Pareto Optimal Points Research Articles

Use of Nash equilibrium in finding game theoretic robust security bound on quantum bit error rate

Nash equilibrium is employed to find a game theoretic robust security bound on quantum bit error rate (QBER) for DL04 protocol which is a scheme for quantum secure direct communication that has been experimentally realized recently. The receiver, sender and eavesdropper (Eve) are considered to be quantum players (players having the capability to perform quantum operations). Specifically, Eve is considered to have the capability of performing quantum attacks (e.g., Wójcik’s original attack, Wójcik’s symmetrized attack and Pavičić attack) and classical intercept and resend attack. Game theoretic analysis of the security of DL04 protocol in the above scenario is performed by considering several game scenarios. The analysis revealed the absence of a Pareto optimal Nash equilibrium point within these game scenarios. Consequently, mixed strategy Nash equilibrium points are identified and employed to establish both upper and lower bounds for QBER. Further, the vulnerability of the DL04 protocol to Pavičić attack in the message mode is established. In addition, it is observed that the quantum attacks performed by Eve are more powerful than the classical attack, as the QBER value and the probability of detecting Eve’s presence are found to be lower in quantum attacks compared to classical ones.

Multi-objective optimization of heat transfer performance of H-type fin with vortex generator based on NSGA-II

To further enhance the performance of heat exchangers and bolster waste heat recovery, vortex generators (VGs) of various shapes are added to the H-type fins. This study explores the impact of VGs’ attack angles and configurations on the thermal performance of H-type finned tubes under different Reynolds (Re) numbers. Additionally, multiple dimensionless evaluation metrics are introduced to assess the flow and heat transfer characteristics with VGs, and correlations for predicting the Nusselt (Nu) number and pressure drop at varying attack angles are developed. The results reveal that at low Re numbers, trapezoidal winglets yield the highest comprehensive performance factor (R-factor), while at high Re numbers, rectangular winglets prevail. Compared to trapezoidal winglet configurations, rectangular winglets enhance the Nu by 6.49%-6.67%. Among the various attack angle configurations, the 45° rectangular winglets exhibit the most favorable overall heat transfer performance, with a Nu increase of 12.07% compared to standard H-type fins. It is observed that installing more than two VGs can result in an R-value less than 1, suggesting that excessive VG placement in H-type fin heat exchangers is not advisable. Finally, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to identify Pareto optimal points, which exhibit lower resistance and enhanced convective heat transfer. The Pareto optimal set, in comparison to different attack angle CFD data, shows a 31.27% reduction in resistance and a 15.72% increase in Nu.

Managing low–acuity patients in an Emergency Department through simulation–based multiobjective optimization using a neural network metamodel

This paper deals with Emergency Department (ED) fast-tracks for low-acuity patients, a strategy often adopted to reduce ED overcrowding. We focus on optimizing resource allocation in minor injuries units, which are the ED units that can treat low-acuity patients, with the aim of minimizing patient waiting times and ED operating costs. We formulate this problem as a general multiobjective simulation-based optimization problem where some of the objectives are expensive black-box functions that can only be evaluated through a time-consuming simulation. To efficiently solve this problem, we propose a metamodeling approach that uses an artificial neural network to replace a black-box objective function with a suitable model. This approach allows us to obtain a set of Pareto optimal points for the multiobjective problem we consider, from which decision-makers can select the most appropriate solutions for different situations. We present the results of computational experiments conducted on a real case study involving the ED of a large hospital in Italy. The results show the reliability and effectiveness of our proposed approach, compared to the standard approach based on derivative-free optimization.

Multi-objective optimization of transpiration cooling for high pressure turbine vane

Transpiration cooling is a promising cooling measure for high-temperature components in gas turbines. Although the flow and heat transfer characteristics of transpiration cooling have been investigated in several experimental and numerical researches, the design optimization of transpiration cooling is less studied until now. In this paper, a multi-objective optimization framework based on the ANN surrogate model and the NSGA-Ⅱ is built to optimize the transpiration cooling of C3X turbine vane. The transpiration cooled C3X vane consists of multiple porous zones whose porosities could be different and are treated as the design parameters. The optimization objectives are minimum area-averaged vane surface temperature and minimum aerodynamic loss. A total of 960 CFD simulations are conducted to prepare the sample dataset. After the validation of the surrogate-based optimization framework, the Pareto front is obtained as an output. Three representative Pareto-optimal points are chosen from the Pareto front, considering the best cooling performance, the lowest aerodynamic loss, and a balance between them. The porosity distributions and coolant allocations, the cooling performances, and the aerodynamic losses for the three Pareto points are discussed, and the involved flow and heat transfer characteristics are analyzed. The results reveal that to reach a balance between the cooling efficiency and the aerodynamic loss for an optimal transpiration cooled C3X vane, coolant should be appropriately distributed to the leading edge, as well as zones immediately downstream of the leading edge.

