Pareto Front Research Articles

Multi‐objective and multi‐stage low‐carbon planning of park integrated energy system considering random outages from superior power grid

AbstractThis article proposes a multi‐objective and multi‐stage low‐carbon planning approach for park integrated energy systems (PIES) considering the impacts of random outages from the superior electrical grid. This approach incorporates optimal multi‐stage construction sequencing and stepped carbon emission trading to leverage the economic and low‐carbon benefits of long‐term planning. First, the islanding modes of PIES are described using four random variables: island type, duration, start time, and typical day of occurrence, from which islanding scenarios are generated based on scenario tree. Next, a multi‐objective planning model that considers both economics and reliability is constructed, with the objectives of minimizing the total lifecycle planning cost and the expected economic loss during islanding. The improved Normalized Normal Constraint (NNC) method is proposed to solve the multi‐objective planning problem. Then, the fuzzy membership function is used to determine the optimal compromise solution, resulting in a planning scheme that balances economic efficiency and supply reliability. Finally, simulations indicate that, at the cost of a slight increase in planning expenses, the proposed model significantly reduces the loss costs under islanding modes compared with single‐objective economic‐focused planning. Additionally, the improved NNC method can achieve a more uniform Pareto frontier compared with the conventional NNC method.

Optimal Capacity Allocation for Life Cycle Multiobjective Integrated Energy Systems Considering Capacity Tariffs and Eco-Indicator 99

Traditional energy systems pose a significant threat to human social development due to fossil fuel depletion and environmental pollution. Integrated energy systems (IESs) are widely studied and applied due to their clean and low-carbon characteristics to achieve sustainable development. However, as integrated energy systems expand, their impact on ecosystems becomes more pronounced. This paper introduces the concept of the ecological damage index (EDI) to promote the sustainable development of integrated energy systems. Moreover, the introduction of a capacity tariff mechanism will impact the energy structure, making it essential to consider its effects on capacity allocation within integrated energy systems. This paper proposes a multiobjective optimization framework for constructing a capacity planning model for integrated energy systems, focusing on achieving a multidimensional balance between the economy, environment, and ecosystem using the life cycle assessment (LCA) method. Finally, the nondominated sorting genetic algorithm-II (NSGA-II) is employed to optimize the three objectives and obtain the Pareto frontier solution set. The optimal solution is selected from the solution set by combining the technique for order preference by similarity to ideal solution (TOPSIS) and Shannon entropy method. In comparison to scenarios with incomplete considerations, the multiobjective capacity optimization model proposed in this study exhibits significant improvements across the three metrics of cost, carbon emissions, and the ecological damage index, with a 19.05% reduction in costs, a 26.24% decrease in carbon emissions, and an 8.85% decrease in the ecological damage index. The study demonstrates that the model abandons traditional single-objective research methods by incorporating a multidimensional balance of the economy, environment, and ecosystems. This approach forms a foundational basis for selecting the optimal energy mix and achieving sustainable development in integrated energy systems. The life cycle assessment methodology evaluates impacts across all stages of integrated energy systems, providing a comprehensive basis for assessing and planning the sustainable development of the systems. The study offers guidance for the rational allocation of the integrated energy system capacity and advances the sustainable development of such systems.

