% References should come from https://iridia-ulb.github.io/references/ @article{Jen03, title = {Reducing the run-time complexity of multiobjective {EA}s: The {NSGA-II} and other algorithms}, author = {M. T. Jensen}, journal = {IEEE Transactions on Evolutionary Computation}, volume = 7, number = 5, pages = {503--515}, year = 2003 } @article{Deb02nsga2, author = { Kalyanmoy Deb and A. Pratap and S. Agarwal and T. Meyarivan}, title = {A fast and elitist multi-objective genetic algorithm: {NSGA-II}}, journal = {IEEE Transactions on Evolutionary Computation}, year = 2002, volume = 6, number = 2, pages = {182--197}, doi = {10.1109/4235.996017} } @incollection{FonGueLopPaq2011emo, address = { Heidelberg }, publisher = {Springer}, year = 2011, series = {Lecture Notes in Computer Science}, volume = 6576, editor = { Takahashi, R. H. C. and others}, booktitle = { Evolutionary Multi-criterion Optimization, EMO 2011}, author = { Carlos M. Fonseca and Andreia P. Guerreiro and Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Lu{\'i}s Paquete }, title = {On the Computation of the Empirical Attainment Function}, doi = {10.1007/978-3-642-19893-9_8}, pages = {106--120}, abstract = {The attainment function provides a description of the location of the distribution of a random non-dominated point set. This function can be estimated from experimental data via its empirical counterpart, the empirical attainment function (EAF). However, computation of the EAF in more than two dimensions is a non-trivial task. In this article, the problem of computing the empirical attainment function is formalised, and upper and lower bounds on the corresponding number of output points are presented. In addition, efficient algorithms for the two and three-dimensional cases are proposed, and their time complexities are related to lower bounds derived for each case.} } @article{DiaLop2020ejor, author = { Juan Esteban Diaz and Manuel L{\'o}pez-Ib{\'a}ñez }, title = {Incorporating Decision-Maker's Preferences into the Automatic Configuration of Bi-Objective Optimisation Algorithms}, journal = {European Journal of Operational Research}, year = 2021, volume = 289, number = 3, pages = {1209--1222}, doi = {10.1016/j.ejor.2020.07.059}, abstract = {Automatic configuration (AC) methods are increasingly used to tune and design optimisation algorithms for problems with multiple objectives. Most AC methods use unary quality indicators, which assign a single scalar value to an approximation to the Pareto front, to compare the performance of different optimisers. These quality indicators, however, imply preferences beyond Pareto-optimality that may differ from those of the decision maker (DM). Although it is possible to incorporate DM's preferences into quality indicators, e.g., by means of the weighted hypervolume indicator (HV$^w$), expressing preferences in terms of weight function is not always intuitive nor an easy task for a DM, in particular, when comparing the stochastic outcomes of several algorithm configurations. A more visual approach to compare such outcomes is the visualisation of their empirical attainment functions (EAFs) differences. This paper proposes using such visualisations as a way of eliciting information about regions of the objective space that are preferred by the DM. We present a method to convert the information about EAF differences into a HV$^w$ that will assign higher quality values to approximation fronts that result in EAF differences preferred by the DM. We show that the resulting HV$^w$ may be used by an AC method to guide the configuration of multi-objective optimisers according to the preferences of the DM. We evaluate the proposed approach on a well-known benchmark problem. Finally, we apply our approach to re-configuring, according to different DM's preferences, a multi-objective optimiser tackling a real-world production planning problem arising in the manufacturing industry.