Pareto Optimal Research Articles

Design optimization of offshore wind farm layout based on game theory

In offshore wind farm (OWF) planning, traditional methods usually use global optimal strategies. In this paper, game theory is applied to the multi-objective optimization of wind turbine (WT) micro-siting and cabling in an OWF. This method considers the real situation where two different teams may choose the global optimal or the local optimal solution. Firstly, the wind speed deficit in the OWF is estimated using the Gaussian wake model. The objective function and constraints of this optimization problem are formulated. Secondly, the game strategies are exhaustively enumerated. The strategies are allocated to the game space matrix and the payoffs are calculated. The above steps are repeated after redistributing the design permissions. Finally, the Nash front is formed and compared with the Pareto optimum. From simulation results, it can be observed that different Nash solutions can be obtained using different strategy permission allocation methods. So the final layout of the OWF should be determined according to different strategy allocation methods when planning the OWF.

Effect of ergonomic aspects on single‐ and multiproduct assembly‐line balancing problems

AbstractIncorporating ergonomic considerations into an assembly‐line balancing problem (ALBP) enhances productivity and minimizes ergonomic concerns. The assembly process, characterized by repetitive motions and handling numerous components, can lead to worker overload. Consequently, the inclusion of ergonomic aspects results in an appropriate distribution of assembly operations and relative workloads. This study investigates a multi‐objective ALBP aimed at minimizing the number of workstations, overall skill level required, and variance in workers' energy expenditure across workstations. To address the ALBP while considering the ergonomic aspects, this study proposes an approach based on the non‐dominated sorting genetic algorithm II (NSGA‐II) and multi‐objective simulated annealing (MOSA) using Pareto optimality. A comparative analysis of the NSGA‐II and MOSA is conducted in single‐ and multiproduct production scenarios, and a computational study involving various factors is performed to identify the dominant algorithm. The computational analysis indicates that the runtime performance of MOSA is 73.287% better than that of NSGA‐II; therefore, MOSA outperforms NSGA‐II. This study aims at applying scientific knowledge concerning manufacturing ergonomics to assist manufacturing industries in enhancing their productivity.

Elastokinematic design and optimization of the multi-link torsion axle – a novel rear axle concept for BEVs

This work describes the elastokinematic design and optimization for a new, package space saving rear suspension especially intended for small battery electric vehicles. Mainly for reasons of cost and weight efficiency, the twist-beam axle is widely used, especially in the A and B segments. One of the main disadvantages of twist-beam axles is that they limit the rear package space because of the torsion profile. The basic idea of this work was to reverse the installation direction of the twist-beam axle to create an additional package space for the battery. To obtain an optimized elastokinematic design, a new algorithm was introduced that allows modeling of the elastokinematic behavior of the new mechanism. A Pareto optimization of the body connecting bushing was performed, revealing that a specific spatial orientation enables effective compensation for camber compliance deficits. Finally, the Pareto-optimized elastokinematic design was compared to compliance measurement results of a prototype vehicle equipped with the new suspension concept.

A multi-objective optimisation approach with improved pareto-optimal solutions to enhance economic and environmental dispatch in power systems

This work implements the recently developed nth state Markovian jumping particle swarm optimisation (PSO) algorithm with local search (NS-MJPSOloc) awareness method to address the economic/environmental dispatch (EED) problem. The proposed approach, known as the Non-dominated Sorting Multi-objective PSO with Local Best (NS-MJPSOloc), aims to enhance the performance of the PSO algorithm in multi-objective optimisation problems. This is achieved by redefining the concept of best local candidates within the search space of multi-objective optimisation. The NS-MJPSOloc algorithm uses an evolutionary factor-based mechanism to identify the optimum compromise solution, a Markov chain state jumping technique to control the Pareto-optimal set size, and a neighbourhood’s topology (such as a ring or a star) to determine its size. Economic dispatch refers to the systematic allocation of available power resources in order to fulfill all relevant limitations and effectively meet the demand for electricity at the lowest possible operating cost. As a result of heightened public consciousness regarding environmental pollution and the implementation of clean air amendments, nations worldwide have compelled utilities to adapt their operational practises in order to comply with environmental regulations. The (NS-MJPSOloc) approach has been utilised for resolving the EED problem, including cost and emission objectives that are not commensurable. The findings illustrate the efficacy of the suggested (NS-MJPSOloc) approach in producing a collection of Pareto-optimal solutions that are evenly dispersed within a single iteration. The comparison of several approaches reveals the higher performance of the suggested (NS-MJPSOloc) in terms of the diversity of the Pareto-optimal solutions achieved. In addition, a measure of solution quality based on Pareto optimality has been incorporated. The findings validate the effectiveness of the proposed (NS-MJPSOloc) approach in addressing the multi-objective EED issue and generating a trade-off solution that is both optimal and of high quality. We observed that our approach can reduce ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}6.4% of fuel costs and ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}9.1% of computational time in comparison to the classical PSO technique. Furthermore, our method can reduce ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}9.4% of the emissions measured in tons per hour as compared to the PSO approach.

