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A COMPROMISE PROGRAMMING APPROACH TO MULTIOBJECTIVE MARKOV DECISION PROCESSES

INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2013年第5期12卷 1021-1053页

作者： Ogryczak, Wlodzimierz Perny, Patrice Weng, Paul Warsaw Univ Technol ICCE PL-00661 Warsaw Poland Univ Paris 06 LIP6 Paris France

A Markov decision process (MDP) is a general model for solving planning problems under uncertainty. It has been extended to multiobjective MDP to address multicriteria or multiagent problems in which the value of a decision must be evaluated according to several viewpoints, sometimes conflicting. Although most of the studies concentrate on the determination of the set of Pareto-optimal policies, we focus here on a more specialized problem that concerns the direct determination of policies achieving well-balanced tradeoffs. To this end, we introduce a reference point method based on the optimization of a weighted ordered weighted average (WOWA) of individual disachievements. We show that the resulting notion of optimal policy does not satisfy the Bellman principle and depends on the initial state. To overcome these difficulties, we propose a solution method based on a linear programming (LP) reformulation of the problem. Finally, we illustrate the feasibility of the proposed method on two types of planning problems under uncertainty arising in navigation of an autonomous agent and in inventory management.

关键词： Multiobjective optimization Markov decision processes compromise programming reference point method ordered weighted average linear programming

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USE OF reference pointS FOR MOLP PROBLEMS ANALYSIS

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1993年第3期68卷 374-378页

作者： METEV, B YORDANOVA, I BULGARIAN ACAD SCI INST INFORMATACAD G BONCHEO STRBL 2BU-1113 SOFIABULGARIA

Two scalar problems intended for analysis of multiple objective linear programming (MOLP) problems are considered in the paper. These problems use reference points and it is shown how to change the reference point in ... 详细信息

关键词： DECISION OPTIMIZATION MULTIPLE OBJECTIVE (CRITERIA) LINEAR PROGRAMMING reference point method

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Trade-off analysis tool for interactive nonlinear multiobjective optimization 20

Trade-off analysis tool for interactive nonlinear multiobjec...

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20th International Conference/Euro Mini Conference on Continuous Optimization and Knowledge-Based Technologies (EurOPT 2008)

作者： Eskelinen, Petri Miettinen, Kaisa Helsinki Sch Econ FI-00101 Helsinki Finland

ISBN: (纸本)9789955282839

In interactive methods, a decision maker (DM) directs the search for the most preferred Pareto optimal solution with his/her preferences. We propose a tool that can be used to support the DM. With this tool, the DM can conveniently learn about local trade-offs and judge whether they are worthwhile. The tool is based on an idea where the DM is able to vary a selected Pareto optimal objective vector. The varied vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set at the selected Pareto optimal solution. This information can be used to reflect what kind of Pareto optimal solutions and trade-offs are available in a local neighborhood of the selected solution. This tool is especially useful when trade-off analysis must be carried out fast and without increasing computation workload.

关键词： multiobjective optimization interactive methods reference point method trade-off analysis

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Multicriteria support of choosing a group decision

Multicriteria support of choosing a group decision

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Federated Conference on Computer Science and Information Systems (FedCSIS)

作者： Lodzinski, Andrzej Warsaw Univ Life Sci Ul Nowoursynowska 159 PL-02776 Warsaw Poland

ISBN: (纸本)9788360810668

The paper presents the method of a group decision making in a competitive environment. We deal with a group decision when the group of people with different preferences are to make one single decision. The group decision selection process is modeled with the use of multi-criteria optimization task. It is solved with the use of reference point method. This method is an interactive method in which every person specifies its requirements in the form of a reference point, expressing the desired values for its evaluation function. On the basis of the provided reference point, a scalar achievement function is built. Maximization of this function generates a solution of the multicriteria task. This solution is presented to every person for acceptance or as a basis for the modification of the reference point. The paper contains the example of application of the proposed method to support a group decision by three people with different preferences.