}, supplement = {https://doi.org/10.5281/zenodo.3749288} } @incollection{Grunert01, year = 2001, series = {Lecture Notes in Computer Science}, volume = 1993, publisher = {Springer, Heidelberg, Germany}, editor = { Eckart Zitzler and Kalyanmoy Deb and Lothar Thiele and Carlos A. {Coello Coello} and David Corne }, booktitle = {Evolutionary Multi-criterion Optimization, EMO 2001}, author = { Viviane {Grunert da Fonseca} and Carlos M. Fonseca and Andreia O. Hall }, key = {Fonseca et al., 2001}, title = {Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function}, pages = {213--225}, alias = {Fonseca01}, doi = {10.1007/3-540-44719-9_15}, annote = {Proposed looking at anytime behavior as a multi-objective problem}, keywords = {EAF} } @phdthesis{LopezIbanezPhD, author = { Manuel L{\'o}pez-Ib{\'a}ñez }, title = {Operational Optimisation of Water Distribution Networks}, school = {School of Engineering and the Built Environment}, year = 2009, address = {Edinburgh Napier University, UK}, url = {https://lopez-ibanez.eu/publications#LopezIbanezPhD} } @incollection{GruFon2009:emaa, editor = { Thomas Bartz-Beielstein and Marco Chiarandini and Lu{\'i}s Paquete and Mike Preuss }, year = 2010, address = {Berlin, Germany}, publisher = {Springer}, booktitle = {Experimental Methods for the Analysis of Optimization Algorithms}, author = { Viviane {Grunert da Fonseca} and Carlos M. Fonseca }, title = {The Attainment-Function Approach to Stochastic Multiobjective Optimizer Assessment and Comparison}, pages = {103--130} } @incollection{LopPaqStu09emaa, editor = { Thomas Bartz-Beielstein and Marco Chiarandini and Lu{\'i}s Paquete and Mike Preuss }, year = 2010, address = {Berlin, Germany}, publisher = {Springer}, booktitle = {Experimental Methods for the Analysis of Optimization Algorithms}, author = { Manuel L{\'o}pez-Ib{\'a}ñez and Lu{\'i}s Paquete and Thomas St{\"u}tzle }, title = {Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization}, pages = {209--222}, doi = {10.1007/978-3-642-02538-9_9}, abstract = {This chapter introduces two Perl programs that implement graphical tools for exploring the performance of stochastic local search algorithms for biobjective optimization problems. These tools are based on the concept of the empirical attainment function (EAF), which describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space. In particular, we consider the visualization of attainment surfaces and differences between the first-order EAFs of the outcomes of two algorithms. This visualization allows us to identify certain algorithmic behaviors in a graphical way. We explain the use of these visualization tools and illustrate them with examples arising from practice.} } @article{BinGinRou2015gaupar, title = {Quantifying uncertainty on {P}areto fronts with {G}aussian process conditional simulations}, volume = 243, doi = {10.1016/j.ejor.2014.07.032}, abstract = {Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob'ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob'ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.}, number = 2, journal = {European Journal of Operational Research}, author = {Binois, M. and Ginsbourger, D. and Roustant, O.}, year = 2015, keywords = {Attainment function, Expected Hypervolume Improvement, Kriging, Multi-objective optimization, Vorob'ev expectation}, pages = {386--394} } @phdthesis{ChiarandiniPhD, author = { Marco Chiarandini }, title = {Stochastic Local Search Methods for Highly Constrained Combinatorial Optimisation Problems}, school = {FB Informatik, TU Darmstadt, Germany}, year = 2005 } @article{JohAraMcGSch1991, author = {David S. Johnson and Cecilia R. Aragon and Lyle A. McGeoch and Catherine Schevon}, title = {Optimization by Simulated Annealing: An Experimental Evaluation: Part {II}, Graph Coloring and Number Partitioning}, journal = {Operations Research}, year = 1991, volume = 39, number = 3, pages = {378--406} } @incollection{FonPaqLop06:hypervolume, address = {Piscataway, NJ}, publisher = {IEEE Press}, month = jul, year = 2006, booktitle = {Proceedings of the 2006 Congress on Evolutionary Computation (CEC 2006)}, key = {IEEE CEC}, author = { Carlos M. Fonseca and Lu{\'i}s Paquete and Manuel L{\'o}pez-Ib{\'a}ñez }, title = {An improved dimension-sweep algorithm for the hypervolume indicator}, pages = {1157--1163}, doi = {10.1109/CEC.2006.1688440}, pdf = {FonPaqLop06-hypervolume.pdf}, } @article{BeuFonLopPaqVah09:tec, author = { Nicola Beume and Carlos M. Fonseca and Manuel L{\'o}pez-Ib{\'a}ñez and Lu{\'i}s Paquete and Jan Vahrenhold }, title = {On the complexity of computing the hypervolume indicator}, journal = {IEEE Transactions on Evolutionary Computation}, year = 2009, volume = 13, number = 5, pages = {1075--1082}, doi = {10.1109/TEVC.2009.2015575}, } @article{ZitThiLauFon2003:tec, author = { Eckart Zitzler and Lothar Thiele and Marco Laumanns and Carlos M. Fonseca and Viviane {Grunert da Fonseca}}, title = {Performance Assessment of Multiobjective Optimizers: an Analysis and Review}, journal = {IEEE Transactions on Evolutionary Computation}, year = 2003, volume = 7, number = 2, pages = {117--132}, alias = {perfassess} } @incollection{BezLopStu2017emo, editor = {Heike Trautmann and G{\"{u}}nter Rudolph and Kathrin Klamroth and Oliver Sch{\"{u}}tze and Margaret M. Wiecek and Yaochu Jin and Christian Grimme}, year = 2017, series = {Lecture Notes in Computer Science}, address = {Cham, Switzerland}, publisher = {Springer International Publishing}, booktitle = {Evolutionary Multi-criterion Optimization, EMO 2017}, author = { Leonardo C. T. Bezerra and Manuel L{\'o}pez-Ib{\'a}ñez and Thomas St{\"u}tzle }, title = {An Empirical Assessment of the Properties of Inverted Generational Distance Indicators on Multi- and Many-objective Optimization}, pages = {31--45}, doi = {10.1007/978-3-319-54157-0_3} } @incollection{CoeSie2004igd, publisher = {Springer, Heidelberg, Germany}, volume = 2972, series = {Lecture Notes in Artificial Intelligence}, booktitle = {Proceedings of MICAI}, editor = {Monroy, Ra{\'u}l and Arroyo-Figueroa, Gustavo and Sucar, Luis Enrique and Sossa, Humberto}, author = { Carlos A. {Coello Coello} and Reyes-Sierra, Margarita}, title = {A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm}, year = 2004, pages = {688--697}, keywords = {IGD}, annote = {Introduces Inverted Generational Distance (IGD)} } @incollection{IshMasTanNoj2015igd, editor = { Ant{\'o}nio Gaspar{-}Cunha and Carlos Henggeler Antunes and Carlos A. {Coello Coello} }, volume = 9018, year = 2015, series = {Lecture Notes in Computer Science}, publisher = {Springer, Heidelberg, Germany}, booktitle = {Evolutionary Multi-criterion Optimization, EMO 2015 Part {I}}, author = { Ishibuchi, Hisao and Masuda, Hiroyuki and Tanigaki, Yuki and Nojima, Yusuke}, title = {Modified Distance Calculation in Generational Distance and Inverted Generational Distance}, pages = {110--125} } @article{SchEsqLarCoe2012tec, author = { Oliver Sch{\"u}tze and X. Esquivel and A. Lara and Carlos A. {Coello Coello} }, journal = {IEEE Transactions on Evolutionary Computation}, title = {Using the Averaged {Hausdorff} Distance as a Performance Measure in Evolutionary Multiobjective Optimization}, year = 2012, volume = 16, number = 4, pages = {504--522} } @inproceedings{VelLam1998gp, year = 1998, publisher = {Stanford University Bookstore}, address = {Stanford University, California}, month = jul, editor = {John R. Koza}, booktitle = {Late Breaking Papers at the Genetic Programming 1998 Conference}, alias = {Veldhuizen98a}, key = {Van Veldhuizen and Lamont, 1998a}, title = {Evolutionary Computation and Convergence to a {P}areto Front}, author = { David A. {Van Veldhuizen} and Gary B. Lamont }, pages = {221--228}, keywords = {generational distance} } @incollection{AugBadBroZit2009gecco, address = {New York, NY}, publisher = {ACM Press}, year = 2009, editor = {Franz Rothlauf}, booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2009}, author = { Anne Auger and Johannes Bader and Dimo Brockhoff and Eckart Zitzler }, title = {Articulating User Preferences in Many-Objective Problems by Sampling the Weighted Hypervolume}, pages = {555--562} } @article{ZhoZhaJin2009igdx, author = "Zhou, A. and Zhang, Qingfu and Yaochu Jin ", title = {Approximating the set of {Pareto}-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm}, journal = {IEEE Transactions on Evolutionary Computation}, year = 2009, volume = 13, number = 5, pages = {1167--1189}, doi = {10.1109/TEVC.2009.2021467}, keywords = {multi-modal, IGDX} }