Bi-objective Optimization in Role Mining

Role mining is a technique that is used to derive a role-based authorization policy from an existing policy. Given a set of users U , a set of permissions P and a user-permission authorization relation UPA ⊆ U × P , a role mining algorithm seeks to compute a set of roles R , a user-role authorization relation UA ⊆ U × R and a permission-role authorization relation PA ⊆ R × P , such that the composition of UA and PA is close (in some appropriate sense) to UPA . Role mining is therefore a core problem in the specification of role-based authorization policies. Role mining is known to be hard in general and exact solutions are often impossible to obtain, so there exists an extensive literature on variants of the role mining problem that seek to find approximate solutions and algorithms that use heuristics to find reasonable solutions efficiently. In this paper, we first introduce the Generalized Noise Role Mining problem (GNRM) – a generalization of the MinNoise Role Mining problem – which we believe has considerable practical relevance. In particular, GNRM can produce “security-aware” or “availability-aware” solutions. Extending work of Fomin et al., we show that GNRM is fixed parameter tractable, with parameter r + k , where r is the number of roles in the solution and k is the number of discrepancies between UPA and the relation defined by the composition of UA and PA . We further introduce a bi-objective optimization variant of GNRM, where we wish to minimize both r and k subject to upper bounds \(r \le \bar{r} \) and \(k\le \bar{k} \) , where \(\bar{r} \) and \(\bar{k} \) are constants. We show that the Pareto front of this bi-objective optimization problem (BO-GNRM) can be computed in fixed-parameter tractable time with parameter \(\bar{r} +\bar{k} \) . From a practical perspective, a solution to BO-GNRM gives security managers the opportunity to identify a mined policy offering the best trade-off between the number of policy discrepancies and the number of roles. We then report the results of our experimental work using the integer programming solver Gurobi to solve instances of BO-GNRM. Our key findings are that (a) we obtained strong support that Gurobi’s performance is fixed-parameter tractable, (b) our results suggest that our techniques may be useful for role mining in practice, based on our experiments in the context of three well-known real-world authorization policies. We observed that, in many cases, our solver is capable of obtaining optimal solutions when the values of either k or r are small.

Direct MultiSearch optimization of TPMS scaffolds for bone tissue engineering

BackgroundScaffolds designed for tissue engineering must consider multiple parameters, namely the permeability of the design and the wall shear stress experienced by the cells on the scaffold surface. However, these parameters are not independent from each other, with changes that improve wall shear stress, negatively impacting permeability and vice versa. This study introduces a novel multi-objective optimization framework using Direct MultiSearch (DMS) to design triply periodic minimal surface (TPMS) scaffolds for bone tissue engineering. MethodThe optimization algorithm focused on maximizing the permeability of the scaffolds and obtaining a desired value of average wall shear stress (which ranges between the values that promote osteogenic differentiation of 0.1 mPa and 10 mPa). Multiple fluid inlet velocities and target wall shear stress were analyzed. The DMS method successfully generated Pareto fronts for each configuration, enabling the selection of optimized scaffolds based on specific structural requirements. ResultsThe findings reveal that increasing the target wall shear stress results in a greater number of non-dominated points on the Pareto front, highlighting a more robust optimization process. Additionally, it was also demonstrated that the tested Schwartz diamond scaffolds had a better permeability-wall shear stress relation when compared to Schoen gyroid geometries. ConclusionsDirect MultiSearch was proven as an effective tool to aid in the design of tissue engineering scaffolds. This adaptable optimization framework has potential applications beyond bone tissue engineering, including cartilage tissue differentiation.

An archive-assisted multi-modal multi-objective evolutionary algorithm

The multi-modal multi-objective optimization problems (MMOPs) pertain to characteristic of the decision space that exhibit multiple sets of Pareto optimal solutions that are either identical or similar. The resolution of these problems necessitates the utilization of optimization algorithms to locate multiple Pareto sets (PSs). However, existing multi-modal multi-objective evolutionary algorithms (MMOEAs) encounter difficulties in concurrently enhancing solution quality in both decision space and objective space. In order to deal with this predicament, this paper presents an Archive-assisted Multi-modal Multi-objective Evolutionary Algorithm, called A-MMOEA. This algorithm maintains a main population and an external archive, which is leveraged to improve the fault tolerance of individual screening. To augment the quality of solutions in the archive, an archive evolution mechanism (AEM) is formulated for updating the archive and an archive output mechanism (AOM) is used to output the final solutions. Both mechanisms incorporate a comprehensive crowding distance metric that employs objective space crowding distance to facilitate the calculation of decision space crowding distance. Besides, a data screening method is employed in the AOM to alleviate the negative impact on the final results arising from undesirable individuals resulting from diversity search. Finally, in order to enable individuals to effectively escape the limitation of niches and further enhance diversity of population, a diversity search method with level-based evolution mechanism (DSMLBEM) is proposed. The proposed algorithm’s performance is evaluated through extensive experiments conducted on two distinct test sets. Final results indicate that, in comparison to other commonly used algorithms, this approach exhibits favorable performance.

