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multiobjective dynamic programming in bipolar multistage method

ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 1259-1279页

作者： Trzaskalik, Tadeusz Univ Econ Ul 1 Maja 50 PL-40287 Katowice Poland

The multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman's optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.

关键词： Bipolar multistage method multiobjective dynamic programming MCDA Reference sets Multistage alternatives

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AN ALGORITHM FOR GENERATING EFFICIENT SOLUTIONS OF multiobjective dynamic-programming PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1995年第1期80卷 156-165页

作者： ABOSINNA, MA HUSSEIN, ML TANTA UNIV FAC EDUCDEPT MATHKAFR AL SHEIKHEGYPT

This paper presents an algorithm for generating efficient solutions of multiobjective mathematical programming problem. The generation of efficient solutions is based on the principle of optimality in dynamic programming. A generalized functional equation of dynamic programming is derived from the constraint method assuming the separability and monotonicity of the problem. The basic notion of stability in convex programming problems with parameters in the constraints is redefined and analyzed quantitatively for the problem. A numerical example is given for the sake of illustration.

关键词： multiobjective dynamic programming EFFICIENT SOLUTIONS STABILITY CONSTRAINT METHOD

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AN ALGORITHM FOR DECOMPOSING THE PARAMETRIC SPACE IN multiobjective dynamic-programming PROBLEMS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第3期73卷 532-538页

作者： ABOSINNA, MA HUSSEIN, ML TANTA UNIV FAC EDUCDEPT MATHKAFR AL SHEIKHEGYPT

This paper presents an algorithm for decomposing the parametric space in multiobjective dynamic programming (MODP) problems by using the weighted norm approach. Also, the basic notions of stability in convex programming problems with parameters in the objective functions are redefined and analyzed qualitatively for MODP problems. A numerical example is given to clarify the developed algorithm.

关键词： multiobjective dynamic programming STABILITY EFFICIENT SOLUTIONS

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A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 1155-1181页

作者： Nowak, Maciej Trzaskalik, Tadeusz Univ Econ Katowice Dept Operat Res Ul 1 Maja 50 PL-40287 Katowice Poland

We consider a stochastic discrete multiobjective programming process with a finite number of stages. The number of states at each stage and the number of feasible decisions at each state are also finite. The aim of the paper is to propose a new interactive procedure for such a problem based on trade-off analysis. The procedure is illustrated with project portfolio selection. There are many organizations with moderately large portfolios of projects. Although the problem under discussion is not very large, it is difficult to solve, since projects are not implemented simultaneously. Moreover, the companies must take into account the risk that a particular project, which is planned to start in the future, may not be ready for implementation. We present an interactive trade-off procedure, based on the stochastic approach, as a new proposition to solve such a problem.

关键词： multiobjective dynamic programming Interactive approach Trade-offs Project portfolio selection

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VECTOR APPROACH TO CHANGEABLE IMPORTANCE OF PERIOD OBJECTIVES IN multiobjective dynamic programming

VECTOR APPROACH TO CHANGEABLE IMPORTANCE OF PERIOD OBJECTIVE...

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10th International Symposium on Operational Research

作者： Trzaskalik, Tadeusz Karol Adamiecki Univ Econ Katowice Dept Operat Res PL-40226 Katowice Poland

ISBN: (纸本)9789616165303

When analyzing multiple objective, multiperiod decision processes it is worth while to describe relations among objectives considered in consecutive periods and objectives for the whole process. The aim of the paper is to describe a situation in which period objectives have changeable importance in consecutive periods. The problem of a-importance of period objectives is formulated and definitions of the importance function for the considered process and of a-efficient realizations are given. Relations between sets of efficient solutions and a-efficient solutions are analyzed, and some decision recommendations are given. Numerical examples are also presented.