A new method to quantify the source contribution of mixed biodegraded oil based on pareto-optimized nonnegative matrix factorization and chord diagram visualization

The biogenic information of different components in crude oils with varying degrees of biodegradation is partially obscured, making traditional molecular indicators ineffective in determining the contributions of mixed sources. Previous studies have mainly focused on calculating mixed source proportion for normal oils, with few investigations involving biodegraded mixed oils. Developing a quantitative method for the mixed source contribution of biodegraded oils using machine learning (ML) algorithms is a significant attempt both to the exploration practice and theoretical progress. Taking the biomarker parameters resistant to biodegradation of 150 oil samples as input datasets, a new method called Pareto-Optimized NMF (PONMF) was proposed in this study, which combines multi-objective optimization (Pareto optimization) with non-negative matrix factorization (NMF) to analyze the relationship between biodegraded oils in the absence of source rock samples or original end-member (EM) oils while satisfying non-negativity constraints and additional constraint conditions. This method decomposes the matrix of crude oil samples into multiple end-members, each representing a possible input from a hydrocarbon source rock. Analysis of the end-member characteristics facilitates the deduction of potential hydrocarbon source layers and the traits of their depositional environments. This examination is supported by data derived from 15 prospective hydrocarbon source rock samples, which were employed to ascertain the actual geological significance of the end-members. The chord diagram depicts the visualization results of the overall relative contribution of source rock end members to crude oil in each area after the PONMF calculation results. The relative contribution of source rocks in different areas to the investigated crude oil samples is proportionate, and the arc length can reflect the contribution of the three sets of source rocks to a certain area. The findings indicate that the oils extracted from the stratified reservoirs in Eastern Chepaizi are primarily derived from the Permian source strata within the Shawan Depression, with a significant contribution ranging from 30% to 90% (EM2), and a lesser extent from the Carboniferous sources, contributing between 5% and 30% (EM1). Conversely, the provenance of oil in Western Chepaizi is overwhelmingly attributed to the Jurassic source interval located in the Sikeshu Depression, where EM3 accounts for over 85% of the source. Meanwhile, the oils in the Central Zone exhibit a composite origin, intermingling contributions from both EM1 and EM3. The advantage of this method is that it does not require direct access to hydrocarbon source rock samples or end-member oils but infers potential hydrocarbon source layers through the existing mixed-source oil samples. The PONMF method provides an effective tool for identifying the sources of biodegraded oils and can be used to study potential hydrocarbon source rock analysis for oils that have undergone biodegradation after hydrocarbon accumulation.

Sparsity-Preserved Pareto Optimization for Subset Selection

Subset selection that selects a limited number of variables optimizing many given criteria, is a fundamental problem with various applications such as sparse regression and unsupervised feature selection. Among the existing algorithms for subset selection, evolutionary algorithms (EAs) have achieved great performance in obtaining the subsets with high quality. However, as the selected subsets are sparse, i.e., most variables of these solutions are zero, most existing EAs for subset selection problems pose great challenges to find the optimal solutions effectively and efficiently, especially when the size of original set is large. To this end, we propose the SPESS approach which is a sparsity preserved evolutionary algorithm for subset selection. To be specific, we design two sparsity preserved operators (i.e., sparsity preserved crossover operator and sparsity preserved mutation operator), which can be used in SPESS to ensure the sparsity of the generated solutions in the process of Pareto optimization. The main advantages of the proposed sparsity preserved operators are that they can obtain high quality solutions and improve the search efficiency of the algorithm. According to the experimental results on 12 sparse regression problems and 12 unsupervised feature selection problems, the proposed SPESS is superior over the state-of-the-arts in solving subset selection tasks and the effectiveness of the proposed two sparsity preserved operators is also verified.

