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Alexander S. Poznyak - One of the best experts on this subject based on the ideXlab platform.
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multiobjective markov chains optimization problem with strong Pareto Frontier
Expert Systems With Applications, 2017Co-Authors: Julio B. Clempner, Alexander S. PoznyakAbstract:We formulate a regularized penalty function solution for the multi-objective constrained problem.We prove that exists a solution of the original problem with minimal weighted norm which is unique.We suggest a projection-gradient algorithm for computing the penalty function.We prove the convergence of the gradient method and the rate of convergence.We present a method that make the Pareto Frontier more useful as decision support system. In this paper, we present a novel approach for computing the Pareto Frontier in Multi-Objective Markov Chains Problems (MOMCPs) that integrates a regularized penalty method for poly-linear functions. In addition, we present a method that make the Pareto Frontier more useful as decision support system: it selects the ideal multi-objective option given certain bounds. We restrict our problem to a class of finite, ergodic and controllable Markov chains. The regularized penalty approach is based on the Tikhonov's regularization method and it employs a projection-gradient approach to find the strong Pareto policies along the Pareto Frontier. Different from previous regularized methods, where the regularizator parameter needs to be large enough and modify (some times significantly) the initial functional, our approach balanced the value of the functional using a penalization term (µ) and the regularizator parameter (ź) at the same time improving the computation of the strong Pareto policies. The idea is to optimize the parameters µ and ź such that the functional conserves the original shape. We set the initial value and then decrease it until each policy approximate to the strong Pareto policy. In this sense, we define exactly how the parameters µ and ź tend to zero and we prove the convergence of the gradient regularized penalty algorithm. On the other hand, our policy-gradient multi-objective algorithms exploit a gradient-based approach so that the corresponding image in the objective space gets a Pareto Frontier of just strong Pareto policies. We experimentally validate the method presenting a numerical example of a real alternative solution of the vehicle routing planning problem to increase security in transportation of cash and valuables. The decision-making process explored in this work correspond to the most frequent computational intelligent models applied in practice within the Artificial Intelligence research area.
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Multiobjective Markov chains optimization problem with strong Pareto Frontier: Principles of decision making
Expert Systems with Applications, 2017Co-Authors: Julio B. Clempner, Alexander S. PoznyakAbstract:In this paper, we present a novel approach for computing the Pareto Frontier in Multi-Objective Markov Chains Problems (MOMCPs) that integrates a regularized penalty method for poly-linear functions. In addition, we present a method that make the Pareto Frontier more useful as decision support system: it selects the ideal multi-objective option given certain bounds. We restrict our problem to a class of finite, ergodic and controllable Markov chains. The regularized penalty approach is based on the Tikhonov's regularization method and it employs a projection-gradient approach to find the strong Pareto policies along the Pareto Frontier. Different from previous regularized methods, where the regularizator parameter needs to be large enough and modify (some times significantly) the initial functional, our approach balanced the value of the functional using a penalization term (μ) and the regularizator parameter (δ) at the same time improving the computation of the strong Pareto policies. The idea is to optimize the parameters μ and δ such that the functional conserves the original shape. We set the initial value and then decrease it until each policy approximate to the strong Pareto policy. In this sense, we define exactly how the parameters μ and δ tend to zero and we prove the convergence of the gradient regularized penalty algorithm. On the other hand, our policy-gradient multi-objective algorithms exploit a gradient-based approach so that the corresponding image in the objective space gets a Pareto Frontier of just strong Pareto policies. We experimentally validate the method presenting a numerical example of a real alternative solution of the vehicle routing planning problem to increase security in transportation of cash and valuables. The decision-making process explored in this work correspond to the most frequent computational intelligent models applied in practice within the Artificial Intelligence research area.
Julio B. Clempner - One of the best experts on this subject based on the ideXlab platform.