关键词： multiobjective dynamic programming multiperiod decision process period objectives multiperiod objectives alpha-efficient realization

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Adaptive differential dynamic programming for multiobjective optimal control

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AUTOMATICA 2002年第6期38卷 1003-1015页

作者： Liao, LZ Li, DA Chinese Univ Hong Kong Dept Syst Engn & Engn Management Sha Tin Hong Kong Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China

An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the "optimal" weighting coefficients for various performance indices are time-varying as the system evolves along any noninferior trajectory. Recognizing this prominent feature in multiobjective control, the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal time-varying weighting sequence with the solution concept in the conventional differential dynamic programming. Convergence of the proposed adaptive differential dynamic programming methodology is addressed. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： multiobjective optimal control dynamic programming multiobjective dynamic programming differential dynamic programming adaptive differential dynamic programming

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DECOMPOSITION OF multiobjective programming-PROBLEMS BY HYBRID FUZZY-dynamic programming

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FUZZY SETS AND SYSTEMS 1993年第1期60卷 25-32页

作者： HUSSEIN, ML ABOSINNA, MA MENOUFIA UNIV FAC ENGNDEPT MATHSHEBIN EL ROMEGYPT TANTA UNIV FAC EDUCDEPT MATHKAFR AL SHEIKHEGYPT

In this paper, a method of generating efficient solutions of multiobjective programming problems is considered. This method is based on the principle of optimality in dynamic programming and fuzzy decision approach (hybrid approach). Also, this paper shows that solutions obtained by this approach are always efficient solutions. A numerical example is given for the sake of illustration.

关键词： multiobjective dynamic programming EFFICIENT SOLUTIONS FUZZY DECISION APPROACH HYBRID APPROACH

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NEW APPROACH FOR NONSEPARABLE dynamic-programming PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第2期64卷 311-330页

作者： LI, D HAIMES, YY UNIV VIRGINIA CTR RISK MANAGEMENT ENGN SYSTCHARLOTTESVILLEVA 22903

A general class of nonseparable dynamic problems is studied in a dynamic programming framework by introducingkth-order separability. The solution approach uses multiobjective dynamic programming as a separation strategy forkth-order separable dynamic problems. The theoretical grounding on which the optimal solution of the original nonseparable dynamic problem can be attained by a noninferior solution of the corresponding multiobjective dynamic programming problem is established. The relationship between the overall optimal Lagrangian multipliers and the stage-optimal Lagrangian multipliers and the relationship between the overall weighting vector and the stage weighting vector are explored, providing the basis for identifying the optimal solution of the original nonseparable problem from among the set of noninferior solutions generated by the envelope approach.

关键词： Nonseparable dynamic programming kth-order separability multiobjective dynamic programming envelope approach

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AN APPLICATION OF MOP AND GP TO WILDLIFE MANAGEMENT (DEER)

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 1995年第1期44卷 29-38页

作者： BERBEL, J ZAMORA, R ETS INGN AGRON & MONTES APDO 3048 E-14080 CORDOBA SPAIN

The case study presented in this paper has been developed after several years of spreadsheet-based model and trial and error analysis for game management in Southern Spain. The experience gained in this applied planning permitted the authors to make a model for the average manager's criteria. This research proves that management models can be improved by using multicriteria approaches, especially when a satisfactory combination of methods is employed. First, an efficient set is generated for analysing the conflict between economic and ecological objectives. Second, a lexicographical GP model obtains the management plan.

关键词： WILDLIFE MANAGEMENT GOAL programming multiobjective dynamic programming MULTICRITERIA DECISION MAKING

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Interactive procedure for a multiobjective stochastic discrete dynamic problem

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第2期57卷 315-330页

作者： Nowak, Maciej Trzaskalik, Tadeusz Univ Econ Katowice Katowice Poland

Multiple objectives and dynamics characterize many sequential decision problems. In the paper we consider returns in partially ordered criteria space as a way of generalization of single criterion dynamic programming models to multiobjective case. In our problem evaluations of alternatives with respect to criteria are represented by distribution functions. Thus, the overall comparison of two alternatives is equivalent to the comparison of two vectors of probability distributions. We assume that the decision maker tries to find a solution preferred to all other solutions (the most preferred solution). In the paper a new interactive procedure for stochastic, dynamic multiple criteria decision making problem is proposed. The procedure consists of two steps. First, the Bellman principle is used to identify the set of efficient solutions. Next interactive approach is employed to find the most preferred solution. A numerical example and a real-world application are presented to illustrate the applicability of the proposed technique.

关键词： multiobjective dynamic programming Partial order Stochastic dominance Interactive approach

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