Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions

Leschine, Thomas M.; Wallenius, Hannele; Verdini, William A.

doi:10.1016/0377-2217(92)90228-2

Cited by 48 publications

(18 citation statements)

References 11 publications

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“…As most of the real business decision making problems involve more than one objectives, the MOLP model has been widely applied in many fields and has become a useful tool for decision making. (For applications, for example, see Leschine et al [18], Gravel et al [15], Prabuddha et al [20]. ) A Pareto solution of a MOLP problem is a solution that cannot improve some objectives without sacrificing others.…”

Section: Introductionmentioning

confidence: 99%

Constructing efficient solutions structure of multiobjective linear programming

Yan

Wei

Wang

2005

Journal of Mathematical Analysis and Applications

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It is not a difficult task to find a weak Pareto or Pareto solution in a multiobjective linear programming (MOLP) problem. The difficulty lies in finding all these solutions and representing their structure. This paper develops an algorithm for solving this problem. We investigate the solutions and their relationships in the objective space. The algorithm determines finite number of weights, each of which corresponds to a weighted sum problems. By solving these problems, we further obtain all weak Pareto and Pareto solutions of the MOLP and their structure in the constraint space. The algorithm avoids the degeneration problem, which is a major hurdle of previous works, and presents an easy and clear solution structure.  2004 Published by Elsevier Inc.

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Section: Introductionmentioning

confidence: 99%

Constructing efficient solutions structure of multiobjective linear programming

Yan

Wei

Wang

2005

Journal of Mathematical Analysis and Applications

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“…This model introduced¯fty years ago (by Bellman 1 and Howard 2 ) is used in many applications of Operations Research (investment planning, inventory systems management, manufacturing, resource allocation) 3,4 and Arti¯cial Intelligence (path-planning, game search, trading agents, robotics and reinforcement learning). 5,6 Several variants of MDPs have been already considered and investigated, depending on the nature of the set of states (¯nite or not), the nature of the reward function (quantitative or qualitative, scalar-valued or vector-valued), the nature of uncertainty (probabilistic, possibilistic, ordinal) and the observability of the system (partial or total), etc.…”

Section: Introductionmentioning

confidence: 99%

A Compromise Programming Approach to Multiobjective Markov Decision Processes

Ogryczak

Perny

Weng

2013

Int. J. Info. Tech. Dec. Mak.

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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 con°icting. 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 tradeo®s. 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 di±culties, 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.

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“…An MOLP problem is to minimize or maximize several linear objective functions subject to a set of linear constraints. As most of the real business decision making problems involve more than one objective, the MOLP model has been widely applied in many fields and has become a useful tool for decision making [5,13,20].…”

Section: Introductionmentioning

confidence: 99%

Determining maximal efficient faces in multiobjective linear programming problem

Pourkarimi

Yaghoobi

Mashinchi

2009

Journal of Mathematical Analysis and Applications

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Keywords:Multiobjective linear programming Maximal efficient face Minimal index set Efficiency Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly.

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Interactive multiobjective analysis and assimilative capacity-based ocean disposal decisions

Cited by 48 publications

References 11 publications

Constructing efficient solutions structure of multiobjective linear programming

Constructing efficient solutions structure of multiobjective linear programming

A Compromise Programming Approach to Multiobjective Markov Decision Processes

Determining maximal efficient faces in multiobjective linear programming problem

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