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Academic literature on the topic 'Nondominated set'

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Published: 21 February 2024

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Journal articles on the topic "Nondominated set"

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Regan, Kevin, and Craig Boutilier. "Robust Policy Computation in Reward-Uncertain MDPs Using Nondominated Policies." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 1127–33. http://dx.doi.org/10.1609/aaai.v24i1.7740.

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The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.
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Nyiam, Paschal B., and Abdellah Salhi. "A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm." Advances in Operations Research 2021 (July 5, 2021): 1–11. http://dx.doi.org/10.1155/2021/1857030.

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The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.
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Noghin, Vladimir D. "Estimation of the set of nondominated solutions." Numerical Functional Analysis and Optimization 12, no. 5-6 (January 1991): 507–15. http://dx.doi.org/10.1080/01630569108816446.

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Henig, M. I. "Characterizing the nondominated set by separable functions." Journal of Optimization Theory and Applications 59, no. 3 (December 1988): 423–44. http://dx.doi.org/10.1007/bf00940308.

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Noghin, Vladimir D. "Upper estimate for a fuzzy set of nondominated solutions." Fuzzy Sets and Systems 67, no. 3 (November 1994): 303–15. http://dx.doi.org/10.1016/0165-0114(94)90258-5.

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Pereira, Javier, Broderick Crawford, Fernando Paredes, and Ricardo Soto. "A Bicriteria Approach Identifying Nondominated Portfolios." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/957108.

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We explore a portfolio constructive model, formulated in terms of satisfaction of a given set of technical requirements, with the minimum number of projects and minimum redundancy. An algorithm issued from robust portfolio modeling is adapted to a vector model, modifying the dominance condition as convenient, in order to find the set of nondominated portfolios, as solutions of a bicriteria integer linear programming problem. In order to improve the former algorithm, a process finding an optimal solution of a monocriteria version of this problem is proposed, which is further used as a first feasible solution aiding to find nondominated solutions more rapidly. Next, a sorting process is applied on the input data or information matrix, which is intended to prune nonfeasible solutions early in the constructive algorithm. Numerical examples show that the optimization and sorting processes both improve computational efficiency of the original algorithm. Their limits are also shown on certain complex instances.
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Abd Elazeem, Abd Elazeem M., Abd Allah A. Mousa, Mohammed A. El-Shorbagy, Sayed K. Elagan, and Yousria Abo-Elnaga. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems." Sustainability 13, no. 3 (January 28, 2021): 1372. http://dx.doi.org/10.3390/su13031372.

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Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.
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Ginanjar, Rikip, and Nur Hadisukmana. "An Algorithm to construct nondominated k-coteries." Indonesian Journal of Electrical Engineering and Computer Science 18, no. 2 (May 1, 2020): 953. http://dx.doi.org/10.11591/ijeecs.v18.i2.pp953-960.

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<p><span>One of the solution in solving k mutual exclusion problem is the concept of k-coterie. A k-coterie under a set S is a set of subsets of S or quorums such that any k + 1 quorums, there are at least two quorums intersect each other. The k mutual exclusion problern is the problem of managing processes in such a way that at most k processes can enter their critical sections simultaneously. Nondominated k-coteries are more resilient to network and site failures than doninated k-coteries; that is the availability and reliability of a distributed system is better if nondominated k-coteries are used. Algorithms to construct k-coteries have been proposed, unfortunately they have some restrictions, especially in constructing nondominated k-coteries. The restrictions are due to the combination of N, the number of nodes in a distributed system, and k, the number of processes allowed to enter their critical sections simultaneously. To solve this problem, this paper proposes an algorithm to construct nondominated k-coteries for all combination of N and k.</span></p>
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Qu, Dan, Xianfeng Ding, and Hongmei Wang. "An Improved Multiobjective Algorithm: DNSGA2-PSA." Journal of Robotics 2018 (September 2, 2018): 1–11. http://dx.doi.org/10.1155/2018/9697104.