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multiobjective markov chains optimization problem with strong Pareto Frontier
Expert Systems With Applications, 2017Co-Authors: Julio B. Clempner, Alexander S. PoznyakAbstract:We formulate a regularized penalty function solution for the multi-objective constrained problem.We prove that exists a solution of the original problem with minimal weighted norm which is unique.We suggest a projection-gradient algorithm for computing the penalty function.We prove the convergence of the gradient method and the rate of convergence.We present a method that make the Pareto Frontier more useful as decision support system. In this paper, we present a novel approach for computing the Pareto Frontier in Multi-Objective Markov Chains Problems (MOMCPs) that integrates a regularized penalty method for poly-linear functions. In addition, we present a method that make the Pareto Frontier more useful as decision support system: it selects the ideal multi-objective option given certain bounds. We restrict our problem to a class of finite, ergodic and controllable Markov chains. The regularized penalty approach is based on the Tikhonov's regularization method and it employs a projection-gradient approach to find the strong Pareto policies along the Pareto Frontier. Different from previous regularized methods, where the regularizator parameter needs to be large enough and modify (some times significantly) the initial functional, our approach balanced the value of the functional using a penalization term (µ) and the regularizator parameter (ź) at the same time improving the computation of the strong Pareto policies. The idea is to optimize the parameters µ and ź such that the functional conserves the original shape. We set the initial value and then decrease it until each policy approximate to the strong Pareto policy. In this sense, we define exactly how the parameters µ and ź tend to zero and we prove the convergence of the gradient regularized penalty algorithm. On the other hand, our policy-gradient multi-objective algorithms exploit a gradient-based approach so that the corresponding image in the objective space gets a Pareto Frontier of just strong Pareto policies. We experimentally validate the method presenting a numerical example of a real alternative solution of the vehicle routing planning problem to increase security in transportation of cash and valuables. The decision-making process explored in this work correspond to the most frequent computational intelligent models applied in practice within the Artificial Intelligence research area.
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Multiobjective Markov chains optimization problem with strong Pareto Frontier: Principles of decision making
Expert Systems with Applications, 2017Co-Authors: Julio B. Clempner, Alexander S. PoznyakAbstract:In this paper, we present a novel approach for computing the Pareto Frontier in Multi-Objective Markov Chains Problems (MOMCPs) that integrates a regularized penalty method for poly-linear functions. In addition, we present a method that make the Pareto Frontier more useful as decision support system: it selects the ideal multi-objective option given certain bounds. We restrict our problem to a class of finite, ergodic and controllable Markov chains. The regularized penalty approach is based on the Tikhonov's regularization method and it employs a projection-gradient approach to find the strong Pareto policies along the Pareto Frontier. Different from previous regularized methods, where the regularizator parameter needs to be large enough and modify (some times significantly) the initial functional, our approach balanced the value of the functional using a penalization term (μ) and the regularizator parameter (δ) at the same time improving the computation of the strong Pareto policies. The idea is to optimize the parameters μ and δ such that the functional conserves the original shape. We set the initial value and then decrease it until each policy approximate to the strong Pareto policy. In this sense, we define exactly how the parameters μ and δ tend to zero and we prove the convergence of the gradient regularized penalty algorithm. On the other hand, our policy-gradient multi-objective algorithms exploit a gradient-based approach so that the corresponding image in the objective space gets a Pareto Frontier of just strong Pareto policies. We experimentally validate the method presenting a numerical example of a real alternative solution of the vehicle routing planning problem to increase security in transportation of cash and valuables. The decision-making process explored in this work correspond to the most frequent computational intelligent models applied in practice within the Artificial Intelligence research area.
Alexander V Lotov - One of the best experts on this subject based on the ideXlab platform.
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comparison of two Pareto Frontier approximations
Computational Mathematics and Mathematical Physics, 2014Co-Authors: V E Berezkin, Alexander V LotovAbstract:A method for comparing two approximations to the multidimensional Pareto Frontier in nonconvex nonlinear multicriteria optimization problems, namely, the inclusion functions method is described. A feature of the method is that Pareto Frontier approximations are compared by computing and comparing inclusion functions that show which fraction of points of one Pareto Frontier approximation is contained in the neighborhood of the Edgeworth-Pareto hull approximation for the other Pareto Frontier.