关键词： group decision support systems optimisation group decision making group decision selection process interactive method multicriteria optimization task reference point method Computer science Computers Decision making Information systems Life sciences Optimization Yttrium

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On Ordered Weighted reference point Model for Multi-attribute Procurement Auctions

On Ordered Weighted Reference Point Model for Multi-attribut...

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3rd International Conference on Computational Collective Intelligence (ICCCI 2011)

作者： Kozlowski, Bartosz Ogryczak, Wlodzimierz Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

ISBN: (纸本)9783642239342;9783642239359

Multi-attribute auctions (also called multidimensional auctions) facilitate negotiations based on multiple attributes, thus escape from the standard price-only domain into a rich multidimensional domain that can comprise additional attributes like e.g. guarantee conditions or quality. Most multi-attribute preference models used in auction mechanisms are based on a ranking derived from weighted sum. Recently, the reference point method (RPM) approach has been applied to express the multi-attribute preference models within the auction mechanisms allowing to overcome the weighted sum drawbacks. The Ordered Weighted RPM model enables us to introduce importance weights to affect achievements importance by rescaling their measures accordingly within the distribution of all achievements. The concept presented and discussed in this paper in the context of procurement auctions takes advantage of the so-called Weighted Ordered Weighted Average (WOWA) aggregations of the partial achievements.

关键词： multi-attribute auction ordered weighted average reference point method

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Interactive multi-objective vehicle routing via GA-based dynamic programming 3

Interactive multi-objective vehicle routing via GA-based dyn...

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3rd International Conference on Transportation Information Safety

作者： Khan, Raza Saleem Handl, Julia Yang, Jian-Bo Univ Manchester Manchester Business Sch Decis & Cognit Sci Res Ctr Manchester M15 6PB Lancs England

ISBN: (纸本)9781479986941

This research is focused on dealing with multiple conflicting objectives in vehicle scheduling problem in an urban delivery context. The distinctive feature of this research is that an interactive reference point approach is applied to support the trade-off analysis of multiple conflicting objectives, including the minimization of total time, distance and CO2 emissions in the context of time-varying congestion data, derived as time-dependent historical average travel speed data from the UK road network. Due to congestion, average travel speeds on different roads change throughout the day and optimal routes may differ across time slots. Because of the conflict among the objectives, a solution that is optimal for one objective may or may not be optimal for other objectives. A hybrid algorithm mixing dynamic programming with an evolutionary algorithm is first developed to generate sets of efficient solutions. The proposed interactive approach is then described, which alternates between solution generation and preference elicitation from a decision maker. The effectiveness of the approach is illustrated using a case study that combines synthetic demand data for a company with the actual road and congestion information in the UK. The results obtained using the proposed interactive approach are compared to those obtained when a single objective is optimised.

关键词： Interactive VRP Multi-objective Time-varying congestion CO2 emissions reference point method

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Efficient linear combination method for multi-objective problems with convex polyhedral preference functions

Efficient linear combination method for multi-objective prob...

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IEEE International Conference on Industrial Technology

作者： Phruksaphanrat, B Ohsato, A Nagaoka Univ Technol Grad Sch Engn Nagaoka Niigata 9402188 Japan

ISBN: (纸本)0780376579

At present, the most commonly used method for multiobjective linear, programming (MOLP) is goal programming (GP) based methods but these methods do not always generate efficient solutions. Recently, an efficient GP-based method, which is called reference goal programming (RGP), has been proposed. However, it is limited to only a certain target point preference, which is too rigid. The more flexible preferences are preferred in many practical problems. In this research, an effective linear combination method for MOLP problems with convex polyhedral preference functions is proposed. The concept of the convex cone is used to formulate convex polyhedral preference functions and the existing reference point method (RPM) is integrated to ensure the efficiency of the solution of the problem. The formulated model can be solved by existing linear programming solvers and can find the satisfactory efficient solution. The convex polyhedral function enriches the existing preferences for efficient methods and increases the flexibility in designing preferences for decision makers. For some situations, it is difficult for the decision maker to state the certain aspiration level for each objective function. Fuzzy goals, which can be considered as convex polyhedral preference functions, can be used to represent aspiration levels with respect to linguistic terms.