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In general, the proximities to a certain diversity along the front and the Pareto front have the equal importance for solving multiobjective optimization problems (MOPs). However, most of the existing evolutionary algorithms give priority to the proximity over the diversity. To improve the diversity and decrease execution time of the nondominated sorting genetic algorithm II (NSGA-II), an improved algorithm is presented in this paper, which adopts a new vector ranking scheme to decrease the whole runtime and utilize Part and Select Algorithm (PSA) to maintain the diversity. In this algorithm, a more efficient implementation of nondominated sorting, namely, dominance degree approach for nondominated sorting (DDA-NS), is presented. Moreover, an improved diversity preservation mechanism is proposed to select a well-diversified set out of an arbitrary given set. By embedding PSA and DDA-NS into NSGA-II, denoted as DNSGA2-PSA, the whole runtime of the algorithm is decreased significantly and the exploitation of diversity is enhanced. The computational experiments show that the combination of both (DDA-NS, PSA) to NSGA-II is better than the isolated use cases, and DNSGA2-PSA still performs well in the high-dimensional cases.
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Savsani, Vimal, Vivek Patel, Bhargav Gadhvi, and Mohamed Tawhid. "Pareto Optimization of a Half Car Passive Suspension Model Using a Novel Multiobjective Heat Transfer Search Algorithm." Modelling and Simulation in Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/2034907.

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Most of the modern multiobjective optimization algorithms are based on the search technique of genetic algorithms; however the search techniques of other recently developed metaheuristics are emerging topics among researchers. This paper proposes a novel multiobjective optimization algorithm named multiobjective heat transfer search (MOHTS) algorithm, which is based on the search technique of heat transfer search (HTS) algorithm. MOHTS employs the elitist nondominated sorting and crowding distance approach of an elitist based nondominated sorting genetic algorithm-II (NSGA-II) for obtaining different nondomination levels and to preserve the diversity among the optimal set of solutions, respectively. The capability in yielding a Pareto front as close as possible to the true Pareto front of MOHTS has been tested on the multiobjective optimization problem of the vehicle suspension design, which has a set of five second-order linear ordinary differential equations. Half car passive ride model with two different sets of five objectives is employed for optimizing the suspension parameters using MOHTS and NSGA-II. The optimization studies demonstrate that MOHTS achieves the better nondominated Pareto front with the widespread (diveresed) set of optimal solutions as compared to NSGA-II, and further the comparison of the extreme points of the obtained Pareto front reveals the dominance of MOHTS over NSGA-II, multiobjective uniform diversity genetic algorithm (MUGA), and combined PSO-GA based MOEA.
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Dissertations / Theses on the topic "Nondominated set"

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Tamby, Satya. "Approches génériques pour la résolution de problèmes d'optimisation discrète multiobjectif." Electronic Thesis or Diss., Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED048.

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Lorsque les problèmes de décision font intervenir plusieurs critères contradictoires, la notion d'optimum n'a plus réellement de sens. Dès lors, les décideurs sont amenés à considérer tous les différents compromis possibles. Même s'il est possible d'éliminer ceux qui sont dominés, c'est à dire moins bons qu'un autre sur tous les critères, l'ensemble est d'autant plus complexe à déterminer que ses éléments peuvent être très nombreux. Nous nous intéressons ici aux problèmes d'optimisation combinatoire multicritères. Afin que notre méthode soit adaptable pour un grand nombre de problèmes, nous employons la programmation mathématique en nombres entiers pour définir l'ensemble des solutions réalisables
Real world problems often involve several conflicting objectives. Thus, solution of interests are efficient solutions which have the property that an improvement on one objective leads to a decay on another one. The image of such solutions are referred to as nondominated points. We consider here the standard problem of computing the set of nondominated points, and providing a corresponding efficient solution for each point
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Jamain, Florian. "Représentations discrètes de l'ensemble des points non dominés pour des problèmes d'optimisation multi-objectifs." Phd thesis, Université Paris Dauphine - Paris IX, 2014. http://tel.archives-ouvertes.fr/tel-01070041.