Multi-objective optimization of heat charging performance of phase change materials in tree-shaped perforated fin heat exchangers

To enhance the convective heat transfer and overall thermal performance of horizontal latent heat storage (LHS) units, an innovative tree-shaped fin structure with perforations was introduced. A numerical simulation study examined the impact of perforation layers on the unit's overall performance. For a comprehensive analysis of the perforations' cumulative effect on the LHS unit, the Response Surface Methodology (RSM) was utilized to assess the influence of variations in perforation diameter and number on material consumption and heat exchange targets, deriving predictive correlations. The results indicated that compared to a non-perforated structure, the maximum improvement was observed with three layers of perforations, reducing material usage by 0.93%, while increasing the Nusselt number (Nu) and heat exchange by 10.19% and 36.51%, respectively. Moreover, the average temperature of the phase change material (PCM) in one and three perforated layers was higher than in the non-perforated tree-shaped fins, with complete melting times reduced by 5.37% and 2.51%, respectively. RSM results showed a negative linear correlation between increased perforation diameter and number with reduced material consumption, with the number of perforations having a more significant impact on heat exchange than their diameter. The Pareto optimal points obtained using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) demonstrated lower material usage and higher heat exchange. Compared to the non-perforated tree-shaped fins, the Pareto-optimized solutions reduced material consumption by 2%–2.68% and increased heat exchange by 79.42%–94.45%. Analysis of the flow field, temperature field, and phase change process revealed that perforations significantly enhanced the mixing of PCM in different areas of the tree-like fins and secondary flow, with temperatures near the perforations increasing by 5–7K and flow velocity by 3–4 times, significantly promoting convective heat transfer.

Multi-objective optimization of composite sandwich structures using Artificial Neural Networks and Genetic Algorithm

Sandwich structures offer significant opportunities to improve the performance of many industrial applications such as aerospace, automotive, and marine. The design of a composite sandwich structure is often challenging because it is driven by the balance between the weight and cost of these structures. In this paper, a multi-objective optimization model using a Genetic Algorithm (GA) and an Artificial Neural Network (ANN) is presented to evaluate a new optimization approach in terms of weight and cost minimization for the composite sandwich structures. Classical lamination and beam bending theories were used, along with Monte Carlo simulation, to generate the design data for the proposed composite sandwich structure, which is applied as a floor panel for a high-speed train. Multilayer feedforward neural networks were used for predicting safety factors, cost, and weight of the designed structure based on the following inputs: core density, core thickness, face sheet materials’ combinations, and applied load. The trained Neural Network model was able to predict the considered results with a good performance metric, namely the coefficient of determination (R2 = 0.99) and the Mean Square Error (MSE = 1.3·10−5).Multi-objective optimization for cost and weight minimization was performed with a Genetic Algorithm using the derived ANN model. The obtained Pareto front provided several non-dominated optimal points leading to insights on the optimization process. The Finite Element Method (FEM) was used to model the key points of the optimal designs (i.e. the design with the lowest cost, weight, and Pareto optimal points). The FEM and optimization results had a maximum deviation of about 8.9%, indicating a good agreement between the two techniques.The newly elaborated methodology demonstrates a new approach for obtaining the optimum design of the investigated composite sandwich structure constructed from honeycomb core and laminated face sheets in terms the cost and weight. The study concluded that the use of Carbon Fiber-Reinforced Plastic (CFRP) or Fiber-Metal Laminate (FML) face sheets results in significant weight savings of about 59.5% and 48.6%, respectively, compared to an all-aluminum sandwich structure.

A Slug Flow Platform with Multiple Process Analytics Facilitates Flexible Reaction Optimization.

Flow processing offers many opportunities to optimize reactions in a rapid and automated manner, yet often requires relatively large quantities of input materials. To combat this, the use of a flexible slug flow reactor, equipped with two analytical instruments, for low-volume optimization experiments are reported. A Buchwald-Hartwig amination toward the drug olanzapine, with 6 independent optimizable variables, is optimized using three different automated approaches: self-optimization, design of experiments, and kinetic modeling. These approaches are complementary and provide differing information on the reaction: pareto optimal operating points, response surface models, and mechanistic models, respectively. The results are achieved using <10% of the material that would be required for standard flow operation. Finally, a chemometric model is built utilizing automated data handling and three subsequent validation experiments demonstrate good agreement between the slug flow reactor and a standard (larger scale) flow reactor.

