Multi-objective Optimization Algorithm Research Articles

A Raster-Based Multi-Objective Spatial Optimization Framework for Offshore Wind Farm Site-Prospecting

Siting an offshore wind project is considered a complex planning problem with multiple interrelated objectives and constraints. Hence, compactness and contiguity are indispensable properties in spatial modeling for Renewable Energy Sources (RES) planning processes. The proposed methodology demonstrates the development of a raster-based spatial optimization model for future Offshore Wind Farm (OWF) multi-objective site-prospecting in terms of the simulated Annual Energy Production (AEP), Wind Power Variability (WPV) and the Depth Profile (DP) towards an integer mathematical programming approach. Geographic Information Systems (GIS), statistical modeling, and spatial optimization techniques are fused as a unified framework that allows exploring rigorously and systematically multiple alternatives for OWF planning. The stochastic generation scheme uses a Generalized Hurst-Kolmogorov (GHK) process embedded in a Symmetric-Moving-Average (SMA) model, which is used for the simulation of a wind process, as extracted from the UERRA (MESCAN-SURFEX) reanalysis data. The generated AEP and WPV, along with the bathymetry raster surfaces, are then transferred into the multi-objective spatial optimization algorithm via the Gurobi optimizer. Using a weighted spatial optimization approach, considering and guaranteeing compactness and continuity of the optimal solutions, the final optimal areas (clusters) are extracted for the North and Central Aegean Sea. The optimal OWF clusters, show increased AEP and minimum WPV, particularly across offshore areas from the North-East Aegean (around Lemnos Island) to the Central Aegean Sea (Cyclades Islands). All areas have a Hurst parameter in the range of 0.55–0.63, indicating greater long-term positive autocorrelation in specific areas of the North Aegean Sea.

Multi-Objective Optimization Algorithm Based Bidirectional Long Short Term Memory Network Model for Optimum Sizing of Distributed Generators and Shunt Capacitors for Distribution Systems

In this paper, a multi-objective grey wolf optimization (GWO) algorithm based Bidirectional Long Short Term Memory (BiLSTM) network machine learning (ML) model is proposed for finding the optimum sizing of distributed generators (DGs) and shunt capacitors (SHCs) to enhance the performance of distribution systems at any desired load factor. The stochastic traits of evolutionary computing methods necessitate running the algorithm repeatedly to confirm the global optimum. In order to save utility engineers time and effort, this study introduces a BiLSTM network-based machine learning model to directly estimate the optimal values of DGs and SHCs, rather than relying on load flow estimates. At first, a multi-objective grey wolf optimizer determines the most suitable locations and capacities of DGs and SHCs at the unity load factor and the same locations are used to obtain optimum sizing of DGs and SHCs at other load factors also. The base case data sets consisting of substation apparent power, real power load, reactive power load, real power loss, reactive power loss and minimum node voltage at various load factors in per unit values are taken as input training data for the machine learning model. The optimal sizes of the DGs and SHCs for the corresponding load factors obtained using GWO algorithm are taken as target data sets in per unit values for the machine learning model. An adaptive moment estimation (adam) optimization approach is employed to train the BiLSTM ML model for identifying the ideal values of distributed generations and shunt capacitors at different load factors. The efficacy of the proposed ML-based sizing algorithm is demonstrated via simulation studies.

Modeling Thermal Impedance of IGBT Devices Based on Fractional Calculus Techniques

The thermal impedance characteristics of insulated gate bipolar transistor (IGBT) modules are critical for the thermal management and design of electronic devices. This paper proposes a fractional-order equivalent thermal impedance model, which is inspired by the correlation between multi-time-scale dissipation characteristics of heat conduction processes and fractional calculus. The fractional-order equivalent thermal impedance model is derived based on the connection between fractional-order calculus and the Foster thermal network model in mathematical operations, with only two parameters to be identified: heat capacity C and fractional order α. Moreover, this paper provides a parameter identification method for the proposed fractional-order equivalent thermal impedance model based on the multi-objective particle swarm optimization (MOPSO) algorithm. In order to validate the effectiveness and superiority of this work, experiments and comparative works are provided in this paper. The results indicate that the fractional-order equivalent thermal impedance model can accurately describe the frequency domain characteristic curves of the thermal impedance of the Foster thermal network model for IGBT modules, with the difference between the amplitude frequency characteristics not exceeding 1 dB and the difference between the phase frequency characteristics not exceeding 1° within the operating frequency range of (1 kHz, 1 MHz).