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Le but de cette thèse est de proposer des méthodes générales afin de contourner l'intractabilité de problèmes d'optimisation multi-objectifs.Dans un premier temps, nous essayons d'apprécier la portée de cette intractabilité en déterminant une borne supérieure, facilement calculable, sur le nombre de points non dominés, connaissant le nombre de valeurs prises par chaque critère.Nous nous attachons ensuite à produire des représentations discrètes et tractables de l'ensemble des points non dominés de toute instance de problèmes d'optimisation multi-objectifs. Ces représentations doivent satisfaire des conditions de couverture, i.e. fournir une bonne approximation, de cardinalité, i.e. ne pas contenir trop de points, et si possible de stabilité, i.e. ne pas contenir de redondances. En s'inspirant de travaux visant à produire des ensembles ε-Pareto de petite taille, nous proposons tout d'abord une extension directe de ces travaux, puis nous axons notre recherche sur des ensembles ε-Pareto satisfaisant une condition supplémentaire de stabilité. Formellement, nous considérons des ensembles ε-Pareto particuliers, appelés (ε, ε′)-noyaux, qui satisfont une propriété de stabilité liée à ε′. Nous établissons des résultats généraux sur les (ε, ε′)-noyaux puis nous proposons des algorithmes polynomiaux qui produisent des (ε, ε′)-noyaux de petite taille pour le cas bi-objectif et nous donnons des résultats négatifs pour plus de deux objectifs.
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Ou, Yang Hong, and 歐陽洪. "TOLERANCE ANALYSIS OF A NONDOMINATED SET IN MOLP." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/12753718059490602811.

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碩士
國立清華大學
工業工程研究所
82
Tolerance analysis in multiple objective linear programmes has been drawn much attention in recent years. All of these papers were assumed that a decision maker can provide his/her preference structure as a weight of importance explicitly, so the sensitivity analysis was done on one nondominated extreme point only. That is, the most preferred solution by the DM. However, DM may not realize his/her preference structure. Moreover, the final decision is not necessarily a nondominated extreme point. Instead, it can be any nondominated point. Therefore, it is necessary to analyze the entire nondominated set in order to provide more complete information for decision makings. To achieve our aim of study, three cases are considered in the tolerance analysis of a nondominated set: (1) when the cost coefficients are perturbed, (2) when the RHS is perturbed, (3) when both the cost coefficients and the RHS are perturbed simultaneously. P.L.Yu and M.Zeleny have presented a theory which shows that a nondominated set can be divided into a group of nondominated faces. Based on the theory, we propose a method to obtain the tolerance region of a nondominated set from the tolerance regions of nondominated extreme points systematically.
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OU, MING-GING, and 區明清. "Finding the set of all nondominated solutions for multiple objective linear programs." Thesis, 1986. http://ndltd.ncl.edu.tw/handle/56888085398298640306.

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Book chapters on the topic "Nondominated set"

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Jaszkiewicz, Andrzej, and Roman Słowiński. "Outranking-Driven Search Over a Nondominated Set." In Lecture Notes in Economics and Mathematical Systems, 340–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59132-7_37.

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Steuer, Ralph E. "Non-Fully Resolved Questions about the Efficient/Nondominated Set." In Multicriteria Analysis, 585–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60667-0_57.

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Metev, Boyan, and Ilia Braianov. "Choosing a Finite Set of Nondominated Points with Respect to a Finite Set of Reference Points." In Lecture Notes in Economics and Mathematical Systems, 372–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59132-7_40.

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Zhou, Zhiang, Wenbin Wei, and Kequan Zhao. "Weakly Nondominated Solutions of Set-Valued Optimization Problems with Variable Ordering Structures in Linear Spaces." In Combinatorial Optimization and Applications, 185–95. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-49611-0_13.

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Ghosh, Debdas, and Debjani Chakraborty. "On Fuzzy Ideal Cone Method to Capture Entire Fuzzy Nondominated Set of Fuzzy Multi-criteria Optimization Problems with Fuzzy Parameters." In Springer Proceedings in Mathematics & Statistics, 249–60. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2301-6_19.

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Bielza, C., D. R. íos-Insua, and S. R. íos-Insua. "Influence Diagrams under Partial Information." In Bayesian Statistics 5, 491–98. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198523567.003.0026.

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Abstract We consider influence diagrams in which only partial information is available about probabilities and utilities. Algorithms for computation of optimal alternatives in ID’s may be generalised to compute non-dominated alternatives in ID’s under partial information. Typically, the set of nondominated alternatives is too big so we introduce additional criteria to select one of those alternatives.
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Conference papers on the topic "Nondominated set"

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Yang, Ruiyue, Wei Liu, Xiaozhou Qin, Zhongwei Huang, Yu Shi, Zhaoyu Pang, Yiqun Zhang, Jingbin Li, and Tianyu Wang. "A Physics-Constrained Data-Driven Workflow for Predicting Coalbed Methane Well Production Using A Combined Gated Recurrent Unit and Multi-Layer Perception Neural Network Model." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/205903-ms.