Pareto-based guaranteed cost control of discrete-time uncertain stochastic systems

The Pareto-based guaranteed cost control (GCC) of discrete-time uncertain stochastic systems in the infinite horizon is studied. Firstly, the convexity of the weighted sum objective function is proved. Based on this convexity, we demonstrate the relationship between Pareto optimality and minimization of the weighted sum objective function. This relationship confirms that the Pareto-based GCC strategy can be obtained by optimizing the weighted sum objective function. Secondly, to address the Pareto-based GCC issue for discrete-time uncertain stochastic systems, we derive the generalized algebraic Riccati inequality (GARI) specific to these systems. Thirdly, the necessary condition for a Pareto-based guaranteed cost controller is derived using the Karush–Kuhn–Tucker (KKT) condition. Lastly, we introduce a method based on linear matrix inequality (LMI) to determine the Pareto-based GCC strategy. This method reduces computational complexity and establishes the sufficient conditions for a Pareto-based guaranteed cost controller. To validate our findings, we provide a example implemented in MATLAB, confirming the accuracy of the proposed approach.

Design method for suspension parameters of high-speed railway vehicles considering uncertainties

A design method for suspension parameters is proposed to ensure the desired performance of a railway vehicle despite uncertainties. The method used in this study consists of two loops: a sub-loop, which uses parameter uncertainties to determine the minimum value of target performance, and a main loop, which optimises suspension parameters such that the minimal performance achieves Pareto optimality. Thus, by selecting a suitable Pareto solution that ensures the minimum performance is equal to or higher than the required performance, the robustness of the designed vehicle against the parameter uncertainties can be achieved. The lowest low-frequency damping ratio in the service speed range was selected as one of the design targets. The other target was the critical speed. Two wheel-rail contact characteristics were applied, considering the worst conditions for each design target. The distribution of the parameter uncertainties that minimised the vehicle performance showed distinct characteristics between the longitudinal and lateral suspension parameters, which provides useful information for the maintenance of railway vehicles. The performance analysis for 100,000 random samples shows that the vehicle performed better than the targets with a high probability despite the parameter uncertainties. Further, the simulation results using multi-body dynamics simulation software validated the viability of the proposed method.

Design of Path-Planning System for Interventional Thermal Ablation of Liver Tumors Based on CT Images.

Aiming at the shortcomings of artificial surgical path planning for the thermal ablation of liver tumors, such as the time-consuming and labor-consuming process, and relying heavily on doctors' puncture experience, an automatic path-planning system for thermal ablation of liver tumors based on CT images is designed and implemented. The system mainly includes three modules: image segmentation and three-dimensional reconstruction, automatic surgical path planning, and image information management. Through organ segmentation and three- dimensional reconstruction based on CT images, the personalized abdominal spatial anatomical structure of patients is obtained, which is convenient for surgical path planning. The weighted summation method based on clinical constraints and the concept of Pareto optimality are used to solve the multi-objective optimization problem, screen the optimal needle entry path, and realize the automatic planning of the thermal ablation path. The image information database was established to store the information related to the surgical path. In the discussion with clinicians, more than 78% of the paths generated by the planning system were considered to be effective, and the efficiency of system path planning is higher than doctors' planning efficiency. After improvement, the system can be used for the planning of the thermal ablation path of a liver tumor and has certain clinical application value.

Non-Cutting Moving Toolpath Optimization with Elitist Non-Dominated Sorting Genetic Algorithm-II

Path planning (PP) is fundamental in the decision-making and control processes of computer numerical control (CNC) machines, playing a critical role in smart manufacturing research. Apart from improving optimization in PP, enhancing efficiency while decreasing CNC machine cycle time is important in manufacturing. Many methods have been offered in the literature to improve the cycle time for obtaining optimal trajectories in toolpath optimization, but these methods are mostly considered for improvements in path length or machining time in optimal PP. This study demonstrates a method for creating a smoothing path. It aims to minimize both cycle time and toolpath length, while demonstrating that the non-dominated sorting genetic algorithm (NSGA-II) is efficient in addressing the multi-objective PP problems within static situations. Pareto optimality for performance comparisons with multi-objective genetic algorithms (MOGAs) is presented in order to highlight the positive features of the non-dominant solving generated by the NSGA-II. According to the comprehensive analysis results, the optimization of the path carried out with the NSGA-II emphasizes its shorter and smoother attributes, with the optimal trajectory achieving approximately 30% and 7% reductions in path length and machining cycle time, respectively.