关键词： linear combination multi-objective problems convex polyhedral functions reference point method fuzzy goals and efficient solutions

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Trust-Region Algorithm based local search for Multi-objective Optimization

Trust-Region Algorithm based local search for Multi-objectiv...

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1st International Conference on Innovative Engineering Systems (ICIES)

作者： El-Sawy, A. A. Hendawy, Z. M. El-Shorbagy, M. A. Qassim Univ Dept Math Fac Sci Buraydah Saudi Arabia

ISBN: (纸本)9781467344395;9781467344401

In this paper, a new algorithm is proposed to solve multi-objective optimization problems (MOOPs) through applying the trust-region (TR) method based local search (LS) techniques;where the MOOP converting to a single objective optimization problem (SOOP) by using reference point method. In the proposed algorithm, for each reference point the TR algorithm for solving a SOOP is used to obtain a point on the Pareto frontier. In addition a LS method is used, in order to find more points on the Pareto frontier. The algorithm is coded in MATLAB 7.2 and the simulations are run on a Pentium 4 CPU 900 MHz with 512 MB memory capacity. The numerical results show that the proposed method is feasible, and illustrate the ability of finding an approximation of Pareto optimal set.

关键词： Multi-objective optimization trust region methods local search technique Pareto optimal solution reference point method

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Multiple objective project portfolio selection based on reference points

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Journal of Business Economics 2016年第1-2期86卷 23-33页

作者： Stewart, Theodor J. Department of Statical Sciences University of Cape Town 7701 Rondebosch Cape Town South Africa Alliance Manchester Business School University of Manchester Manchester M15 6PB United Kingdom

The problem of selecting a portfolio of research and development projects from a set of proposed projects subject to resource constraints is formulated as a multiobjective optimization problem. Three categories of objectives are identified, namely quantitative, qualitative and balance/distributional. The first two are linear in the binary decision variables, but the third involves nonlinear measures of discrepancy between desired and actual distributions of activity amongst defined categories. The result is a nonlinear combinatorial multiobjective optimization problem. A form of reference point approach is motivated and developed as a solution method, and a special purpose genetic algorithm is implemented for obtaining the solution numerically. Extensions to interactive approaches for exploration of the efficient frontier are presented and discussed. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： Multiobjective programming Project portfolios reference point method

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EUROPEAN UNION MEMBER STATES PREPARING FOR EUROPE 2020. AN APPLICATION OF THE MULTIMOORA method

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TECHNOLOGICAL AND ECONOMIC DEVELOPMENT OF ECONOMY 2012年第4期18卷 567-587页

作者： Brauers, Willem Karel M. Balezentis, Alvydas Balezentis, Tomas Vilnius Gediminas Tech Univ Vilnius Lithuania Univ Antwerp Fac Appl Econ B-2000 Antwerp Belgium Mykolas Romeris Univ LT-08303 Vilnius Lithuania Lithuanian Inst Agr Econ LT-03105 Vilnius Lithuania

It is the intention of the European Union to create a growing and sustainable European economy by 2020, a much more moderate target than the 2010 target of becoming the most competitive and dynamic knowledge-based economy in the world. This intention has to be supported by an adequate Optimization and Decision Support System. Therefore, MULTIMOORA is proposed. MULTIMOORA is a quantitative method, which compares multiple and optimum objectives, expressed in different units, as much as possible on a non-subjective basis. In opposition to similar methods MULTIMOORA does not need normalization, being based on dimensionless measures. Importance of an objective can eventually be given by the stakeholders concerned. MULTIMOORA is composed of three approaches: Ratio System, reference point and Multiplicative Form methods, all of the same importance and each controlling each other. Twenty two objectives, 10 originating from statistics and 12 from statistics and forecasts, important for the future, characterize the 27 EU-Countries economies as a preparation for 2020. Which of these countries are the best prepared for 2020? A Dominance Theory, summarizing the three obtained ordinal numbers per country, ranks the 27 countries for that purpose.

关键词： multi-objective optimization European Union Ratio System reference point method Full Multiplicative Form MULTIMOORA

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