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Abstract Coalbed methane (CBM) has emerged as one of the clean unconventional resources to supplement the rising demand of conventional hydrocarbons. Analyzing and predicting CBM production performance is critical in choosing the optimal completion methods and parameters. However, the conventional numerical simulation has challenges of complicated gridding issues and expensive computational costs. The huge amount of available production data that has been collected in the field site opens up a new opportunity to develop data-driven approaches in predicting the production rate. Here, we proposed a novel physics-constrained data-driven workflow to effectively forecast the CBM productivity based on a Gated Recurrent Unit (GRU) and Multi-Layer Perceptron (MLP) combined neural network (GRU-MLP model). The model architecture is optimized by the multiobjective algorithm: nondominated sorting genetic algorithm Ⅱ (NSGA Ⅱ). The proposed framework was used to predict synthetic cases with various fracture-network-complexities and two multistage-fractured wells in field sites located at Qinshui basin and Ordos basin, China. The results indicated that the proposed GRU-MLP combined neural network was able to accurately and stably predict the production performance of multi-fractured horizontal CBM wells in a fast manner. Compared with Simple Recurrent Neural Network (RNN), Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM), the proposed GRU-MLP had the highest accuracy and stability especially for gas production in late-time. Consequently, a physics-constrained data-driven approach performed better than a pure data-driven method. Moreover, the optimum GRU-MLP model architecture was a group of optimized solutions, rather than a single solution. Engineers can evaluate the tradeoffs within this set according to the field-site requirements. This study provides a novel machine learning approach based on a GRU-MLP combined neural network model to estimate production performances in CBM wells. The method is simple and gridless, but is capable of predicting the productivity in a computational cost-effective way. The key findings of this work are expected to provide a theoretical guidance for the intelligent development in oil and gas industry.
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Zanic, Vedran, Stanislav Kitarovic, and Pero Prebeg. "Safety as Objective in Multicriterial Structural Optimization." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20712.

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Multicriterial design methodology with safety as one of the design objectives is presented. The aim of the paper is to analyze the influence of safety based design objectives on generated nondominated designs on the Pareto frontier. Possible improvements in nondominated designs are investigated by comparison to ones obtained with the standard design procedure when safety criteria are used as design constraints only. It is assumed that safety based objectives and targets act as attractors, driving nondominated designs along the constant cost/weight contours in design space towards its safer regions. Global safety objectives (for hogging/sagging modes), are based on the maximization of ultimate longitudinal strength in vertical bending calculated via the extended IACS incremental-iterative method. Applied compound safety measures for gross-panel (stiffened panel with associated girders) are based upon 34 failure modes, belonging to serviceability/collapse subsets. Objectives based on the maximization of safety measures are applied together with standard design objectives such as minimization of initial cost and weight. The following problems were solved with different sets of objectives: (a) minimize cost and weight objectives subject to safety constraints (used for reference), (b) only the maximization of local safety measures is added to (a) as additional objectives, (c) only the maximization of global safety measures is added to (a) as additional objectives, (d) maximization of safety measures ad (b) and (c) are added to (a) as additional objectives. For each of the problems (a–d) the developed design procedure is executed. It contains two basic tasks for structural design of realistic (non-academic) problems: (1) multicriterial optimization with topology / geometry design variables; (2) multicriterial optimization of gross-panels with scantling / material design variables. Design procedure steps are executed using a fast and balanced collection of analysis and synthesis modules/methods of the OCTOPUS design system: • Determination of design load sets; • MOGA / MOPSO based generation of nondominated designs for the selected ship structure; • For each design the following analysis blocks are executed: – calculation of ship’s primary and racking response fields, – calculation of ship’s ultimate longitudinal strength, – calculation of serviceability and collapse safety criteria on the gross-panel level. Comparisons of results, based on generated Pareto hyper-surfaces and on subset of preferred designs, are given for problems (a–d). Insights into the results of optimization process, using 5-D graphics for design and attribute spaces, are also presented. Design problems of modern RoPax and SWATH structures are used in case studies.
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Guadagnini, Jacopo, and Gabriele De Zaiacomo. "Multidisciplinary Design Optimisation for Missionisation of Re-entry Vehicles: Preliminary Mission Design and Mission Capabilities Evaluation of Winged Re-Entry Vehicles Case Study." In ESA 12th International Conference on Guidance Navigation and Control and 9th International Conference on Astrodynamics Tools and Techniques. ESA, 2023. http://dx.doi.org/10.5270/esa-gnc-icatt-2023-126.