Optimization of operational parameters of marine methanol dual-fuel engine based on RSM-MOPSO

Methanol and natural gas, as green fuels for environmental protection, have shown great potential in the field of maritime transportation. This study explores how the methanol energy fraction (MEF), exhaust gas recirculation (EGR), excess air ratio (λ), and engine injection timing (EIT) influence combustion and emission traits in marine dual-fuel (DF) engine. Initially, a DF engine model was formulated through experiments using CONVERGE software, while the CHEMKIN program devised a chemical mechanism involving 100 compounds and 512 reactions. The response surface methodology (RSM) was subsequently utilized to design the experiment and develop the regression model. The improved multi-objective particle swarm optimization (MOPSO) algorithm was applied to optimize three critical variables: brake thermal efficiency (BTE), carbon monoxide (CO), and nitrogen oxide (NOx) emissions. Ultimately, feature-optimized scenarios from the Pareto front were chosen for comparative evaluation to derive the optimal configuration. The results show that when the decision variables MEF, EGR, λ and EIT are 22.33 %, 10 %, 1.81 and 11°CA BTDC respectively, there is a better trade-off between the three target variables. Compared with the original case, the change of ITE, NOx and CO emissions in the optimal case are +0.97 %, −39.53 % and −14.51 %, respectively. Overall, based on the intelligent optimization approach, the rational selection of DF engine parameters improved the ITE and most NOx and CO emissions were effectively suppressed.

A novel design optimization framework to sustain remanufacturability

The ever-increasing global carbon emissions have urged the need for environmentally conscious/sustainable product design, for which the design for remanufacturing (DfRem) is one potential approach. DfRem targets at designing products that have multiple life cycles, thus significantly reducing raw material usage, energy consumption, and carbon emissions. In this paper, we develop a three-stage framework that consists of (1) systematic design space exploration and a multi-objective optimization formulation to minimize the likelihood of failure causes (such as fatigue and wear) and environmental footprint, (2) topology optimization to further reduce material usage without significantly affecting the load-carrying capability of the product, and (3) post-topology optimization design verification to ensure the proposed design satisfies all design constraints. The environmental impact can be assessed at varying comprehensiveness levels (e.g., design and manufacturing phase, use phase) and in terms of carbon or GHG emission, energy use, and waste generation. Because the novel design framework predominantly adjusted the geometry, we focused on mass-based change and energy savings due to sustained remanufacturability. The multi-objective optimization formulation in the first step results in a Pareto optimal set of possible design solutions that the designer can use for the second step. We demonstrate the utility of this framework through a case study of an engine cylinder head subjected to thermo-mechanical loads, where we find that about 5% of the product mass can be conserved with only about a 3% increase in surface area that has a fatigue life less than 10,000 cycles.

Multi-objective optimization of chemical reaction characteristics of selective catalytic reduction in denitrification of diesel engine using ELM-MOPSO methodology

This study systematically investigated the effects of structural parameters in a two-stage selective catalytic reduction (SCR) catalyst on ammonia storage, NO conversion efficiency, and ammonia slip using computational fluid dynamics (CFD) simulations. The rank ordering of the correlations between structural parameters and performance metrics was determined by gray relational analysis (GRA). Both the catalyst diameter and the upstream catalyst porosity had correlations exceeding 0.9, making them key parameters affecting SCR performance. An extreme learning machine (ELM) prediction model was trained using data obtained from CFD simulations. The prediction performance of this ELM model was then evaluated using statistical metrics. Finally, the optimized Pareto frontier diagram was obtained through the multi-objective particle swarm optimization (MOPSO) algorithm, and the optimal results were selected for further CFD modeling analysis. The results showed that the upstream NO conversion efficiency of the SCR system was improved by 7.7 %, the downstream NO conversion efficiency was improved by 18.67 %, the ammonia slip was reduced by 71.97 %, and the upstream ammonia storage capacity was improved by 6.83 % compared with the original model.