.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.

Enhancing end-of-life product recyclability through modular design and social engineering optimiser

Amidst the thriving landscape of manufacturing, the vision of sustainability in Industry 5.0 is becoming increasingly significant. The implementation of recycling represents a crucial step in the pursuit of sustainability, particularly in light of the mounting challenge posed by the proliferation of end-of-life (EOL) products. Addressing this challenge, we propose a novel Design for Modular Recyclability (DFMR) approach aimed at facilitating the recycling of EOL products. Our study develops a multi-objective optimisation model with a focus on maximising green recyclability and independence while minimising aggregation. We introduce an innovative Social Engineering Optimiser (SEO) to simulate behavioural patterns in complex environments, aiding in identifying and implementing effective strategies for optimal or near-optimal results in diverse scenarios. The practical effectiveness of the proposed models and algorithms is demonstrated by applying them to a real-life case study in an internal combustion engine, followed by performance comparisons with existing well-established multi-objective optimisation algorithms. The findings of our study demonstrate the efficacy of the proposed DFMR model, offering a novel approach for decision-makers to undertake EOL product recovery. This contributes to the further exploration of complex and promising paths towards sustainable manufacturing and green production that are more in line with Industry 5.0.

Wind Farm Layout Optimization/Expansion of Real Wind Turbines with a Parallel Collaborative Multi-Objective Optimization Algorithm

The objective of this paper is to study the Wind Farm Layout Optimization/expansion problem. This problem is formulated here as a Multi-Objective Optimization Problem considering the total power output and net efficiency of Wind Farms as objectives along with specific constraints. Once formulated, this problem needs to be solved efficiently. For that, a new approach based on a combination of five Multi-Objective Optimization algorithms, which is named the Parallel Collaborative Multi-Objective Optimization Algorithm, is developed and implemented. This technique is checked on seven test cases; for each case, the goal is to find a set of optimal solutions called the Pareto Front, which can be exploited later. The acquired solutions were compared with other approaches and the proposed approach was found to be the better one. Finally, this work concludes that the proposed approach gives, in a single run, a set of optimal solutions from which a designer/planner can select the best layout of a designed Wind Farm using expertise and applying technical and economic constraints.

Art Pattern Design Based on Visual Semantic Segmentation and Evolutionary Algorithm Optimization

This paper aims to address the issue of traditional art patterns not fully leveraging contextual information in image semantic segmentation. It proposes a multi-level feature aggregation method for image semantic segmentation based on visual Transformer and coordinate attention adjustment (CA Adjustment). Initially, the input image is segmented into slices for linear projection, incorporating learnable positional embeddings to derive an encoded input sequence. Subsequently, employing a visual Transformer-based encoder, the image is transformed into patches to capture global context across the network. CA Adjustment is then introduced to adaptively merge fusion features and visual backbone features using weighted adjustments. Lastly, a multi-objective grasshopper optimization algorithm is designed based on a clustering evolution mechanism to further enhance algorithm performance. Extensive experimental results demonstrate that our proposed algorithm effectively models global contextual information for image feature extraction. Compared to existing advanced algorithms, our method achieves high segmentation accuracy in semantic segmentation tasks, consistently exceeding 95%. Ablation experiments further validate the efficacy of our approach, underscoring its broad applicability in high-precision image semantic segmentation.

