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Combinatorial Dominance Guarantees for Heuristic Algorithms

Daniel Berend, Steven S. Skiena, Yochai Twitto
2007 Discrete Mathematics & Theoretical Computer Science  
Certain general results relating approximation ratio and combinatorial dominance guarantees for optimization problems over subsets are established.  ...  We introduce new general analysis techniques which apply to a wide range of problems and heuristics for this measure.  ...  Acknowledgements We thank Michael Bender, Gregory Gutin, David Johnson, Matya Katz, and Saurabh Sethia for helpful discussions.  ... 
doi:10.46298/dmtcs.3537 fatcat:rbxjfc7oofhj7ac47hbd2jt6de

Multi-objective optimization of high speed vehicle-passenger catamaran by genetic algorithm

Zbigniew Sekulski
2011 Polish Maritime Research  
In the paper an evolutionary algorithm where selection takes place based on the aggregated objective function combined with domination attributes as well as distance to the asymptotic solution, is proposed  ...  Methods for solution of the multi-criteria optimization problems have been discussed with the focus on the evolutionary optimization algorithms.  ...  means that either the approximation a is better than the approximation B, or the approximations a and B are incomparable with regard to a specified quality measure.  ... 
doi:10.2478/v10012-011-0020-0 fatcat:6v3xjldlqbethlqeaf5fpihqjm

Biobjective Performance Assessment with the COCO Platform [article]

Dimo Brockhoff, Tea Tušar, Dejan Tušar, Tobias Wagner, Nikolaus Hansen, Anne Auger
2016 arXiv   pre-print
The evaluation is based on a hypervolume of all non-dominated solutions in the archive of candidate solutions and measures the runtime until the hypervolume value succeeds prescribed target values.  ...  This document details the rationales behind assessing the performance of numerical black-box optimizers on multi-objective problems within the COCO platform and in particular on the biobjective test suite  ...  The authors would like to thank Thanh-Do Tran for his contributions and assistance with the preliminary code of the bi-objective setting and for providing us with his extensive experimental data.  ... 
arXiv:1605.01746v1 fatcat:foztlkaj4jditgwi4wziygzw5u

A Correlation Analysis of Set Quality Indicator Values in Multiobjective Optimization

Arnaud Liefooghe, Bilel Derbel
2016 Proceedings of the 2016 on Genetic and Evolutionary Computation Conference - GECCO '16  
The authors would like to acknowledge Fabio Daolio and Joshua Knowles for fruitful discussions related to the results presented in the paper.  ...  Monotonicity: An indicator is monotonic with respect to the weak Pareto dominance relation (Pareto-compliant in [16, 29] ) if for any approximation set that dominates another approximation set, its indicator  ...  Let us now analyze the correlation between the indicator values obtained by the sample of approximation sets for the different problem functions.  ... 
doi:10.1145/2908812.2908906 dblp:conf/gecco/LiefoogheD16 fatcat:oqugvxef3vc5tgq2mtdvtcps5m

Performance assessment of multiobjective optimizers: an analysis and review

E. Zitzler, L. Thiele, M. Laumanns, C.M. Fonseca, V.G. da Fonseca
2003 IEEE Transactions on Evolutionary Computation  
how to evaluate the quality of approximation sets.  ...  Most popular are methods that assign each approximation set a vector of real numbers that reflect different aspects of the quality. Sometimes, pairs of approximation sets are considered too.  ...  Ramey for the tip about the proof of Theorem 2, T. Erlebach, S. Chakraborty, and B. Schwikowski for interesting discussions regarding this work, and the anonymous reviewers for their helpful comments.  ... 
doi:10.1109/tevc.2003.810758 fatcat:4nfee4wwlnbvxbydgdtl7uug3y

Impact of selection methods on the diversity of many-objective Pareto set approximations

Luis Martí, Eduardo Segredo, Nayat S´nchez-Pi, Emma Hart
2017 Procedia Computer Science  
Algorithmic approaches are assessed via a set of performance indicators specifically proposed for measuring the diversity of a solution set, such as the Diversity Measure and the Diversity Comparison Indicator  ...  multi-objective optimisers when dealing with many-objective problems.  ...  Diversity Comparison Indicator (DCI) The great majority of those indicators aimed to measure the amount of diversity of a Pareto set approximation are not suitable for problems with a large number of objective  ... 
doi:10.1016/j.procs.2017.08.077 fatcat:oy5d7dqjqrfx3nwus7ph6dqqde

A fast approximation-guided evolutionary multi-objective algorithm

Markus Wagner, Frank Neumann
2013 Proceeding of the fifteenth annual conference on Genetic and evolutionary computation conference - GECCO '13  
This holds for problems with many objectives, but AGE's performance is not competitive on problems with few objectives.  ...  This allows for trading-off approximation and runtime, and it enables a faster approximation process.  ...  The reason is that it does not adjust itself to the optimization problem, but it works with a pre-set value for the target approximation.  ... 
doi:10.1145/2463372.2463448 dblp:conf/gecco/0007N13 fatcat:zuk7oh7o3nasrnfxvwg2qlz5iq