Multi-objective placement and sizing of energy hubs in energy networks considering generation and consumption uncertainties

This paper presents the placement and sizing of energy hubs (EHs) in electricity, gas, and heating networks. EH is a coordinator framework for various power sources, storage devices, and responsive loads. For simultaneous modeling of economic, operation, reliability, and flexibility indices, the proposed scheme is expressed as a three-objective optimization in the form of Pareto optimization based on the sum of weighted functions. The objective functions of this problem respectively minimize the planning cost of EHs (equal to the total cost of construction of hubs and their expected operating cost), the expected energy loss of the mentioned networks, and the expected energy not-supplied (EENS) of these networks in the case of an N − 1 event. The problem is constrained by power flow equations and operation and reliability constraints of these network together with the EH planning and operation model, and flexibility constraints of the EHs. Then, to achieve unique optimal solution in the shortest possible time, a linear approximation model is extracted for the proposed scheme. Moreover, scenario-based stochastic programming (SBSP) is employed to model uncertainties of load, energy cost, renewable power, and accessibility of the mentioned network equipment. Finally, the obtained numerical results indicate the capability of the proposed scheme in enhancing the economic and flexibility situation of EHs and improving the reliability and operation status of energy networks along with achieving optimal planning and operation for EHs.

Spectral-like conjugate gradient methods with sufficient descent property for vector optimization.

Several conjugate gradient (CG) parameters resulted in promising methods for optimization problems. However, it turns out that some of these parameters, for example, 'PRP,' 'HS,' and 'DL,' do not guarantee sufficient descent of the search direction. In this work, we introduce new spectral-like CG methods that achieve sufficient descent property independently of any line search (LSE) and for arbitrary nonnegative CG parameters. We establish the global convergence of these methods for four different parameters using Wolfe LSE. Our algorithm achieves this without regular restart and assumption of convexity regarding the objective functions. The sequences generated by our algorithm identify points that satisfy the first-order necessary condition for Pareto optimality. We conduct computational experiments to showcase the implementation and effectiveness of the proposed methods. The proposed spectral-like methods, namely nonnegative SPRP, SHZ, SDL, and SHS, exhibit superior performance based on their arrangement, outperforming HZ and SP methods in terms of the number of iterations, function evaluations, and gradient evaluations.

Unveiling the origins of non-performance-oriented behavior in China’s local governments: a game theory perspective on the performance-based promotion system

Performance evaluation has great potential to encourage government officials to improve their behavior (performance-oriented government behavior, POGB), but it also tends to lead to behaviors that are detrimental to government performance (non-performance-oriented government behavior, NPOGB). The latter behaviors are prevalent in many parts of the world, especially in areas with fiscal federalist characteristics such as China. This study analyzes POGB and NPOGB and employs game theory to develop a theoretical model to explain the causes of NPOGBs in China, exploring how competition among different jurisdictions leads to them. The findings show that (1) POGB is a condition of Pareto optimality in government behavior, but only represents a very small share of all government behaviors. The majority of behaviors can be categorized as NPOGBs. (2) The primary reason continuous and volatile NPOGBs persist is that, from the perspective of local officials operating under the constraints of information scarcity and risk aversion, they are rational choices, and officials have to imitate one another’s behaviors so as not to be defeated in the competition with others.

Computing Pareto-Optimal and Almost Envy-Free Allocations of Indivisible Goods

We study the problem of fair and efficient allocation of a set of indivisible goods to agents with additive valuations using the popular fairness notions of envy-freeness up to one good (EF1) and equitability up to one good (EQ1) in conjunction with Pareto-optimality (PO). There exists a pseudo-polynomial time algorithm to compute an EF1+PO allocation and a non-constructive proof of the existence of allocations that are both EF1 and fractionally Pareto-optimal (fPO), which is a stronger notion than PO. We present a pseudopolynomial time algorithm to compute an EF1+fPO allocation, thereby improving the earlier results. Our techniques also enable us to show that an EQ1+fPO allocation always exists when the values are positive and that it can be computed in pseudo-polynomial time. We also consider the class of k-ary instances where k is a constant, i.e., each agent has at most k different values for the goods. For such instances, we show that an EF1+fPO allocation can be computed in strongly polynomial time. When all values are positive, we show that an EQ1+fPO allocation for such instances can be computed in strongly polynomial time. Next, we consider instances where the number of agents is constant and show that an EF1+PO (likewise, an EQ1+PO) allocation can be computed in polynomial time. These results significantly extend the polynomial-time computability beyond the known cases of binary or identical valuations. We also design a polynomial-time algorithm that computes a Nash welfare maximizing allocation when there are constantly many agents with constant many different values for the goods. Finally, on the complexity side, we show that the problem of computing an EF1+fPO allocation lies in the complexity class PLS.