An improved multi-objective artificial physics optimization algorithm based on R2 indicator and its application

Artificial Physics Optimization (APO) algorithms in solving constrained multi-objective problems often encounter challenges such as uneven population distribution and imbalances between global and local search capabilities. To address these issues, we propose the Constrained Rank Multi-Objective Artificial Physical Optimization based on the R2 indicator (R2-ICRMOAPO) algorithm. This algorithm integrates non-dominated sorting with the R2 indicator and updates the external storage set using the contribution value derived from the R2 indicator formula, ensuring both set distribution and convergence. It also dynamically adjusts inertia weights and gravitational factors to enhance its global and local search capabilities. To evaluate the performance of the R2-ICRMOAPO algorithm, we compared it with four other multi-objective optimization algorithms using standard test functions. The results indicate that it demonstrates superior distribution and optimization performance. Furthermore, we applied it to optimize the parameters of a hydro-pneumatic suspension system. The experimental results show that it can reduce the root mean square value of car body vertical acceleration by approximately 21.4% and the root mean square value of dynamic tire load by about 19.6%. This reduction effectively enhances vehicle smoothness within a reasonable range. Consequently, these results confirm the feasibility of the R2-ICRMOAPO algorithm to solve practical problems.

Improving the potential of fifth-generation district heating and cooling networks through robust design and operational optimization under future energy market and demand uncertainties

Network investments and projected energy prices greatly impact the financial viability and environmental impact of fifth-generation district heating and cooling (5GDHC) networks. Compared to the previous generation, the upfront investment costs in 5GDHC networks are relatively high due to the decentralized energy demand and supply of the participating prosumers. The transition to 5GDHC is also hindered by uncertain energy markets and the fluctuating energy demands of the prosumers. It makes investors hesitant to commit, even for promising business cases. In this work, a framework is presented to assess the economic and environmental performance of a 5GDHC business case, based on a multi-objective robust optimization algorithm (MO-RDO), to identify the optimal trade-offs between environmental and economic designs. The proposed methodology consists of four steps. In the first two steps, a specific business case is modeled, and techno-economic and environmental performances are analyzed against uncertain energy markets. In the third step, the techno-economic and environmental indicator responses are used to develop a data-driven machine-learning model. This model offers better computational efficiency than a high-fidelity nonlinear model and assesses the most influential parameters driving economic and environmental performance via a global sensitivity analysis. This aids in refining the multi-objective robust design optimization (MO-RDO) framework by pinpointing key design variables and objectives amid data uncertainties. Additionally, the formulated MO-RDO provides a mix of environmentally and economically optimal network designs and operational parameters and highlights the trade-offs between them. The designs and trade-offs are evaluated using financial metrics like net present value (NPV), return on investment, and discounted payback period. These metrics are calculated over the project life, considering the initial investment and net savings. For the considered case, the environmental design has a 10% higher investment cost compared to the economically optimal solution but reduces total emissions (TE) by 13% and improves operational cost savings, which is crucial for better financial indicators. The proposed framework aligns with the EU transition plan to incorporate waste energy sources and decarbonization paths, estimating only a 3% increase in NPV as a risk for the environmentally optimal solution on a financial scale.

A decomposition-based many-objective evolutionary algorithm with Q-learning guide weight vectors update

When dealing with regular, simple Pareto fronts (PFs), the decomposition-based multi-objective optimization algorithm (MOEA/D) performs well by presetting a set of uniformly distributed weight vectors. However, its performance declines when faced with complex and irregular PFs. Many algorithms address this problem by periodically adjusting the distribution of the weight vectors, but these methods do not take into account the performance of the population and are likely to update the weight vectors at the wrong time. In addition, for the SBX crossover operator, the setting of its distribution index will largely affect the exploration and convergence ability of the algorithm, so a single parameter setting will have negative impacts. To tackle these challenges, this paper proposes a method to simultaneously adaptively update weight vectors and optimize SBX parameter via Q-learning(RL-MaOEA/D). In order to make the strategies made by Q-learning more accurate, Two different metrics (CD and NCD) are proposed that capture diversity and convergence of individual and population respectively. RL-MaOEA/D is compared with seven state-of-the-art algorithms on different problems, and the simulation results reflect that the proposed algorithm has better performance.