Risk averse submodular utility maximization

Takanori Maehara
2015 Operations Research Letters  
We formulate the problem as a discrete optimization problem of conditional value-at-risk, and prove hardness results for this problem.  ...  In this study, we investigate risk averse solutions to stochastic submodular utility functions.  ...  Unless P = NP, for some constant c > 0, there is no polynomial time c log n approximation algorithm for Minimum Dominating Set problem.  ... 
doi:10.1016/j.orl.2015.08.001 fatcat:dbgvizyfsrbzjnqiop4tr725qy

GECCO 2014 tutorial on evolutionary multiobjective optimization

Dimo Brockhoff
2014 Proceedings of the 2014 conference companion on Genetic and evolutionary computation companion - GECCO Comp '14  
Problem Transformation: Recent view on EMO: First transform problem into a set problem and then define an objective function on sets [Zitzler et al. 2010] Preferences are needed in both cases, but the  ...  • Many problems are NP-hard • What does representative actually mean?  Find a good approximation of the Pareto set? • What is a good approximation?  ...  set problem to solve  but what is the optimum?  ... 
doi:10.1145/2598394.2605339 dblp:conf/gecco/Brockhoff14 fatcat:3rjyn4udejg4fiimvtnzvxq3ne

Enhancement of Sandwich Algorithms for Approximating Higher-Dimensional Convex Pareto Sets

Gijs Rennen, Edwin R. van Dam, Dick den Hertog
2011 INFORMS journal on computing  
In this paper, we consider the approximation of Pareto sets for problems with three or more convex objectives and with convex constraints.  ...  To find a good solution for such multi-objective optimization problems, an approximation of the Pareto set is often generated.  ...  Acknowledgements The authors wish to thank David Craft for providing the data and problem description of the 2D phantom pancreas IMRT-case.  ... 
doi:10.1287/ijoc.1100.0419 fatcat:bdg2atzkhvcepbitivrg2oujjy

Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets

Gijs Rennen, Edwin van Dam, Dick den Hertog
2009 Social Science Research Network  
In this paper, we consider the approximation of Pareto sets for problems with three or more convex objectives and with convex constraints.  ...  To find a good solution for such multi-objective optimization problems, an approximation of the Pareto set is often generated.  ...  Acknowledgements The authors wish to thank David Craft for providing the data and problem description of the 2D phantom pancreas IMRT-case.  ... 
doi:10.2139/ssrn.1427721 fatcat:juwr6annh5cnbmeukexc3e2gqa

Quality Assessment of Pareto Set Approximations [chapter]

Eckart Zitzler, Joshua Knowles, Lothar Thiele
2008 Lecture Notes in Computer Science  
The chapter should be of interest to anyone concerned with generating and analysing Pareto set approximations.  ...  This chapter reviews methods for the assessment and comparison of Pareto set approximations.  ...  Acknowledgements Sections 14.1 to 14.5 summarize the results of the discussion of the working group on set quality measures during the Dagstuhl seminar on evolutionary multiobjective optimization 2006.  ... 
doi:10.1007/978-3-540-88908-3_14 fatcat:te534mwsprhqllenqyi7vspzei

Ensuring Smoothly Navigable Approximation Sets by Bézier Curve Parameterizations in Evolutionary Bi-objective Optimization [chapter]

Stefanus C. Maree, Tanja Alderliesten, Peter A. N. Bosman
2020 Lecture Notes in Computer Science  
We show that high-quality approximation sets can be obtained with BezEA, sometimes even outperforming the domination-and UHV-based algorithms, while smoothness of the navigation trajectory through decision  ...  Therefore, we use the recently introduced uncrowded hypervolume (UHV) to reformulate the multi-objective optimization problem as a single-objective problem in which parameterized approximation sets are  ...  We furthermore acknowledge financial support of the Nijbakker-Morra Foundation for a highperformance computing system.  ... 
doi:10.1007/978-3-030-58115-2_15 fatcat:3w4qn7rmnzbazczrj2nwzyw3vi

A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem

Bogdana Stanojević, Milan Stanojević
2019 Reserche operationelle  
The main contribution of this paper is the procedure that constructs a good approximation to the non-dominated set of multiple objective linear fractional programming problem using the solutions to certain  ...  In our approach we propose a way to generate a discrete set of feasible solutions that are further used as starting points in any procedure for deriving efficient solutions.  ...  Measures of approximation In this section we briefly present the metrics introduced in [20] for measuring the quality of the approximation of the non-dominated set of MOLFP problems.  ... 
doi:10.1051/ro/2018083 fatcat:77qyllofgzd4lklxm2yhkmtyxu

A Tutorial on Evolutionary Multiobjective Optimization [chapter]

Eckart Zitzler, Marco Laumanns, Stefan Bleuler
2004 Lecture notes in economics and mathematical systems  
As evolutionary algorithms possess several characteristics that are desirable for this type of problem, this class of search strategies has been used for multiobjective optimization for more than a decade  ...  This paper gives an overview of evolutionary multiobjective optimization with the focus on methods and theory.  ...  The Model Problem As the example problem for this analysis, we consider the maximization of a 2-dimensional vector valued function, Lotz, which maps n binary decision variables to 2 objective functions  ... 
doi:10.1007/978-3-642-17144-4_1 fatcat:ifi4g2nydrcujd3spa5ecjuvtu
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