Exploring the Scientific Mechanism of Tree Structure Network based on LiDAR Point Cloud Data

Abstract. To explore how trees optimize their structure, we developed a method based on Pareto optimality theory. This method consists of the following operations. Firstly, we utilize Quantitative Structure Models for Single Trees from Laser Scanner Data (TreeQSM) to extract tree structures from point clouds acquired through Light Detection and Ranging (LiDAR). Subsequently, we utilize a graph-theoretical model to characterize the natural tree structure networks and implement a greedy algorithm to generate Pareto optimal tree structure networks. Finally, based on the Pareto optimality theory, we explore whether tree structures are multi-objective optimized. This paper demonstrates that tree structures lie along the Pareto front between minimizing "transport distance" and minimizing "total length". The growth pattern of trees, which produces multi-objective optimized structures, is likely an intrinsic mechanism in the generation of tree structure networks. The location of tree structures along the Pareto front varies under different environmental conditions, reflecting their diverse survival strategies.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 2 – Model calibration and experimental validation

Flow boiling offers increased heat transfer coefficients and effective heat capacity rates that can be leveraged by topology optimization (TO) to generate high-performance microchannel heat sinks. Topology optimization of heat sinks having two-phase flows can be accomplished using the homogenization approach wherein designs are represented as spatially varying distributions of microstructures, as demonstrated in Part 1 of this two-part study. Flow and heat transfer within the microstructures are captured using a two-phase mixture model featuring an effective porous medium formulation. However, closure of these governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. This Part 2 of our study successfully demonstrates a comprehensive end-to-end process for two-phase flow model calibration, topology optimized design generation, and experimental validation of optimized performance for flow boiling heat sinks. To this end, a TO algorithm with the homogenization approach and a two-phase mixture model is implemented using available flow boiling correlations for microchannels. A set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach.

A hierarchical model with hexagon grids for multi-objective route planning in large-scale off-road environments

Off-road route planning plays a vital role across various domains, including civil transportation, earthquake relief and civil production. Off-road route planning requires the consideration of a diverse range of environmental constraints, which is a considerable challenge compared with conventional route planning along existing networks. We aimed to present a multi-objective route planning method for off-road environments. Specifically, we designed a heuristic function incorporating multiple characteristics to generate reliable route planning solutions based on Pareto optimality. We also constructed a hierarchical hexagonal grid model by merging similar grid cells and reconstructing adjacency relationships with other grid cells to achieve high efficiency. The proposed method was compared with conventional route planning methods using single- and multi-objective approaches in traditional and hierarchical hexagonal grid models. The proposed method can effectively plan off-road routes, improve optimal route distance and trafficability, and provide more efficient route solutions. It reduced the planning time by 97.1% compared with multi-objective route planning based on a traditional hexagonal grid model.

786: Utilizing Pareto optimization to refine ML training data in prostate radiotherapy planning

786: Utilizing Pareto optimization to refine ML training data in prostate radiotherapy planning

NAS-MFF: NAS-Guided Multiscale Feature Fusion Network With Pareto Optimization for Sonar Images Classification

NAS-MFF: NAS-Guided Multiscale Feature Fusion Network With Pareto Optimization for Sonar Images Classification

Optimization and performance indication of surrounding gate tunnel field‐effect transistors based on machine learning

AbstractSelecting designs that efficiently optimize multiple objectives simultaneously is an important problem in several distinct industries. Typically, there is not a single ideal design; rather, there are several Pareto‐optimal designs that provide the best possible trade‐offs between the objectives. However, evaluating every design might be expensive, making a thorough search for the whole Pareto optimum set impractical. The aforementioned issue with technology computer‐aided design (TCAD) while investigating a multidimensional parameter set for device design is addressed using Pareto active learning (PAL) and the nondominated sorting genetic algorithm‐III (NSGA‐III) which are metaheuristics‐based multiobjective optimization (MOO) techniques. NSGA‐III adeptly analyzes the tradeoffs among multiple objectives while ensuring diversity in the design space. PAL forecasts the Pareto‐optimal set with intelligence by deliberately sampling the design space. This work focusses on improving the performance of surrounding gate tunnel field‐effect transistors (SGTFETs) by optimizing and assessing their complex designs in terms of multiple objectives, including power, energy, speed, and variability. This paper presents a novel MOO framework that incorporates machine learning (ML) approaches, including NSGA‐III and PAL in SGTFETs technology. The framework provides effective global optimization without gradients, allowing for the automatic recognition of the best solutions. The outcomes show the possibility of ML‐based MOO to create next‐generation nanoscale transistors.