Tradeoff-based decomposition and decision-making in multiobjective programming

Engau, Alexander

doi:10.1016/j.ejor.2009.01.061

Cited by 9 publications

(4 citation statements)

References 40 publications

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“…Our main contribution is a scheme that retains the quality of the best previous algorithm while achieving a more benign ratio between computational effort and problem dimension. The presented algorithm also generalizes sandwich algorithms to be compatible with cone-based preference models (see, e.g., Engau 2009, Hunt and Wiecek 2003, Monz 2006. Ordering cones have proven useful in multicriteria IMRT planning for excluding parts of the Pareto surface that are known a priori not to be of interest (Serna et al 2009).…”

Section: Introductionmentioning

confidence: 94%

An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques

Bokrantz

Forsgren

2013

INFORMS Journal on Computing

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W e consider the problem of approximating Pareto surfaces of convex multicriteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that optimally limit the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem can be solved by enumerative techniques but at a cost that increases exponentially with the number of objectives. We present an algorithm for solving the Pareto surface approximation problem that is practical with 10 or less conflicting objectives, motivated by an application to radiation therapy optimization. Our enumerative scheme is, in a sense, dual to a family of previous algorithms. The proposed technique retains the quality of the best previous algorithm in this class while solving fewer subproblems. A further improvement is provided by a procedure for discarding subproblems based on reusing information from previous solves. The combined effect of the enhancements is empirically demonstrated to reduce the computational expense of solving the Pareto surface approximation problem by orders of magnitude. For problems where the objectives have positive curvature, an improved bound on the approximation error is demonstrated using transformations of the initial objectives with strictly increasing and concave functions.

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Section: Introductionmentioning

confidence: 94%

An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques

Bokrantz

Forsgren

2013

INFORMS Journal on Computing

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“…A metric has to be specific for an industry and an objective, but if there are different objectives to take into consideration to facilitate trade-offs between different points of view (disciplines, designers, services), the metric building process is the same for each metric, and a lot of multi-objective optimization techniques [48][49] [50], or techniques based on weighting considerations can be used to achieve an optimal global metric.…”

Section: Discussion and Future Workmentioning

confidence: 99%

Metrics Generation Process for Mechatronics

Warniez¹,

Penas²,

Choley³

et al. 2016

J. Robot. Mechatron.

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[abstFig src='/00280001/05.jpg' width=""300"" text='Metrics generation process overview' ]Due to the complexity of designing mechatronic systems, providers of these systems need to precisely evaluate their products, design processes and projects all along the design phase and beyond. We propose a metrics generation process and then define related specifications to develop an evaluation tool to build customized metrics for the mechatronic industry with respect to its specific process and expectations. The proposed process has been experimented on the modularity measure of two generations of vacuum cleaner robots.

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“…Finally, the last group of MOP problems provides solutions based on a continuous interaction with DM and tries to reach the preferred solution at the end of the algorithm. Based on this sound idea, there are many developed methods categorized in this group [13][14][15][16][17][18][19][20][21]. Different procedures may be better suited for different types of decision makers, for different types of decision situations, or for different stages in the decision making process [22].…”

Section: Introductionmentioning

confidence: 99%

“…The interaction with DM proceeds by generating smaller subsets of the efficient set until a final solution is located [19]. The proposed method by Engau [14] decomposes the original MOP problem into a collection of smaller-sized subproblems to facilitate the evaluation of tradeoffs and the articulation of preferences. A priori preferences on objective tradeoffs are integrated into this process, and DM is supported by an interactive procedure to coordinate any remaining tradeoffs.…”

Section: Introductionmentioning

confidence: 99%

A New Interactive Method to Solve Multiobjective Linear Programming Problems

Sadrabadi¹,

Sadjadi²

2009

JSEA

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Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the pro-posed algorithm is demonstrated by two numerical examples

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Tradeoff-based decomposition and decision-making in multiobjective programming

Cited by 9 publications

References 40 publications

An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques

An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques

Metrics Generation Process for Mechatronics

A New Interactive Method to Solve Multiobjective Linear Programming Problems

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