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The work presented in this paper is part of the European H2020 ASCenSIon program. In this context, the overall purpose of this research is the definition and development of a Mission Analysis and GNC missionisation tool for autonomous re-entry vehicles. In recent years, space agencies and private firms are investing in reusable spacecraft and launch vehicles to make space access and in-orbit studies more economically and environmentally sustainable. The re-flight capability, requested by a reusable space system, motivates the need for a dedicated missionisation tool. The objective of missionisation is, indeed, the minimization of the tailoring effort during the mission design phase of each flight. One approach, which can address this aim, is to provide solutions for re-entry vehicles that are qualified for multiple missions. For this reason, a crucial step for missionisation is the computation of the set of missions that a vehicle can perform concerning its design parameters. The focus of this paper is on the preliminary mission design and the evaluation of the mission capabilities of a winged re-entry vehicle by means Multidisciplinary Design Optimization (MDO) approach available within the proposed MA and GNC missionisation tool. One of the key challenges in missionizing a re-entry vehicle is the need to balance the trade-offs between a broad set of system and mission requirements and constraints to obtain robust trajectories. The missionisation in this context is, indeed, a complex and challenging task that requires a thorough understanding of the multidisciplinary aspects of the system and mission design. For this reason, the paper reports the Multidisciplinary Design Analysis (MDA) framework with an overview of the set of disciplines embedded in the tool. For this scenario, the disciplines deal with weight, geometry, and aerodynamic estimation, evaluation of the static longitudinal equilibrium and stability, computation of the aerothermal-mechanical domain, and range capability. The disciplines numerically quantify the related performance and assess the feasible space domain concerning the design variables. Then, the MDA problem is exploited by the optimization routine to optimize the design variables while maximizing targeted performance. The MDO is a crucial feature because allows for the simultaneous optimization of multiple design parameters and objectives to ensure the overall performance and feasibility of the re-entry vehicle. By using this technique, the goal is to evaluate different design options to perform trade-off studies and identify the optimal design, especially when a multi-objectives approach is considered and nondominated optimal Pareto solutions are obtained. Within the MDO process, indeed, the solution space domain is explored through the variation of the design parameters. In this research, metamodeling techniques have been adopted to reduce the computational cost. One of the main challenges faced by MDO concerns, indeed, the efficiency in solving the optimization problem due to the relatively expensive evaluation of the MDA. In particular, in this work, the MDA has been integrated with the DEIMOS Space proprietary tool (EDLS/GNC Sizing and Analysis Too) ESAT, which employs Radial Basis Functions (RBFs) to create a surrogate model of the original problem. The metamodel is built by evaluating the MDA in different design points (samples). Consequently, the metamodel predicts the performance at any point of the domain space by interpolating the outputs of the known points. ESAT, then, uses the metamodel to perform the optimization and create performance maps. One of the drawbacks of adopting a surrogate model is given by the flaw in the accuracy of the solution, especially if a large number of design parameters is taken into account and a limited number of sample points is used. To validate the optimization process, the obtained results for the scenario analysed in this paper are compared with the outcomes achieved by solving the original problem with a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. The solutions are critically discussed both in terms of accuracy and computational time. The results obtained within the case study reported in this paper show that the proposed multidisciplinary tool embedding an MDO process is a powerful tool for enhancing the missionisation of re-entry vehicles. In particular, the MDA-MDO framework is essential for efficiently missionizing re-entry vehicles, providing a solution qualified for multiple missions. The MDO, indeed, handles the trade-offs between several solutions by considering a broad set of mission and system requirements, and it ensures that the final design is optimized across all relevant disciplines.
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Li, Tao, and Subhashis Mallick. "Prestack waveform inversion of four-component, two-azimuth surface seismic data for orthorhombic elastic media parameters using a nondominated sorting genetic algorithm." In SEG Technical Program Expanded Abstracts 2013. Society of Exploration Geophysicists, 2013. http://dx.doi.org/10.1190/segam2013-0633.1.

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Li*, Tao, and Subhashis Mallick. "Prestack waveform inversion of three-component, two-azimuth surface seismic data for azimuthally dependent anisotropic parameters using a parallelized nondominated sorting genetic algorithm." In SEG Technical Program Expanded Abstracts 2014. Society of Exploration Geophysicists, 2014. http://dx.doi.org/10.1190/segam2014-0358.1.

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