Topology-optimized terahertz real-time reconfigurable multifunctional liquid-crystal-coding metasurface

In this paper, a reflective terahertz reconfigurable multifunctional coding metasurface based on topology optimization using liquid crystal (LC) is presented. First, the LC metasurface unit is topologically optimized using the NSGA-II multi-objective optimization algorithm. By applying the bias voltage to dynamically adjust the dielectric constant of the LC, the metasurface unit is capable of 2-bit coding at the frequency of 0.67 THz. Then, based on the designed metasurface unit, the array arrangements of the coding metasurface are reversely designed, which makes the metasurface realize flexible control and dynamic switching between beam assignment and vortex beam generation. The results show that for the beam assignment, the single-beam and multi-beam control can be realized with the reflected electromagnetic waves at continuous arbitrary angles in the range of elevation angle of 40° and azimuth angle of 360°. Moreover, the elevation angle and azimuth angle of each beam in the multi-beam can be controlled independently. Using the Fourier convolution addition operation, the control range of the single-beam elevation angle can be expanded. For the vortex beam, the single vortex beam and the multi-vortex beam can be generated in the range of elevation angle of 40° and azimuth angle of 360° with topological charges l=±1, ±2, ±3 at arbitrary angles. This provides flexibility and diversity in the generation of vortex beams. Therefore, the proposed terahertz LC metasurface can realize flexible control of reconfigurable functions and has certain application prospects in terahertz communication, phased array radar, and vortex radar.

Multi-Objective Optimization for Controlling Conflicts in Roadway Surrounding Rock Induced by Floor Stress-Relief Groove

This paper studies the effectiveness of the stress-relief groove on the floor of deep coal roadway and determines the influence of the stress-relief groove parameters on the surrounding rock through qualitative analysis. Based on the displacement conflict problem, evaluation indicators were established, and the optimal solution set was obtained. The innovations of this research include: 1. For geotechnical numerical simulations, novel stress monitoring and plastic zone monitoring techniques have been introduced to accurately reflect the condition of the surrounding rock; 2. The effects of floor relief grooves in deep roadway on surrounding rock have been analyzed, and the advantages and utilities of central and corner relief grooves have been determined; 3. The usability of small datasets has been enhanced by applying SEGA to optimize machine learning models with data augmentation techniques; 4. Multi-objective optimization algorithms have been applied to geotechnical engineering, providing valuable references for decision making. The results demonstrate that multi-objective optimization can significantly enhance the effectiveness of surrounding rock control, resolve conflicts, and achieve more reasonable construction plans. This research provides new theoretical foundations and practical guidance for deep mine roadway-surrounding rock control.

Multi-objective optimal configuration of CCHP system containing hybrid electric-hydrogen energy storage system

In order to cope with the increasing energy demand and achieve the “double carbon “goal of China’s 14th Five-Year Plan,” combined with hydrogen energy storage technology, it has the characteristics of zero pollution, high efficiency and rich source. In the context of reducing energy consumption and the vigorous development of hydrogen energy storage technology, a multi-objective optimization configuration model with economy, energy consumption index and carbon emission index is proposed, which takes into account the working characteristics of the hydrogen energy storage system, and the exothermic heat release from the electrolysis tanks and fuel cells when they are working to provide the loads with an additional heat source of the Combined Cooling, Heating and Power (CCHP) system, to reduce energy consumption and carbon emission. Finally, taking a region as an example, a multi-objective optimization algorithm based on decomposition is used to solve the model, so as to obtain a series of alternatives with better optimization effect. At the same time, the two-way projection method based on interval intuitionistic fuzzy information is used to make decisions, and the scheme that optimizes the economy, energy consumption index and carbon emission index is obtained, which verifies the feasibility of the system proposed in this paper.