Koopman-based surrogate models for multi-objective optimization of agent-based systems

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

Overall efficiency increment in a pin-fin microchannel heat sink using response surface methodology and Pareto optimization

In modern technology, anticipating the optimal thermal performance in microchannel heat sinks (MCHSs) is a vital response to overheating challenges in high-performance electronic devices. The Response Surface Methodology (RSM) application presents an innovative way of modeling such equipment's behavior. In the current study, an MCHS with pin fins was chosen to examine the Nusselt number (Nu) and pressure drop (ΔP). Using two RSM models and multi-objective optimization, the study tried to discern the optimal values of the responses in the MCHS. The RSM models examined three key parameters: length, installation angle, and the spacing between pin fins. The interactive impacts of independent parameters and their consequent effect on the responses were also explored. The RSM models attained exceptional predictive accuracy, with the determination coefficient values of 0.9946 and 0.9986 for Nu and ΔP, respectively. The working fluid applied in the present work was water with an inlet temperature of 288 K and a Reynolds number of 300. Besides, the constant heat flux of 100 W/cm2 was exposed to the bottom wall of the MCHS. In pursuit of an optimal MCHS design that maximizes Nu while minimizing ΔP, the study employed the relative efficiency index (η) parameter. Considering heat transfer and ΔP in the pin-fin MCHS, the optimal design showed an impressive improvement of about 64.5 % compared to the fin-free heat sink. Moreover, the study provided Pareto optimal points for Nu, ΔP, and η, adding depth to understanding the complex trade-offs within the investigated MCHS.

Arc-curved microchannels engraved on segmented circular heat sink for heat transfer augmentation; ANN-based performance optimization

The proficient management and supervision of thermal conditions in microelectronic equipment are becoming progressively challenging owing to the imposition of heightened heat fluxes. The exploration of recently developed microchannel heat sinks (MCHSs) is currently underway to effectively tackle this matter. Modifying the geometric characteristics of these gadgets has proven to be highly effective in augmenting their comprehensive performance. In the present study, a novel arc-curved microchannels engraved on segmented circular heat sink and introduced configurations comprising of six discrete segments of spiral microchannels. The study focused on examining the influence of individual partitions on the Nusselt number (Nu) and pressure drop (ΔP) of the MCHS. The obtained results demonstrate that all the proposed configurations exhibit considerably higher values of the Nu in comparison to the reference MCHS consisting of 21 rectangular channels. Nevertheless, the notable augmentation in the value of the parameter Nu occurred simultaneously with an escalated ΔP. Hence, the relative efficiency index was employed as a more precise measure for evaluations. All of the designs suggested in this investigation were found to be effective when subjected to volume flow rates surpassing 47.303 ml/min. In an illustrative case, the segmented circular MCHS encompassing 10 spiral microchannels exhibited an enhanced overall efficiency of 25.9 % when operated at a volume flow rate of 66.225 ml/min, as compared to the benchmark design. In addition, artificial neural networks (ANN) were utilized to comprehensively scrutinize the influence of variables and construct a prognostic model to ascertain the overall effectiveness of the MCHS, obviating the necessity for convoluted, time-consuming, and costly experimental procedures and computations. The presentation of the Pareto optimal points effectively portrayed the optimal and unfavorable outcomes under consideration.

Bicriteria fabrication scheduling of two-component jobs on a single machine

This paper studies the bicriteria problem of non-preemptively scheduling n jobs, each of which is associated with a due date and comprises a standard and a specific component, on a single fabrication machine to minimize makespan and maximum lateness simultaneously. The specific components are processed individually and the standard components are grouped into batches for processing. A setup time is required before each batch of standard components is processed. A standard component is available (i.e., ready for delivery to the next production stage) only when the batch it belongs to is totally completed, whereas a specific component is available on completion of its processing. The completion time of a job is defined as the moment when both its two components have been processed and are available. An O(n2logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2\\log n)$$\\end{document}-time algorithm with linear memory requirements is presented which can generate all Pareto optimal points and find a corresponding Pareto optimal schedule for each Pareto optimal point.

