objective function by weighted summation. Commercial solver like Gurobi is employed for single-objective linear optimization, and we iteratively calculate Pareto-efficient solutions and approximate the Pareto frontier. Ultimately, the precision and efficacy of the proposed model and solution method are validated through real-world travel data. Additionally, detailed analysis of the relationships between different objectives is conducted to reveal their impacts on the overall traffic guidance strategy.

Multi-objective topology optimization for cooling element of precision gear grinding machine tool

The machining accuracy of the gear grinding machine tool is significantly reduced by the thermal error, and then an effective control of thermal error is imperative. To control the thermal error, an innovative idea for directly cooling a moving heat source for the gear grinding machine tool is proposed to replace the substitute hollow screw cooling method, and a multi-objective topology optimization approach is proposed to design the cooling element for precision gear grinding machine tool. The results show that the heat transfer capability of the topology optimization-shaped channel is much more outstanding than that of the traditional serpentine-shaped cooling channel, and the pressure drop is reduced by 2–3 times compared with that of the traditional serpentine-shaped cooling channel. The cooling element is embedded into the precision gear grinding machine tool, leading that the temperature rise of the moving nut is reduced by more than 3 K in and that the thermal elongation of the screw shaft is reduced by 10 %. The improvement rate for the repetitive positioning accuracy is in the range of [29.03 %, 92.59 %] and the grinding accuracy is improved by approximately 65 % by using the designed cooling element with topology optimization-shaped channel.

Optimizing Forest Management: Balancing Environmental and Economic Goals Using Game Theory and Multi-Objective Approaches

Forests are complex ecosystems that require integrated management to balance economic, social, and environmental dimensions. Conflicting objectives among stakeholders make optimal decision-making particularly challenging. This study seeks to balance the economic gains of forest harvesting with the goals of environmental conservation, with a focus on the Shafarood forest in Northern Iran. We applied multi-objective optimization and game theory to maximize the net present value (NPV) of forest harvesting while enhancing carbon sequestration. The research utilized data on stumpage prices, harvesting costs, tree density, volume per ha, growth rates, interest rates, carbon sequestration, and labour costs. Applying the epsilon-constraint method, we derived Pareto optimal solutions for a bi-objective model, and game theory was applied to negotiate between economic and environmental stakeholders. In the fifth round of bargaining, a Nash equilibrium was achieved between the two players. At this equilibrium point, the economic player achieved NPV from forest harvesting of 9001.884 (IRR 10,000/ha) and amount of carbon sequestration of 159.9383 tons/ha. Meanwhile, the environmental player achieved NPV from forest harvesting of 7861.248 (IRR 10,000/ha), along with a carbon sequestration of 159.9731 tons/ha. Results indicate significant trade-offs but reveal potential gains for both economic and environmental goals. These findings provide a robust framework for sustainable forest management and offer practical tools to support informed decision-making for diverse stakeholders.

A Metaheuristic Approach for a Two-dimensional Fuzzy Version of the Variable Size and Cost Bin Packing Problem

The Variable Size and Cost Bin Packing Problem (VSCBPP) focuses on minimizing the overall cost of containers used to pack a specified set of items. This problem has significant applications across various fields, including energy, cargo transport, and informatics, among others. Most research conducted on this problem has concentrated on enhancing solution methodologies. Recently, some studies have investigated the use of fuzzy approaches to VSCBPP, which allow for the relaxation of certain constraints. In this paper, we introduce a metaheuristic method for solving the fuzzy version of VSCBPP, facilitating the simultaneous relaxation of two constraints: the overloading of containers and the exclusion of specific items from the packing process. Consequently, this two-dimensional fuzzy relaxation of the VSCBPP enables us to derive a range of solutions that present varying trade-offs between cost and the satisfaction levels of the original constraints. We employ mechanisms from the multi-objective metaheuristic approach to maximize the degrees of relaxation while minimizing the original cost function. To demonstrate the efficacy of our proposed solution, we utilized two well-known multi-objective evolutionary P-metaheuristics (Multi-Objective Genetic Algorithm and NSGA-II) and two S-metaheuristics (Multi-Objective Local Search and Ulungu Multi-Objective Simulated Annealing) specifically tailored for the fuzzy version of the VSCBPP. Computational experiments were conducted on 39 instances to validate the effectiveness of this approach.