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a framework for participatory decision support using Pareto Frontier visualization goal identification and arbitration
European Journal of Operational Research, 2009Co-Authors: Roman Efremov, David Rios Insua, Alexander V LotovAbstract:There is a growing interest in promoting participation of lay stakeholders in public decision-making processes, possibly with the aid of Internet-based systems. This implies supporting non-sophisticated users and, consequently, developing user-friendly, yet rigorous, participatory decision support methods. We outline a framework to develop such methods based on interactive Pareto Frontier visualization combined with expression of preferences in terms of feasible goals and using feasible goal-based arbitration.
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hybrid adaptive methods for approximating a nonconvex multidimensional Pareto Frontier
Computational Mathematics and Mathematical Physics, 2006Co-Authors: V E Berezkin, G K Kamenev, Alexander V LotovAbstract:New hybrid methods for approximating the Pareto Frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto Frontiers are considered. Since the approximation of the Pareto Frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto Frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto Frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.
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experience of model integration and Pareto Frontier visualization in the search for preferable water quality strategies
Environmental Modelling and Software, 2005Co-Authors: Alexander V Lotov, Vladimir A. Bushenkov, Roman Efremov, Lioubov V Bourmistrova, Alexander L Buber, N A BraininAbstract:Abstract A real-life application of a new approach to integrated assessment and screening of water quality improvement strategies in large river basins is presented. The approach is based on the integration of diverse data and mathematical models as well as on the application of interactive visualization of the Pareto Frontier. The case study water quality planning in the Oka River, the Volga River basin, is presented within the framework of a DSS for screening water quality planning strategies. The Decision Support System (DSS) was commissioned by the Russian Federal Ministry for Natural Resources within the Federal programme “Revival of the Volga River”.
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approximation and visualization of Pareto Frontier in the framework of classical approach to multi objective optimization
Dagstuhl Seminar Proceedings, 2005Co-Authors: Alexander V LotovAbstract:This paper is devoted to a Pareto Frontier generation technique, which is aimed at subsequent visualization of the Pareto Frontier in an interaction with the user. This technique known as the Interactive Decision Maps technique was initiated about 30 years ago. Now it is applied for decision support in both convex and non-convex decision problems in various fields, from machinery design to environmental planning. The number of conflicting criteria explored with the help of the Interactive Decision Maps technique is usually between three and seven, but some users manage to apply the technique in the case of a larger number of criteria. Here we outline the main ideas of the technique, concentrating at nonlinear problems.
Christopher A. Mattson - One of the best experts on this subject based on the ideXlab platform.
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Considering dynamic Pareto Frontiers in decision making
Optimization and Engineering, 2013Co-Authors: Patrick K Lewis, Morgan W. P. Tackett, Christopher A. MattsonAbstract:Considering how the resolution of conflicts changes over time is an aspect of multiobjective optimization that is not commonly explored. These considerations embody changes in both the preferences that dictate the selection of Pareto designs, and changes in the Pareto Frontier itself over time, or s-Pareto Frontier when a set of disparate design concepts are considered. As such, this paper explores the idea of dynamic s-Pareto Frontiers and preferences. Specifically, this paper presents a dynamic multiobjective optimization problem formulation that provides a framework of identifying the s-Pareto Frontier for a series of time steps. The application of the presented dynamic formulation is illustrated through a simple aircraft design example. Through this example it was observed that the identification of the dynamic s-Pareto Frontier enabled the observation of the impact of design decisions on the offset of selected designs from the identified dynamic Frontier. By measuring and minimizing the aircraft design offset, the selected aircraft design offset was improved by an average of roughly 60 % from the next best selected alternative identified using traditional selection methods.
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a design optimization strategy for creating devices that traverse the Pareto Frontier over time
Structural and Multidisciplinary Optimization, 2011Co-Authors: Patrick K Lewis, Vance R Murray, Christopher A. MattsonAbstract:In some instances, the performance or function that is needed by a product naturally and predictably changes over time. Providing solutions that anticipate, account for, and allow for these changes is a significant challenge to manufacturers and design engineers. In this paper, a multiobjective optimization design method involving the strategic use of a series of optimization formulations is introduced to design products that adapt to changing needs by moving from one location on the Pareto Frontier to another through the addition of a module. The design of a simple unmanned air vehicle is used to demonstrate implementation of the method, and results in the development of one aircraft platform and two module designs that adapt the aircraft to perform optimally for the particular mission at hand, thus optimally satisfying all three different mission profiles individually. The authors conclude that the developed method provides a new and general framework for selecting platform and module designs, and is capable of providing a set of designs based on predicted changes in needs.