A Multimodal Multi-Objective Coati Optimization Algorithm Based on Spectral Clustering

Multimodal multi-objective problems refer to situations where more than one Pareto set in the decision space corresponds to the same Pareto front in the objective space. In this paper, we propose a multimodal multi-objective coati optimization algorithm based on spectral clustering (MMOCOA-SC) for use in multimodal multi-objective problems. The algorithm starts by creating stable subpopulations via a spectral clustering method, grouping similar individuals within each subpopulation. Then, an improved coati optimization algorithm is proposed in order to increase the diversity of the population and continuously search for near-Pareto optimal solutions. Finally, we use an improved crowding distance method combined with a non-dominated sorting method to maintain and retain multiple near-Pareto optimal solutions. The MMOCOA-SC is evaluated alongside five state-of-the-art algorithms using the 2020 CEC test suite, IDMP test problems, and twelve classic engineering application problems. In comparison to the other five state-of-the-art algorithms, the experimental results show that MMOCOA-SC exhibits a superior performance when applied to the problems. This study explores multimodal multi-objective optimization algorithms with a focus on the concept of symmetry, which is crucial for multimodal multi-objective optimization problems in terms of achieving a balanced decision space and a diversity of solutions in the objective space.

Dynamic multi-objective optimization based on classification response of decision variables

In recent years, many dynamic multi-objective optimization algorithms (DMOAs) have been proposed to address dynamic multi-objective optimization problems (DMOPs). Most existing DMOAs treat all decision variables uniformly and respond to them in an identical manner. This paper proposes a dynamic multi-objective optimization algorithm based on the classification response of decision variables (CRDV-DMO). Firstly, CRDV-DMO categorizes the decision variables into convergence variables and diversity variables. Different decision variables adopt distinct response strategies. The response strategy of diversity variable (RSDV) uses Latin hypercube sampling to generate the diversity variables of the new environment. For each dimensional convergence variable, the response strategy of convergence variable (RSCV) first evaluates whether the basic center prediction strategy (CPS) yields positive feedback or negative feedback, further determining the predictability of that dimensional convergence variable. RSCV then decides to either use the basic CPS to generate the convergence variable for that dimension or to retain that dimensional convergence variable from the current environment, based on the predictability of that dimensional convergence variable. The proposed algorithm is extensively studied through comparison with several advanced DMOAs, demonstrating its effectiveness in dealing with the benchmark DMOPs and the parameter-tuning problem of the PID controller on a dynamic system.

A Reformulated-Vortex-Particle-Method-Based Aerodynamic Multi-Objective Design Optimization Strategy for Proprotor in Hover and High-Altitude Cruise

An improved multi-objective design optimization framework is proposed for the efficient design of proprotor blades tailored to specific high-altitude mission requirements. This framework builds upon existing methods by leveraging a reformulated Vortex Particle Method (rVPM) and incorporates three key stages: (1) rapid determination of overall proprotor parameters using a semi-empirical model, (2) optimized blade chord and twist distribution bounds based on minimum energy loss theory, and (3) global optimization with a high-fidelity rVPM-based aerodynamic solver coupled with a multi-objective hybrid optimization algorithm. Applied to a small high-altitude tiltrotor, the framework produced Pareto-optimal proprotor designs with a figure of merit of 0.814 and cruise efficiency of 0.896, exceeding mission targets by over 15%. Key findings indicate that large taper ratios and low twist improve hover performance, while elliptical blade planforms with high twist enhance cruise efficiency, and a tip anhedral further boosts overall performance. This framework streamlines the industrial customization of proprotor blades, significantly reducing the design space for advanced optimization while improving performance in demanding high-altitude environments.