Multi-objective optimization design of steel cross section of integrated supports and hangers based on NSGA-Ⅱ and MDOS

The stability and safety of building Mechanical, Electrical, and Plumbing (MEP) systems are significantly influenced by the steel section design of integrated supports and hangers. Traditional design methods, reliant on empirical steel section selection, are often inefficient and can result in unnecessary material usage. This paper introduces a novel multi-objective optimization approach that enhances the section design process by minimizing material costs and maximizing bending performance of supports and hangers. Firstly, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to identify an array of optimal cross-sectional designs that reconcile economic considerations with structural mechanical performance. Subsequently, in order to pinpoint the most suitable design from the resulting Pareto-optimal scheme, the Method of Determining the Optimal Scheme (MDOS) is proposed. MDOS harnesses expert scoring, the Continuous ordered weighted averaging (COWA) operator, game theory, and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to objectively evaluate and prioritize design schemes according to stakeholder preferences and project-specific criteria. Finally, the optimization results are analyzed and the influence of different spacing of supports and hangers and different subjective weight factors on the selection of cross-section is studied. The findings reveal that the method can precisely determine all cross-section designs that adhere to the established constraints, achieving a 4.09-fold enhancement in design efficiency. It was observed that the two outlined objectives are predominantly affected by the height of the web. The distribution trend of the optimal solution value of the independent variable is almost the same under the condition of different values of the supports and hangers spacing. With the change of subjective weight, the cross section selection focuses on three optimal schemes. Therefore, the proposed method can be used as reference for similar steel design optimization.

.A multi-objective search-based approach for position and orientation deviations in assemblies with multiple non-ideal surfaces

Computing position and orientation deviations (PODs) considering non-ideal morphologies and local deformations of mating surfaces is a key challenge in controlling the performances of assembled mechanical products through tolerance analysis. However, existing computational models based on Skin Model Shapes face difficulty in handling the PODs for all types of assembly issues. This paper proposes a novel multi-objective search-based approach for POD computation on a conception of force equilibrium constraints. A multi-objective particle swarm optimization algorithm is employed to solve the multi-objective model, and the efficiency and accuracy of the proposed approach are tested and compared with the NSGA-II and FEM methods. To demonstrate its distinctive capability to deal with assembly issues with multiple non-ideal mating surfaces, the proposed approach is applied to assemblies with multiple planar and cylindrical surfaces. Finally, an application of predicting the coaxial accuracy of a fuel pump is carried out, and the capabilities of the proposed approach are further demonstrated.

A Comprehensive Multi-Objective Energy Management Approach for Wearable Devices with Dynamic Energy Demands

Recent advancements in low-power electronics and machine-learning techniques have paved the way for innovative wearable Internet of Things (IoT) devices. However, these devices suffer from limited battery capacity and computational power. Hence, energy harvesting from ambient sources has emerged as a promising solution for powering low-energy wearables. Optimal management of the harvested energy is crucial for achieving energy-neutral operation and eliminating the need for frequent recharging. This task is challenging due to the dynamic nature of harvested energy and battery energy constraints. To tackle this challenge, we propose tinyMAN, a reinforcement learning-based energy management framework for resource-constrained wearable IoT devices. tinyMAN maximizes the target device utilization under battery energy constraints without relying on the harvested energy forecast, making it a prediction-free approach. It achieves up to 17% higher utility while reducing battery constraint violations by 80% compared to prior work. We also introduce tinyMAN-MO, a multi-objective extension of tinyMan for applications with time-varying energy demands. It learns the tradeoff between meeting the application’s energy demand and maintaining the battery energy level. We deployed our framework on a wearable device prototype using TensorFlow Lite for Micro, leveraging its small (less than 120 KB) memory footprint. Evaluations show that tinyMAN-MO operates within 10% of the Pareto-optimal solutions with only 1.98 ms execution time and 23.17 μJ energy consumption overhead.

Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization

This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp masking highboost filtering with the NSGA-II algorithm. Additionally, a posterior preference articulation is introduced to select three key solutions from the Pareto front: the maximum contrast solution, the maximum detail solution, and the knee point solution. The proposed technique is evaluated on a range of image types, including medical and natural scenes. The final solutions demonstrated significant superiority in terms of contrast and detail compared to the original images. The three selected solutions, although all are optimal, captured distinct characteristics within the images, offering different solutions according to field preferences. This highlights the method’s effectiveness across different types and enhancement requirements and emphasizes the importance of the proposed preferences in different contexts.

Challenges and Strategies for the Sustainable Architectural Education in the Context of Post-Urbanization and Climate Change

The transformation of urbanization patterns due to the pandemic and climate change have significantly reshaped construction market demands, presenting substantial challenges to current architectural education (AE) models. In order to address these challenges and propose effective reform strategies, this study utilizes questionnaires and expert interviews to gather perspectives from architecture students and professionals in a Chinese university. The findings highlight three main issues in AE: (1) misalignment between talent development stages and educational goals; (2) slow updates to curriculum content, leading to lagging behind the needs of times; and (3) inadequate integration of curriculum design with practical application, coupled with excessively lengthy academic programs. To address these challenges, the study proposes the strategies: (1) adopting multi-objective and multi-track approaches for educational goals; (2) reducing length of programs and implementing flexible academic structures; and (3) developing curricula that integrate knowledge with practice. This research offers valuable insights for reforming architectural education within the framework of sustainable development, emphasizing the need for educational goals, curriculum, and cultivation system to evolve to meet the demands of modern practice and development.

Exergy-economic based multi-objective optimization and carbon footprint analysis of solar thermal refrigeration systems

The increasing carbon footprint associated with conventional cooling methods underscores the urgent need for sustainable alternatives. This study investigates the economic and environmental advantages of various solar-thermal cooling systems, with a focus on optimizing their performance across different climate conditions. Employing a multi-objective approach, the research emphasizes exergy-economic indices to optimize selected cycles. The analysis covers multiple refrigeration technologies, including liquid absorption, solid adsorption, and solid desiccant cycles. Results indicate that the liquid absorption cycle performs optimally in hot, arid climates, reducing the payback period to approximately 8 years when optimized. In hot and humid regions, the solid desiccant cycle proves most effective due to its superior humidity control, yielding a payback period of 5.3 years. For cold and mountainous areas, the solid adsorption cycle is preferred, with a payback period of 13.5 years, while moderate and humid climates benefit from the solid desiccant cycle for both cooling and humidity regulation. The exergy-economic factors for the solar refrigeration systems across semi-arid, hot and arid, hot and humid, cold and mountainous, and moderate and humid climates are 0.758, 0.602, 0.698, 0.74, and 0.575, respectively.

A multi-objective constraint programming approach to address clustering problems in mine planning

PurposeThe mine sequencing problem is NP-hard. Therefore, simplifying it is necessary. One way to do this is to employ clusters as input instead of individual blocks. The mining cut clustering problem has been little addressed in the literature, and the solutions used are almost always heuristic. We solve the mining cut clustering problem, which is NP-hard, through single- and multi-objective optimization, finding results that are local optima in acceptable computational time.Design/methodology/approachWe first elaborate an ILP-based model to address the mining cut clustering problem. We employ a mono-objective approach and two multi-objective approaches, solving all these models by constraint programming. To choose the best solutions generated by multi-objective approaches, we employ two multi-criteria decision analysis approaches, considering different weight configurations. We developed a case study using real data.FindingsWe verified that the approaches based on multi-objective optimization performed better than the mono-objective approach for the economic return criterion. The weighted-sum multi-objective approach presented the best results considering all objective functions used. Once viable solutions were obtained through multi-objective optimization, multi-criteria decision analysis approaches almost always selected the same solution. We obtained solutions that are local optima in acceptable computational time.Research limitations/implicationsThis study solves an instance with 80 blocks. Consequently, it is aimed at short-term mine planning. The methodology has not yet been evaluated in large instances related to medium- and long-term mine planning.Originality/valueThis is the first time that multi-objective optimization has been employed to solve the mining cut custering problem. Even other problems related to mine planning were, at most, solved by goal programming, so that multi-objective optimization is a knowledge that is not widespread among mining researchers. The results are consistent, and the study achieves the objective of finding quality solutions to an NP-hard problem in an acceptable computational time.