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

Augmented ɛ‐constraint‐based matheuristic methodology for Bi‐objective production scheduling problems

AbstractMatheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ‐constraint‐based matheuristic methodology (ɛ‐MH) is proposed to apply the idea of ɛ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

SparseAuto: An Auto-scheduler for Sparse Tensor Computations using Recursive Loop Nest Restructuring

Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General sparse tensor algebra compilers are not always versatile enough to generate asymptotically optimal code for sparse tensor contractions. This paper shows how to generate asymptotically better schedules for complex sparse tensor expressions using kernel fission and fusion. We present generalized loop restructuring transformations to reduce asymptotic time complexity and memory footprint. Furthermore, we present an auto-scheduler that uses a partially ordered set (poset)-based cost model that uses both time and auxiliary memory complexities to prune the search space of schedules. In addition, we highlight the use of Satisfiability Module Theory (SMT) solvers in sparse auto-schedulers to approximate the Pareto frontier of better schedules to the smallest number of possible schedules, with user-defined constraints available at compile-time. Finally, we show that our auto-scheduler can select better-performing schedules and generate code for them. Our results show that the auto-scheduler provided schedules achieve orders-of-magnitude speedup compared to the code generated by the Tensor Algebra Compiler (TACO) for several computations on different real-world tensors.

Multi-objective scheduling for an energy-efficient flexible job shop problem with peak power constraint

Controlling electricity costs, which are closely related to the peak power reached, while simultaneously reducing completion time and energy consumption, is crucial for achieving sustainability in the manufacturing industry. However, most existing research on energy-efficient flexible job shop scheduling problems primarily focuses on optimizing completion time and energy consumption, often neglecting the critical aspect of controlling electricity costs. With decreasing resources and increasing energy prices, it is necessary to control electricity costs by limiting the peak power reached during production. To address this gap, this paper investigates an energy-efficient flexible job shop scheduling problem with peak power constraint considering setup and transportation time (EEFJSSP-PPST). We establish a mathematical model for EEFJSSP-PPST and propose an improved non-dominated sorting genetic algorithm II (INSGA-II) incorporating several key improvements. We first introduce three scheduling rules in decoding to optimize objectives and employ heuristic rules to generate a high-quality initial population. Then, we propose an innovative cluster crossover method to accelerate convergence and design an adaptive-based local optimization strategy to further enhance performance. Finally, our experiments explore the impacts of different degrees of the peak power constraint on objectives and evaluate the effectiveness of the three scheduling rules. Additionally, the performance of INSGA-II is tested using 135 benchmark instances. The results indicate that INSGA-II outperformed its variations without improvements, achieving the best hypervolume (HV) indicator in 80% of the instances and the best inverted generational distance (IGD) indicator in 68.89% of the instances. Compared to other state-of-the-art algorithms, INSGA-II achieves the best HV and IGD indicators in 82.2% and 81.5% of the instances, respectively, and demonstrates better convergence and a superior Pareto front. Therefore, we conclude that the improvements in INSGA-II are effective and enhance the algorithm’s performance, making it outstanding in solving EEFJSSP-PPST.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers─as caused by the additional burden of artificial genetic circuits─shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state model of gene expression, capturing characteristics like energy dissipation─which we link to the entropy production rate─and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energetic costs of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Variable Geometry Turbine Turbocharger Optimization Using Machine Learning for On-Highway Fuel Cell Applications