Multi-objective shape optimization of autonomous underwater vehicle by coupling CFD simulation with genetic algorithm

In this paper, a new method of multi-objective optimization of the shape parameters was proposed for the Autonomous Underwater Vehicle (AUV) with both towed and self-propelled, aiming to reduce drag and enhance motion stability during navigation. In this study, the hydrodynamics calculation of AUV was conducted by CFD method covering a wide range of Reynolds number between 105 and 107, and the optimization was performed by NSGA-II multi-objective optimization algorithm. Prior to deploying the optimization process, a sample library was created using the Latin hypercube sampling method to construct the Kriging approximation model. Thereafter, the model was used as the NSGA-II multi-objective optimization function, in which the range of design variables was considered to obtain the Pareto optimal solution. Furthermore, we also introduce and discuss the Pareto optimal points with special characteristics. In addition, the objective function values of these four optimal points were compared with the results of the initial model. The results showed that the drag at the four optimal points were reduced by 12.07%, 11.59%, 10.98% and 7.94%, respectively, and the overturning moments were reduced by 1.96%, 7.38%, 12.73% and 14.08%, respectively. The proposed multi-objective optimization method optimizes the shape of AUV effectively and provides valuable guidance for the design of AUV.

An Adaptive Consensus Based Method for Multi-objective Optimization with Uniform Pareto Front Approximation

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated via scalarization using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based multi-objective optimization method on the search space combined with an additional heuristic strategy to adapt parameters during the computations is proposed. The adaptive strategy aims to distribute the particles uniformly over the image space, in particular over the Pareto front, by using energy-based measures to quantify the diversity of the system. The resulting gradient-free metaheuristic algorithm is mathematically analyzed using a mean-field approximation of the algorithm iteration and convergence guarantees towards Pareto optimal points are rigorously proven. In addition, we analyze the dynamics when the Pareto front corresponds to the unit simplex, and show that the adaptive mechanism reduces to a gradient flow in this case. Several numerical experiments show the validity of the proposed stochastic particle dynamics, investigate the role of the algorithm parameters and validate the theoretical findings.

Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization

In Haeser and Ramos (J Optim Theory Appl, 187:469–487, 2020), a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn–Tucker point. We extend this approach to other generalizations of the normal cone and corresponding weakest constraint qualifications, such that local Pareto optimal points are weak Kuhn–Tucker points, local proper Pareto optimal points are weak and proper Kuhn–Tucker points, respectively, and strict local Pareto optimal points of order one are weak, proper and strong Kuhn–Tucker points, respectively. The constructions are based on an appropriate generalization of polarity to pairs of matrices and vectors.

Design Analysis of a Helium Xenon-Printed Circuit Heat Exchanger for a Closed Brayton Cycle Microtransport Reactor

Microtransport with small size and a wide range of applications is very attractive for the utilization of future reactor modularization. A microreactor uses a closed Brayton cycle (CBC) to achieve high conversion efficiencies at low specific mass. The recuperator is one of the key components of CBC system which recovers heat exhausted from the turbine. A printed circuit heat exchanger (PCHE) is currently the preferred type of recuperator for the closed Brayton cycle due to its high heat transfer efficiency, high compactness, and high pressure and temperature resistance. This work intends to analyze different geometry configurations of a zigzag PCHE to increase its heat transfer efficiency while reducing its weight and size. The effect of geometric structure parameters such as channel diameter, zigzag pitch length, and zigzag angle on the Nusselt number and Fanning friction factor is investigated using a zigzag PCHE unit model. Based on the numerical simulation, the principle of least squares is employed to carry out a nonlinear fitting of the flow and heat transfer criterion correlation equations. Besides, the maximum value of the Nusselt number and minimum value of the Fanning friction factor are optimized as two conflicting objective functions using the nondominated sorting genetic algorithm-II (NSGA-II), with which a set of optimal solutions is obtained. Meanwhile, the shortest normalized distance is used to determine the compromised solution on the Pareto optimal points, and the independent variable’s sensitivity analysis is performed. Finally, a multiobjective optimization analysis is conducted for the PCHE to achieve lightweight and the high heat transfer efficiency design requirements of SIMONS.

A Proof That Using Crossover Can Guarantee Exponential Speed-Ups in Evolutionary Multi-Objective Optimisation

Evolutionary algorithms are popular algorithms for multiobjective optimisation (also called Pareto optimisation) as they use a population to store trade-offs between different objectives. Despite their popularity, the theoretical foundation of multiobjective evolutionary optimisation (EMO) is still in its early development. Fundamental questions such as the benefits of the crossover operator are still not fully understood. We provide a theoretical analysis of well-known EMO algorithms GSEMO and NSGA-II to showcase the possible advantages of crossover. We propose a class of problems on which these EMO algorithms using crossover find the Pareto set in expected polynomial time. In sharp contrast, they and many other EMO algorithms without crossover require exponential time to even find a single Pareto-optimal point. This is the first example of an exponential performance gap through the use of crossover for the widely used NSGA-II algorithm.

Technical Note—Characterizing and Computing the Set of Nash Equilibria via Vector Optimization

What is the relation between the notion of Nash equilibria and Pareto-optimal points? It is well known that Nash equilibria do not need to be Pareto optimal, and Pareto points do not need to be Nash equilibria. However, the paper “Characterizing and Computing the Set of Nash Equilibria via Vector Optimization” by Feinstein and Rudloff takes a deeper look at the relation. It is shown that it is possible to characterize the set of all Nash equilibria as the set of all Pareto-optimal solutions of a certain vector optimization problem. This is accomplished by carefully designing the objective function and the ordering cone of the vector optimization problem such that both notions coincide. This characterization holds for all noncooperative games (nonconvex, convex, linear). It opens up a new way of computing Nash equilibria, as one can now use techniques and algorithms from vector optimization to compute the set of all Nash equilibria, which is in contrast to the classical fixed-point iterations that find just a single Nash equilibrium.

Environmental and financial multi-objective optimization: Hybrid wind-photovoltaic generation with battery energy storage systems

The present study proposes a multi-objective optimization method for wind and photovoltaic (PV) hybrid generation with battery energy storage, considering a tariff policy issue for the grid-connected residential scenario. The proposed method used the Response Surface Methodology (RSM) to model two objective functions, one environmental (Carbon footprint) and the other financial (Net Present Value - NPV) in relation to four controllable variables. To perform the multi-objective optimization, the Normal-Boundary Intersection (NBI) was used to construct the Pareto frontier. Finally, the Levelized Cost of Energy (LCOE) criterion was used to select the best Pareto optimal point. The proposed model was applied in Brazilian cities from different geographic regions. The main results of the study indicated that only regions with favorable environmental conditions and higher energy tariffs became financially viable for the proposed model, with NPV values ranging from R$ −76,080.94 to R$ 69,675.23. As for the Carbon footprint (emission of CO2eq), the values ranged from 8951.47 to 27,939.78 kgCO2/kWh, being strongly influenced by the adopted power generation technology. The use of LCOE to select the best solution provided a metric for the cost of implementing a technology, whose values ranged from 1.093 to 1.981 R$/kWh. It is still not advantageous to opt for the use of batteries for later use at peak hours, even when the tariff modality selected was the white tariff; and energy storage systems that could enable the implementation of this policy proved to be economically unfeasible. In the current Brazilian legislation, the services and benefits generated by energy storage are not remunerated, which penalizes the investment in this type of technology. As proved, solar PV technology, despite being cheaper, was penalized by a greater need for storage capacity, which led to optimal configurations with greater participation of wind generation. This indicates the need for incentives mainly related to wind energy and batteries, which are still expensive elements in the national scenario for a residential generation, reducing the probability of achieving economic viability.

Supply Chain Optimization under Risk and Uncertainty using Nondominated Sorting Genetic Algorithm II for Automobile Industry

In recent decades, the use of supply chain management is essential for developing new technologies and setting the ground in expanding major global markets to integrate suppliers, manufacturers, warehouses, and stores effectively. In addition, the growing competition in the modern business environment has created an increasing trend of new products and improved product quality for attracting more consumers. However, an increase in the related costs and uncertainty in these innovations requires the development of algorithms to solve optimization problems. Therefore, this study is aimed to implement a multi-product supply chain including raw material suppliers, factories, distributors, and customers to maximize the quality and minimize costs. To this aim, supplier quality, distribution centers, and manufacturing products were considered for the quality model, while warehousing costs, product production, transportation, defective raw materials, and the like were regarded for the cost model. Then, the NSGAII algorithm was used for solving the created optimization problem, and accordingly, the optimal Pareto points were calculated. Based on the results, the proposed model can give the manufacturer the ability to decide on a multi-product and multi-time supply chain by involving cost and quality variables. Thus, the owner can manage the supply chain of the factory effectively.

Adversarial Robustness via Fisher-Rao Regularization.

Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce Fire, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, we verify on a simple linear and Gaussian model, that all Pareto-optimal points in the accuracy-robustness region can be reached by Fire while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to a simultaneous 1% of improvement in terms of clean and robust performances while reducing the training time by 20% over the best-performing methods.