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Pareto Frontier Based Concept Selection Under Uncertainty, with Visualization
Optimization and Engineering, 2005Co-Authors: Christopher A. Mattson, Achille MessacAbstract:In a recent publication, we presented a new multiobjective decision-making tool for use in conceptual engineering design. In the present paper, we provide important developments that support the next phase in the evolution of the tool. These developments, together with those of our previous work, provide a concept selection approach that capitalizes on the benefits of computational optimization. Specifically, the new approach uses the efficiency and effectiveness of optimization to rapidly compare numerous designs, and characterize the tradeoff properties within the multiobjective design space. As such, the new approach differs significantly from traditional (non-optimization based) concept selection approaches where, comparatively speaking, significant time is often spent evaluating only a few points in the design space. Under the new approach, design concepts are evaluated using a so-called s-Pareto Frontier ; this Frontier originates from the Pareto Frontiers of various concepts, and is the Pareto Frontier for the set of design concepts. An important characteristic of the s-Pareto Frontier is that it provides a foundation for analyzing tradeoffs between design objectives and the tradeoffs between design concepts. The new developments presented in this paper include; (i) the notion of minimally representing the s-Pareto Frontier, (ii) the quantification of concept goodness using s-Pareto Frontiers, (iii) the development of an interactive design space exploration approach that can be used to visualize n -dimensional s-Pareto Frontiers, and (iv) s-Pareto Frontier-based approaches for considering uncertainty in concept selection. Simple structural examples are presented that illustrate representative applications of the proposed method.
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normal constraint method with guarantee of even representation of complete Pareto Frontier
AIAA Journal, 2004Co-Authors: Achille Messac, Christopher A. MattsonAbstract:Multiobjective optimization is rapidly becoming an invaluable tool in engineering design. A particular class of solutions to the multiobjective optimization problem is said to belong to the Pareto Frontier. A Pareto solution, the set of which comprises the Pareto Frontier, is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other. Accordingly, the Pareto Frontier plays an important role in engineering design—it characterizes the tradeoffs between conflicting design objectives. Some optimization methods can be used to automatically generate a set of Pareto solutions from which a final design is subjectively chosen by the designer. For this approach to be successful, the generated Pareto set must be truly representative of the complete optimal design space (Pareto Frontier). In other words, the set must not overrepresent one region of the design space, or neglect others. Some commonly used methods comply with this requirement, whereas others do not. This paper offers a new phase in the development of the normal constraint method, which is a simple approach for generating Pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives. The even distribution of the generated Pareto solutions can facilitate the process of developing an analytical expression for the Pareto Frontier in n dimension. An even distribution of Pareto solutions also facilitates the task of choosing the most desirable (final) design from among the set of Pareto solutions. The normal constraint method bears some similarities to the normal boundary intersection and � -constraint methods. Importantly, the developments presented in this paper define its critical distinction, namely, the ability to generate a set of evenly distributed Pareto solutions over the complete Pareto Frontier. Examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method, as well as with the original normal constraint method.
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the normalized normal constraint method for generating the Pareto Frontier
Structural and Multidisciplinary Optimization, 2003Co-Authors: Achille Messac, Amir Ismailyahaya, Christopher A. MattsonAbstract:The authors recently proposed the normal constraint (NC) method for generating a set of evenly spaced solutions on a Pareto Frontier – for multiobjective optimization problems. Since few methods offer this desirable characteristic, the new method can be of significant practical use in the choice of an optimal solution in a multiobjective setting. This paper’s specific contribution is two-fold. First, it presents a new formulation of the NC method that incorporates a critical linear mapping of the design objectives. This mapping has the desirable property that the resulting performance of the method is entirely independent of the design objectives scales. We address here the fact that scaling issues can pose formidable difficulties. Secondly, the notion of a Pareto filter is presented and an algorithm thereof is developed. As its name suggests, a Pareto filter is an algorithm that retains only the global Pareto points, given a set of points in objective space. As is explained in the paper, the Pareto filter is useful in the application of the NC and other methods. Numerical examples are provided.