Exploring multi-deformation mechanism and control of arc thin-walled structures during supercritical CO2 assisted micro milling

Titanium alloys are extensively utilized due to their exceptional corrosion resistance, high specific strength, temperature resilience, and biocompatibility. However, the challenges such as poor thermal conductivity, pronounced micro-machining size effects, and the sensitivity of micro-thin wall structures to residual stress complicate the machining of titanium alloy micro-thin walls. This paper investigates the use of supercritical CO2 to assist in arc micro-thin wall milling experiments of titanium alloys, aiming to elucidate the influence of various process parameters on micro-milling performance. The mesoscale prediction model developed in this study shows that the time-varying and static deflection deformations of micro-thin walls cooled by supercritical CO2 are approximately half of those observed under dry cutting conditions. To compare and optimize micro-milling performance metrics, an RVEA-entropy weight TOPSIS optimization scheme was developed, and combined with several high-dimensional multi-objective optimization algorithms. Integrating this with micro-milling finite element model, an iterative optimization and reverification strategy was proposed. The optimized parameters combination achieved through this method reduced micro-milling force, top deformation, and side deformation by 32.5 %, 24.6 %, and 24.3 %, respectively. The research approach and optimization strategy presented in this paper offer valuable insights for enhancing the machining precision of mesoscale titanium alloy micro-thin-wall structures.

Energy-efficient time and cost constraint scheduling algorithm using improved multi-objective differential evolution in fog computing

The recent surge in Internet of Things (IoT) applications and smart devices has led to a substantial rise in the data generation. One of the major issues involved is to meet strict quality of service (QoS) requirements for computing these applications in terms of execution time, cost and in an energy-efficient manner. To extract useful information, fast processing and analysis of data is needed. Consequently, moving all the data to centralized cloud data centers would lead to high processing times, increased cost and energy consumption and more bandwidth usage; thus, processing of applications with strict latency requirements becomes challenging. The addition of fog layer between cloud and IoT devices has provided promising solutions to such issues. However, efficient employment of computing resources in the hybrid infrastructure of fog and cloud nodes is of great significance and demands an optimal scheduling strategy. Toward this direction, a novel Pareto-based algorithm in fog computing, namely energy-efficient time and cost (ETC) constraint scheduling algorithm, is introduced in this paper for scheduling workflow applications. ETC attempts to optimize monetary cost along with time and energy objectives. Improved multi-objective differential evolution (I-MODE) meta-heuristic is introduced and incorporated with deadline-aware stepwise frequency scaling approach that is based on our previously proposed energy makespan multi-objective optimization (EM-MOO) algorithm. Synthetic and real-world application workflows are used to conduct evaluation of the proposed work with existing well-known algorithms from the literature. The experimental results for synthetic workflows reveal that the proposed algorithm lessens energy utilization by 14–21%, execution time by almost 25% and cost consumption by 22–27%, while for real-world application workflows, energy consumption is reduced by 12–24%, execution time by 14–16% and cost consumption by 23–29%.

Research on the application of a hybrid intelligent algorithm in reducing the negative response of shield tunneling construction

Traditional shield project control relies on manual monitoring and management, which suffers from poor reliability, lag, and other defects. In this paper, a hybrid algorithm based on Bayesian optimization (BO), light gradient enhancer (LGBM), and nondominated sorting genetic algorithm-III (NSGA-III) is proposed to realize intelligent control of shield construction safety. The BO-LGBM-NSGA-III is a multiobjective optimization algorithm that takes cutterhead wear and shield energy consumption as objective functions and the nonlinear mapping function of surface settlement and construction parameters as fitness functions. Based on the Pareto distribution of the optimized backing structure construction parameters, reasonable limits of the control parameters of the shield tunneling machine are obtained. The conclusions are as follows. (1) The R2 of the test set for surface subsidence prediction is 0.916, and the RMSE is 2.655. (2) The proposed method can achieve multiobjective optimization, and the surface settlement, cutter head wear, and shield energy consumption are optimized by 49.92%, 24.38%, and 41.88%, respectively. (3) By using this method, both prediction and optimization can be realized, and the optimal control scheme can be obtained. The negative impact of shield tunneling construction has been significantly reduced.

Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization

Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization