Pareto Optimization Problem Research Articles

Encoding prior knowledge in ensemble refinement.

The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we propose how to set the exchange rate a priori to properly balance this trade-off. We focus on gentle ensemble refinement, where the difference between the potential energy surfaces of the reference and refined models is small on a thermal scale. By relating the variance of this energy difference to the Kullback-Leibler divergence between the respective Boltzmann distributions, one can encode prior knowledge about energy uncertainties, i.e., force-field errors, in the exchange rate. The energy uncertainty is defined in the space of observables and depends on their type and number and on the thermodynamic state. We highlight the relation of gentle refinement to free energy perturbation theory. A balanced encoding of prior knowledge increases the quality and transparency of ensemble refinement. Our findings extend to non-Boltzmann distributions, where the uncertainty in energy becomes an uncertainty in information.

Leveraging trust for joint multi-objective and multi-fidelity optimization

In the pursuit of efficient optimization of expensive-to-evaluate systems, this paper investigates a novel approach to Bayesian multi-objective and multi-fidelity (MOMF) optimization. Traditional optimization methods, while effective, often encounter prohibitively high costs in multi-dimensional optimizations of one or more objectives. Multi-fidelity approaches offer potential remedies by utilizing multiple, less costly information sources, such as low-resolution approximations in numerical simulations. However, integrating these two strategies presents a significant challenge. We propose the innovative use of a trust metric to facilitate the joint optimization of multiple objectives and data sources. Our methodology introduces a modified multi-objective (MO) optimization policy incorporating the trust gain per evaluation cost as one of the objectives of a Pareto optimization problem. This modification enables simultaneous MOMF optimization, which proves effective in establishing the Pareto set and front at a fraction of the cost. Two specific methods of MOMF optimization are presented and compared: a holistic approach selecting both the input parameters and the fidelity parameter jointly, and a sequential approach for benchmarking. Through benchmarks on synthetic test functions, our novel approach is shown to yield significant cost reductions—up to an order of magnitude compared to pure MO optimization. Furthermore, we find that joint optimization of the trust and objective domains outperforms sequentially addressing them. We validate our findings with the specific use case of optimizing particle-in-cell simulations of laser-plasma acceleration, highlighting the practical potential of our method in the Pareto optimization of highly expensive black-box functions. Implementation of the methods in existing Bayesian optimization frameworks is straightforward, with immediate extensions e.g. to batch optimization possible. Given their ability to handle various continuous or discrete fidelity dimensions, these techniques have wide-ranging applicability in tackling simulation challenges across various scientific computing fields such as plasma physics and fluid dynamics.

DERNA Enables Pareto Optimal RNA Design.

The design of an RNA sequence that encodes an input target protein sequence is a crucial aspect of messenger RNA (mRNA) vaccine development. There are an exponential number of possible RNA sequences for a single target protein due to codon degeneracy. These potential RNA sequences can assume various secondary structure conformations, each with distinct minimum free energy (MFE), impacting thermodynamic stability and mRNA half-life. Furthermore, the presence of species-specific codon usage bias, quantified by the codon adaptation index (CAI), plays a vital role in translation efficiency. While earlier studies focused on optimizing either MFE or CAI, recent research has underscored the advantages of simultaneously optimizing both objectives. However, optimizing one objective comes at the expense of the other. In this work, we present the Pareto Optimal RNA Design problem, aiming to identify the set of Pareto optimal solutions for which no alternative solutions exist that exhibit better MFE and CAI values. Our algorithm DEsign RNA (DERNA) uses the weighted sum method to enumerate the Pareto front by optimizing convex combinations of both objectives. We use dynamic programming to solve each convex combination in time and space. Compared with a CDSfold, previous approach that only optimizes MFE, we show on a benchmark data set that DERNA obtains solutions with identical MFE but superior CAI. Moreover, we show that DERNA matches the performance in terms of solution quality of LinearDesign, a recent approach that similarly seeks to balance MFE and CAI. We conclude by demonstrating our method's potential for mRNA vaccine design for the SARS-CoV-2 spike protein.

Innovative shielding technique for wireless power transfer systems

AbstractThe High Magnetic Passive Loop (HMCPL) technique is proposed as an innovative passive shielding system to mitigate the undesired dispersion of the magnetic field produced by a wireless power transfer (WPT) system, thus reducing the risk of hazardous human exposure. The magnetic structure is described both in terms of lumped parameters circuit, useful for sizing, and in terms of a geometrical representation solved by finite element method, useful to assess the field attenuation effects. Sizing of the resonance capacitors in the shielded WPT structure is approached as a Pareto optimization problem and solved via genetic algorithm. HMCPL shielding design guidance is provided to reduce the magnetic field emission in the surrounding environment. Furthermore, the influence of the shielding on the performance of the WPT system is also evaluated.

Pricing energy consumption and residential energy‐efficiency investment: An optimal tax approach

AbstractWe analyze a Pareto optimal income tax problem à la Mirrlees in which households consume three types of goods: energy goods, energy‐efficient investments, and nonenergy goods. The two main ingredients of our normative analysis are: (i) an indirect relationship between energy and the satisfaction of energy needs, as energy‐efficient investments transform energy into services, such as light, heating, and air conditioning; and (ii) imperfect information of the policy designer as regards the level of energy efficiency of households' housing and their labor market productivity. Each household differs with respect to these two latter characteristics, and the government designs a nonlinear income tax combined with energy and energy‐efficient investment nonlinear pricing that maximizes a weighted sum of households' utilities. We show that a benevolent social planner should distort energy prices in a way that depends on the difference between the saturation of energy needs and the complementarity between energy and the level of energy efficiency in the provision of energy services. A sufficient condition for energy consumption to be subsidized is that the rebound effect is small. Second, when individuals can invest in energy efficiency on top of energy consumption, these investments should always be subsidized and the marginal subsidy should always be higher than the one on energy consumption.

Pareto optimal filter design with hybrid $ H_{2} /H_{\infty} $ optimization

<abstract><p>In this article, we study the Pareto optimal $ H_{2} $ /$ H_{\infty} $ filter design problem for a generalization of discrete-time stochastic systems. By constructing the estimation equation of the given systems with the estimated signal, a filter error estimation system is obtained. The aim is to obtain a gain matrix $ K^{\star} $ that optimizes both performance indicators we set. To deal with this problem, two different upper bounds for two performance indicators are given respectively. The optimal problem therefore is transformed into a Pareto optimal problem with linear matrix inequalities ($ LMIs $) which can be addressed through the $ LMI $ toolbox in $ MATLAB $.</p></abstract>

GAN-Based Pareto Optimization for Self-Healing of Radio Access Network Slices

Radio Access Network (RAN) slicing is a promising architectural technology to address extremely diversified service demands and provide profitable business models for future mobile networks. In RAN slicing architecture, self-healing is an important functional module to minimize the impact of network failings on the performance of RAN slices. However, self-healing of burgeoning sliced RAN is vastly different from that of traditional RAN and has been rarely investigated. In this paper, we address the Self-healing of RAN Slice (SRANS) problem by modeling it as a Pareto optimization problem with the aim of maximizing the self-healing utilities of individual RAN slices. To deal with the weakness of diversity maintenance in traditional Pareto optimization methods, we propose a Generative Adversarial Network (GAN) based Pareto Optimization (GPO) framework. Specifically, we employ self-conditioned GANs to replace the offspring reproduction module in the traditional Evolutionary Algorithm (EA), where the insufficiency of diversity maintenance in EAs is effectively overcome. Furthermore, we theoretically prove that GPO framework is guaranteed to converge to the optimal Pareto solution set. Numerical results demonstrate that the convergence of proposed GPO framework can be expedited by enhancing the diversity of solution sets in solving the SRANS problem. Compared with traditional schemes, GPO can achieve significant performance gain in terms of the utilities and isolation level of repaired RAN slices.

Multi-object aerodynamic design optimization using deep reinforcement learning

Aerodynamic design optimization is a key aspect in aircraft design. The further evolution of advanced aircraft derivatives requires a powerful optimization toolbox. Reinforcement learning (RL) is a powerful optimization tool but has rarely been utilized in the aerodynamic design. It can potentially obtain results similar to those of a human designer, by accumulating experience from training. In this work, a popular RL method called proximal policy optimization (PPO) is proposed to investigate multi-object aerodynamic design optimization. By observing the aerodynamic performances of different airfoils, the PPO updates a reasonable policy to generate the optimal airfoils in a single step. In a Pareto optimization problem with constraints, the PPO requires only 15% of the computational time of the non-dominated sorted genetic algorithm (II) to achieve the same accuracy. The results from testing show that the agent learns a policy that can achieve ∼4.3%–10.1% improvements of the aerodynamic performance compared with the results of baseline.

Adaptive Pitch Controller of a Large-Scale Wind Turbine Using Multi-Objective Optimization

This paper deals with the control problems of a wind turbine working in its nominal zone. In this region, the wind turbine speed is controlled by means of the pitch angle, which keeps the nominal power constant against wind fluctuations. The non-uniform profile of the wind causes tower displacements that must be reduced to improve the wind turbine lifetime. In this work, an adaptive control structure operating on the pitch angle variable is proposed for a nonlinear model of a wind turbine provided by FAST software. The proposed control structure is composed of a gain scheduling proportional–integral (PI) controller, an adaptive feedforward compensation for the wind speed, and an adaptive gain compensation for the tower damping. The tuning of the controller parameters is formulated as a Pareto optimization problem that minimizes the tower fore-aft displacements and the deviation of the generator speed using multi-objective genetic algorithms. Three multi-criteria decision making (MCDM) methods are compared, and a satisfactory solution is selected. The optimal solutions for power generation and for tower fore-aft displacement reduction are also obtained. The performance of these three proposed solutions is evaluated for a set of wind pattern conditions and compared with that achieved by a classical baseline PI controller.

Multi-objective optimum design of an alpha type Stirling engine using meta-models and co-simulation approach

An alpha type Stirling engine was optimized using meta-models considering uninterrupted electric power supply concurrently with natural gas combi boilers at homes during electricity interruptions. To predict and optimize the power and efficiency of the designed Stirling engine, an artificial neural network (ANN) model was trained as a meta-model. The ANN modeling method was used in solving a multi-objective Pareto optimization problem under some constraints to determine the optimum engine parameters. The design parameters were swept volume, hot and cold cylinder temperatures, gas constant, charge pressure and engine operation speed. Feed forward and Levenberg–Marquardt back propagation algorithms were evaluated to determine the best resulting network architecture that was found as 6–12–8–1. Subsequently, the fraction of variance (Rf) value was calculated close to 1 and the absolute mean error percentage (AMEP) was calculated as 6.07%. Trained ANN model was used in solving the multi-objective optimization problem. Using the optimum design parameters, the meta-model predicted the power as 73.3 W and efficiency as 32.2%. Co-simulation approach was followed to verify the optimization results, and the nominal power output and corresponding efficiency were calculated using the Schmidt theory and the calibrated 1-D model created by the GT-Suite software that yield respectively, 144.6 W and 85.8 W for the power and 35% and 35.1% for the cycle efficiency. Consequently, the use of an ANN model in solving the associated optimization problem proved itself as a fast, accurate enough and powerful method to find the optimum design parameters and predict the engine performance.

Multi-Objective Reactive Power Optimization Based on Improved Particle Swarm Optimization With ε-Greedy Strategy and Pareto Archive Algorithm

This paper proposes combining an improved particle swarm optimization and Pareto archive algorithm to solve the multi-objective reactive power optimization problem. The idea of $\varepsilon $ -greedy strategy is adopted and designed to improve particle swarm optimization algorithm. It makes some particles have stronger global search capability, meanwhile, others have stronger local search capability during the whole iteration process. Henceforth, the strategy significantly explores the possibility of optimal solution in local space at the early stage of the iteration, in addition, it mitigates the tendency to fall into the local optimal solution at the later stage of the iteration. The Pareto optimal solution selection problem is solved by minimizing the sum of the difference between each objective function and its optimal solution. The proposed approach is tested on IEEE39-bus and IEEE118-bus system, and it is demonstrated that the proposed approach not only restores the nodes voltage to the normal range and achieves better value for each objective function, but also outperforms other algorithms including standard particle swarm optimization and non-dominated sorting genetic algorithm II(NSGA-II).

Joint Radar-Communication Transmission: A Generalized Pareto Optimization Framework

Dual-functional radar-communication (DFRC) has been envisioned as a key enabler for a number of emerging applications. Nevertheless, the intrinsic difference between communication and sensing functionalities has imposed challenges in fully realizing the promise of the technology. In this paper, we propose a Pareto optimization framework for a multi-antenna DFRC system, where a single transmitter with multiple antennas communicates with multiple users and detects radar targets simultaneously. To begin with, we define an achievable performance region that is built upon the difference between peak and sidelobe (DPSL) of the radar spatial beampattern and the signal-to-interference-plus-noise ratio (SINR) of each communication user, which is proved to be compact and normal. Then, we formulate a fairness-profile optimization problem with a lowest acceptable performance level of dual functionalities and a pre-defined direction to attain the Pareto boundary of the achievable performance region. Also, we provide a bisection search algorithm to solve the Pareto optimization problem with polynomial complexity, and prove its optimality can be achieved by single-stream transmission. As a further step, we extend the discussion to the DFRC beamforming design given hardware impairments. Finally, we evaluate the effectiveness of the proposed design and the impact brought by the impairments by numerical simulations.

Pareto-Optimal Strategy for Linear Mean-Field Stochastic Systems With H∞ Constraint.

This article presents results on designing the Pareto-optimal strategy under H∞ constraint for the linear mean-field stochastic systems disturbed by external disturbances. First, combining the stochastic H∞ control theory with the stochastic mean-field theory, we derive the stochastic bounded real lemma (SBRL) of our considered linear mean-field stochastic systems with the stochastic initial condition. Second, we use the mean-field forward-backward stochastic differential equation to solve the mean-field linear quadratic Pareto-optimal problem with indefinite cost functionals. It is proved that the existence of a closed-loop Pareto-optimal strategy is equivalent to the solvability of the coupled generalized differential Riccati equations when some conditions are satisfied. Finally, a necessary and sufficient condition for the Pareto-optimal strategy under the H∞ constraint is researched by four-coupled matrix-valued equations. Besides, we also obtain the Pareto frontier for the mean-field stochastic system with only state-dependent noise. A practical example is presented to show the effectiveness of our main results.

Weight-Vibration Pareto Optimization of a Triple Mass Flywheel for Heavy-Duty Truck Powertrains

Enhanced efficiency of heavy-duty truck powertrains with constraints imposed on noise, vibration, and harshness requires novel solutions for torsion vibrations attenuation. In the paper, the weight-vibration Pareto optimization problem for a novel vibration absorber, a triple mass flywheel, for application in heavy-duty truck powertrains is considered. Global sensitivity analysis and Pareto optimization method are used to design a novel vibration absorber. The optimization method attempts to minimize oscillations of the torque at the transmission input shaft as well as to minimize total mass inertia of the absorber. It is shown that there exists a Pareto front between the measure of the attenuation of oscillations of the torque and the total mass inertia of a triple mass flywheel. The optimized design parameters for the absorber are obtained that provide the best attenuation of oscillations of the torque at the transmission input shaft for different mean values of the engine driving torque. The analysis shows real evidence of the feasibility of the application of this concept of vibration absorbers in heavy-duty truck powertrains. It is also shown that optimized design parameters of a triple mass flywheel put this concept in a superior position in comparison with a dual mass flywheel.

P-MOIA-RS: a multi-objective optimization and decision-making algorithm for recommendation systems

Besides accuracy, diversity of recommendation list is also important for users. Hence, the optimization of the recommendation system can be abstracted as a multi-objective problem because accuracy and diversity are contradictory goals. Available multi-objective optimization based recommendation schemes return the Pareto set for the target users. However, the scale of Pareto solutions is uncontrollable. If a Pareto set contains too many solutions, it will not be quite useful for users to make the final decision. In this paper, multi-objective immune algorithm is used to improve recommendation accuracy and diversity, then we can get the pareto set. Further, we introduce PROMETHEE into the recommendation system to get a more precise evaluation of Pareto solutions. By combining PROMETHEE with Pareto, we redefine recommendation as Top-n PROMETHEE Pareto optimization problem and a multi-objective immune optimization and decision-making algorithm is presented. The experimental results show that the proposed algorithm, compared with other existing algorithms, can generate more diverse and accurate recommendation list and provide more precise decision-making for the user.

Pareto optimization for control agreement in patient referral coordination

Imbalanced utilization of medical resources between hospitals at different levels is prevalent in China. Through coordination of an upper-level hospital (ULH) and a lower-level hospital (LLH), ULH-referrals are encouraged so that the ULH can transfer less urgent patients to the LLH to alleviate the utilization imbalance. To the entire system, the patient referral coordination is dependent not only on the agreed transfer quantity but perhaps more on the patient flow characteristics and simultaneously mutual decisions from both the ULH and the LLH. In this paper, we thus investigate a control agreement framework between the ULH and the LLH that helps both hospitals to maximize their respective benefits. More specifically, a control agreement framework allows each hospital applies a threshold-based policy to make decisions on either referral (by ULH) or acceptance (by LLH). And a Pareto-based negotiation process is proposed to carry out the control agreement. To optimize the threshold pair from both hospitals, we formulate a Pareto optimization problem with objectives being revenue-and-monetarized-patient-blockage related benefits of the two hospitals. Given the complexity in analyzing patient flows of the system, we develop a multi-fidelity model-based optimization approach, which integrates the advantages of queueing model and discrete event simulation. Specifically, we adopt the idea of ordinal transformation and optimal sampling. In a real-world case study, we investigate the control policy in light of the referral coordination practice between Shanghai No. 6 People's Hospital and No. 8 People's Hospital. Our Pareto-optimization approach is applicable to many service systems with waiting time sensitive customers. Our work provides a novel perspective of operational level coordination design for the service outsourcing/sharing management literature.

A Multi-Objective Task Scheduling Method for Fog Computing in Cyber-Physical-Social Services

Fog computing provides users with data storage, computing, and other services by using fog layer devices close to edge devices. Tasks and resource scheduling in fog computing has become a research hotspot. For the multi-objective task-scheduling problem in fog computing, an adaptive multi-objective optimization task scheduling method for fog computing (FOG-AMOSM) is proposed in this paper. In this method, the total execution time and the task resource cost in the fog network are taken as the optimization target of resource allocation, and a multi-objective task scheduling model is designed. Since the objective model is a Pareto optimal solution problem, the global optimal solution can be obtained by using multi-objective optimization theory and the improved multi-objective evolutionary heuristic algorithm. Moreover, to obtain a better distribution of the current task scheduling group, the neighborhood is adaptively changed according to the current situation of the task scheduling group in fog computing, which avoids the problem that the neighborhood value caused by the neighborhood policy in the multi-objective algorithm affects the distribution of the task scheduling population. This algorithm is used to solve the non-inferior solution set of the utility function index of fog computing task scheduling to try to solve the multi-objective cooperative optimization problem in fog computing task scheduling. The results show that the proposed method has better performance than other methods in terms of total task execution time, resource cost and load dimensions.

Общий подход к построению математических моделей и алгоритмов для решения прямых и обратных задач для сервопривода жидкости с управлением дроссельной заслонкой

It is pointed out that direct and inverse parametric problems on fluid servo drives with throttle control of energy flows (FSD/T) are usually dealt with using various mathematical models and packages of application computer programs depending on the solution objectives, established drive structure and design, and the type of input information signal. An FSD/T with a mechanical signal is known as a hydromechanical servo drive(HMSD/T), and that with an electrical is known as an electrohydraulical servo drive (EHSD/T). Special-purpose fluid servo drives with throttle control that use a combined signal are also possible. The variety of models is a factor that adds difficulty to development of algorithms and use of the obtained information; in particular, when transition from direct to inverse scenarios is made. At the same time, whatever the type of information signal, the drive structure contains the same energy loop, namely, a combination of the hydraulic amplifier output stage and a hydraulic motor. It is exactly this loop that determines the FSD/T power and dynamic performance characteristics. A universal mathematical model of a single-channel FSD/T, which is equally effective for solving direct and inverse problems as applied to HMSD/T and EHSD/T, is presented. The peculiarities of writing the universal model for HMSD/T and EHSD/T are considered in detail; a block diagram of implementing the software package for numerically solving direct and inverse problems is given, and algorithms for solving direct and inverse parametric problems for this model are presented. A universal algorithm and block diagram for solving the direct and inverse Pareto optimization problem for some particular competition parameters are drawn up. The advantages of using the universal model for the real optimization design of this class of drives are shown.

Consequential LCA and LCC using linear programming: an illustrative example of biorefineries

PurposeThis paper aims to demonstrate how LCA can be improved by the use of linear programming (LP) (i) to determine the optimal choice between new technologies, (ii) to identify the optimal region for supplying the feedstock, and (iii) to deal with multifunctional processes without specifying a certain main product. Furthermore, the contribution of LP in the context of consequential LCA and LCC is illustrated.MethodsWe create a mixed integer linear program (MILP) for the environmental and economic assessment of new technologies. The model is applied in order to analyze two residual beech wood-based biorefinery concepts in Germany. In terms of the optimal consequences for the system under study, the principle of the program is to find a scaling vector that minimizes the life cycle impact indicator results of the system. We further transform the original linear program to extend the assessment by life cycle costing (LCC). Thereby, two multi-objective programming methods are used, weighted goal programming and epsilon constraint method.Results and discussionThe consequential case studies demonstrate the possibility to determine optimal locations of newly developed technologies. A high number of potential system modifications can be studied simultaneously without matrix inversion. The criteria for optimal choices are represented by the objective functions and the additional constraints such as the available feedstock in a region. By combining LCA and LCC targets within a multi-objective programming approach, it is possible to address environmental and economic trade-offs in consequential decision-making.ConclusionsThis article shows that linear programming can be used to extend standard LCA in the field of technological choices. Additional consequential research questions can be addressed such as the determination of the optimal number of new production plants and the optimal regions for supplying the resources. The modifications of the program by additional profit requirements (LCC) into a goal program and Pareto optimization problem have been identified as promising steps toward a comprehensive multi-objective LCSA.

QoE-Driven Adaptive K-Push for HTTP/2 Live Streaming

Dynamic adaptive streaming (DAS) over HTTP has been widely deployed over the Internet. However, due to the pull-based nature of HTTP/1.1, there exists intolerable streaming latency and high request overhead in the current DAS systems. With dynamic k-push , HTTP/2 live streaming promises to achieve low live latency with less overhead and small segment duration. In this paper, we propose a quality of experience (QoE) driven adaptive k-push mechanism (QK-Push) for HTTP/2 live streaming. The client just sends one request to set push length ( $K$ ) and bitrate ( v ) parameters and the server would push back $K$ segments in a batch. To determine k-push parameters, a probabilistic buffer model is first designed to avoid buffer underflow/overflow. Also, three QoE objective functions are designed to ensure the high streaming quality (bitrate), playback continuity, and smoothness. QK-Push casts this multi-objective optimization problem as a Pareto optimal problem . To solve it, a Nash bargaining solution is designed to balance the needs for video quality, bitrate smoothness, and request overhead. Finally, the segments in each push cycle are selected by solving the Nash problem with a discrete space Lagrangian method. We implement an HTTP/2 live streaming prototype system, with the QK-Push algorithm over modified dash.js and media presentation description. To evaluate the performances, the extensive live streaming experiments are carried out over a controllable network test bed and real Internet trace. The results demonstrate that the proposed QK-Push algorithm is able to improve the average bitrate up to 13%, reduce the bitrate oscillations up to 81%, decrease the startup delay up to 58%, and increase the estimate the mean opinion score up to 12% compared to the current HTTP/1.1 system.