Javid Taheri - One of the best experts on this subject based on the ideXlab platform.
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genetic algorithm in finding Pareto Frontier of optimizing data transfer versus job execution in grids
Concurrency and Computation: Practice and Experience, 2016Co-Authors: Javid Taheri, Albert Y Zomaya, Samee U KhanAbstract:This work presents a genetic algorithm GA-based optimization technique, called GA-ParFnt, to find the Pareto Frontier for optimizing data transfer versus job execution time in grids. As the performance of a generic GA is not suitable to find such Pareto relationship, major modifications are applied to it so that it can efficiently discover such relationship. The Frontier curve representing this relationship is then matched against performance of several scheduling techniques-for both data intensive and computationally intensive applications-to measure their overall performances. Results show that few of these algorithms are far from the Pareto front despite their claims of being efficient in optimizing their targeted objectives. Results also provide invaluable insights into this formidable problem and should aid in the design of future schedulers. Copyright © 2012 John Wiley & Sons, Ltd.
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Pareto Frontier for job execution and data transfer time in hybrid clouds
Future Generation Computer Systems, 2014Co-Authors: Javid Taheri, Albert Y Zomaya, Howard Jay Siegel, Zahir TariAbstract:a b s t r a c t This paper proposes a solution to calculate the Pareto Frontier for the execution of a batch of jobs versus data transfer time for hybrid clouds. Based on the nature of the cloud application, jobs are assumed to require a number of data-files from either public or private clouds. For example, gene probes can be used to identify various infection agents such as bacteria, viruses, etc. The heavy computational task of aligning probes of a patient's DNA (private-data) with normal sequences (public-data) with various data sizes is the key to this process. Such files have different characteristics - depends on their nature - and could be either allowed for replication or not in the cloud. Files could be too big to replicate (big data), others might be small enough to be replicated but they cannot be replicated as they contain sensitive information (private data). To show the relationship between the execution time of a batch of jobs and the transfer time needed for their required data in hybrid cloud, we first model this problem as a bi-objective optimization problem, and then propose a Particle Swarm Optimization (PSO)-based approach, called here PSO-ParFnt, to find the relevant Pareto Frontier. The results are promising and provide new insights into this complex problem. © 2013 Elsevier B.V. All rights reserved.
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A Pareto Frontier for Optimizing Data Transfer and Job Execution in Grids
2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum, 2012Co-Authors: Javid Taheri, Albert Y ZomayaAbstract:This work presents a Genetic Algorithm (GA) based optimization technique, called GA-ParFnt, to find the Pareto Frontier for optimizing data transfer versus job execution time in grids. As the performance of a generic GA is not suitable to find such Pareto relationship, several modifications are applied to it so that it can efficiently discover such relationship. The Frontier curve representing this relationship is then matched against performance of several scheduling techniques - for both data intensive and computationally intensive applications -to measure their overall performances. Results show that several of these algorithms are far from the Pareto front despite their claims of being efficient in optimizing their targeted objectives. Results also provide invaluable insights into this formidable problem and should aid in the design of future schedulers.
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IPDPS Workshops - A Pareto Frontier for Optimizing Data Transfer and Job Execution in Grids
2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum, 2012Co-Authors: Javid Taheri, Albert Y ZomayaAbstract:This work presents a Genetic Algorithm (GA) based optimization technique, called GA-ParFnt, to find the Pareto Frontier for optimizing data transfer versus job execution time in grids. As the performance of a generic GA is not suitable to find such Pareto relationship, several modifications are applied to it so that it can efficiently discover such relationship. The Frontier curve representing this relationship is then matched against performance of several scheduling techniques -- for both data intensive and computationally intensive applications -- to measure their overall performances. Results show that several of these algorithms are far from the Pareto front despite their claims of being efficient in optimizing their targeted objectives. Results also provide invaluable insights into this formidable problem and should aid in the design of future schedulers.