<div>Turbocharger design involves adjustment of various geometric parameters to improve the performance and suit mechanical constraints, depending on the application-specific requirements. In designing the turbine stage, these parameters are optimized to maximize durability and efficiencies at the required operating points. For a heavy-duty class eight truck, “road load” and “rated power” are generally considered the two most important operating points. The objective of this article is to improve the efficiencies of these two operating points.</div> <div>The common challenge in the development of a turbine wheel design is the large number and interdependence of parameters to optimize. For example, increasing the blade thickness improves structural strength but reduces the mass flow capacity, thus influencing its performance. It is general practice to optimize the wheel geometry using iterative CFD analysis. However, running simulations for every single change in geometry involves significant computation time and does not guarantee the global optimum.</div> <div>This study proposes a machine learning (ML)-driven optimization process for variable turbine geometry (VTG) wheels with two target operating points. Initial CFD data is collected and used to train/validate a ML model for each operating point. A multi-objective optimization algorithm utilizes these ML models to provide a list of ideal turbine wheel designs, and the best candidates are validated in CFD for accuracy. The results are a balanced maximization in efficiency for both operating points, with an improvement in the pareto front by 1.4% points over CFD optimization alone.</div>

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

Optimal design of vibration resistance of fiber-reinforced composite sandwich plates embedded in a viscoelastic square honeycomb core

This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-β method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.

Multiobjective optimization by using cutting angle methods and hypervolume criterion

We translate a multiobjective optimization problem into a single objective Lipschitz problem by using the hypervolume criterion of the Pareto set. Deterministic global optimization methods allow one to track the whole Pareto front rather than converging to a single non-dominated solution. We augmented an efficient hypervolume computation technique with hypervolume increment strategy, and established Lipschitzianity of the resulting objective function. We used two deterministic Lipschitz optimization methods together with the hypervolume objective and benchmarked them against some state-of-the-art alternative multiobjective optimization methods, establishing the competitiveness of the proposed approach.

Multi-Criteria Calibration of a Thermo-Mechanical Model of Steel Plate Welding in Vacuum

This paper proposes a procedurefor multi-criteria calibration of a thermo-mechanical model for numerical simulation of welding in the space vacuum. A finite-element model of a steel plate is created. Experimental and computational data are obtained. An inverse problem is formulated for the vector identification of five calibration parameters from the heat-flow model. They are evaluated for adequacy with controlled accuracy according to four criteria. An optimization problem is solved using a two-step interactive procedure. The parameter space studying method (PSI) has been applied to the study of multidimensional regions by means of quasi-uniform sounding. A Pareto-optimal set is defined. It is used to determine reduced ranked Pareto subsets by μ-selection. Salukvadze optimum is also determined.

Decomposition based estimation of distribution algorithm for high-level synthesis design space exploration

High-Level Synthesis (HLS) has evolved significantly due to the increasing complexity of integrated circuit design and the demand for efficient design methodologies. HLS, which raises the abstraction level of design specification, allows designers to focus on hardware functionality, thus enhancing productivity and reducing verification efforts. However, a key challenge in HLS is efficiently exploring the vast design space to find the Pareto-optimal designs. In this paper, we introduce a novel approach for multi-objective design space exploration in HLS. Our methodology decomposes the design space exploration problem into simpler sub-problems using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) framework and utilizes the Estimation of Distribution Algorithm (EDA) to build a probabilistic model for generating candidate solutions, thereby reducing the required number of expensive synthesis runs. Experimental results show that the proposed method has a faster convergence speed and reduces the number of syntheses by 24.34% to 32.01%, which significantly outperforms state-of-the-art works. Our approach achieves superior Pareto fronts with the lowest average ADRS value, outperforming Lattice-expl, ϵ -Constraint GA, and NSGA-II by 85.64%, 39.90%, and 33.31% respectively.