Finding preferred subsets of Pareto optimal solutions

Kao, Gio K.; Jacobson, Sheldon H.

doi:10.1007/s10589-007-9070-8

Cited by 14 publications

(25 citation statements)

References 12 publications

(20 reference statements)

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“…Ferreira et al [48] proposed a methodology, based on a weight stress function approach, to select a single solution (or a set of solutions) from the set of non-dominated solutions, taking into account the preferences of the decision-maker. Kao and Jacobson [49] studied the problem of post-optimality selection by providing a framework to obtain a preferred subset of solutions from a very large set of solutions. A value function represents the preferences of a decisionmaker across the objective functions.…”

Section: Preferences In Multi-objective Evolutionary Optimizationmentioning

confidence: 99%

A multi-objective approach for the motion planning of redundant manipulators

Marcos

Machado

Perdicoúlis

2012

Applied Soft Computing

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a b s t r a c tKinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

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Section: Preferences In Multi-objective Evolutionary Optimizationmentioning

confidence: 99%

A multi-objective approach for the motion planning of redundant manipulators

Marcos

Machado

Perdicoúlis

2012

Applied Soft Computing

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“…The optimal process time of machine on each product type should be the same in all planning periods as manager desires so, (7) because of preventive maintenance activities, the available time in each planning period could be different of the others, in other word, the makespan in each planning period should be less than or equal to available time of that period, (8) each product type has its own demand in every planning period that is a finite, deterministic and integer value, (9) there is no initial stock of inventory for each product type, (10) products should be produced in a way that there would be no lost sales until the end of the last planning period, but back order is allowed in every period except the last period. In the other words, the sum of the amounts produced and delivered to customer during all periods should not be less than the sum of demands over all of periods, (11) unit shortage cost and unit inventory holding cost are deterministic values that could be different from a period to another period, (12) setup consists of some activities for each product type such as adjusting the machine speed, changing the tool, brushing and cleaning the machine, etc. And cost of changing the setup is so high.…”

Section: Problem Descriptionmentioning

confidence: 99%

A new lot sizing model for controllable processing times and inventory deterioration

Barzinpour

Aryanezhad

Karimi-Nasab

2010

The 40th International Conference on Computers &Amp; Indutrial Engineering

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Production planning for real cases situations is a very complicated work that is contributed with some of simplification for obtaining efficient results. In this paper a new problem is studied in lot sizing, which is the extension of a well-known NPHard problem in the case of inventory deterioration and controllable processing times and a set of technological constraints. Two models are constructed for the case of dealing with linear time / cost relation and quadratic time / cost trade-off when compressing process times. Afterwards, some of the theorems and lemmas are proved about mathematical characteristics of the both model. Then a new algorithm is proposed to explore the feasible solution space in order to extract a near optimal solution. Finally some of the test problems are analyzed beside a real world case to approve the validity of the algorithm and the model.

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“…If scalarization is done carefully, Pareto optimality of the solutions obtained can be guaranteed. There has been a great deal of effort by the researchers in the area (especially in recent years) for developing methods to generate an approximation of the Pareto front (see e.g., [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]). …”

Section: Introductionmentioning

confidence: 99%

A new scalarization method for finding the efficient frontier in non-convex multi-objective problems

Ghane-Kanafi

Khorram

2015

Applied Mathematical Modelling

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a b s t r a c tOne of the most important issues in multi-objective optimization problems (MOPs) is finding Pareto optimal points on the Pareto frontier. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering need to solve a non-convex multi-objective optimization problem (NMOP) in order to achieve the proper results. Gradient based methods, such as Normal Boundary Intersection (NBI), for solving a MOP require solving at least one optimization problem for each solution point. This method can be computationally expensive with an increase in the number of variables and/or constraints of the optimization problem. Nevertheless, the NBI method is a technique motivated by geometrical intuition to provide a better parameterization of the Pareto set than that provided by other techniques. This parameterization is better in the sense that the points obtained by using the NBI method produce a more even coverage of the Pareto curve and this coverage does not miss the interesting middle part of the Pareto curve.This useful property, provides an incentive to create a new method. The first step in this study is using a modified convex hull of individual minimum (mCHIM) in each iteration. The second step is introducing an efficient scalarization problem in order to find the Pareto points on the Pareto front. It can be shown that the corresponding solutions of the MOP have uniform spread and also weak Pareto optimal points. It is notable that the NBI and proposed methods are independent of the relative scale of different objective functions. However, it is quite possible that obtaining a solution of the NBI method not be Pareto optimal (not even locally). Actually, this method aims at getting boundary points rather than Pareto optimal points that will lead to these points which may or may not be a Pareto optimal point. The effectiveness of this method is demonstrated with various test problems in convex and non-convex MOP cases. After that, a few test instances of the CEC 2009 (Zhang et al. 2008) using the proposed method are studied. Also, the relationship between the optimal solutions of the scalarized problem and the Pareto solutions of the multi-objective optimization problem is presented by several theorems.

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Finding preferred subsets of Pareto optimal solutions

Cited by 14 publications

References 12 publications

A multi-objective approach for the motion planning of redundant manipulators

A multi-objective approach for the motion planning of redundant manipulators

A new lot sizing model for controllable processing times and inventory deterioration

A new scalarization method for finding the efficient frontier in non-convex multi-objective problems

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