% References should come from https://iridia-ulb.github.io/references/ @Article{DiaLop2020dm, author = {Juan Esteban Diaz and Manuel López-Ibáñez}, title = {Incorporating Decision-Maker's Preferences into the Automatic Configuration of Bi-Objective Optimisation Algorithms}, journal = {Under review}, year = 2020 } @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}{\~n}ez }, title = {Operational Optimisation of Water Distribution Networks}, school = {School of Engineering and the Built Environment}, year = 2009, address = {Edinburgh Napier University, UK}, url = {http://researchrepository.napier.ac.uk/3044/} } @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}{\~n}ez 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}{\~n}ez }, title = {An improved dimension-sweep algorithm for the hypervolume indicator}, pages = {1157--1163}, doi = {10.1109/CEC.2006.1688440}, pdf = {FonPaqLop06-hypervolume.pdf}, abstract = {This paper presents a recursive, dimension-sweep algorithm for computing the hypervolume indicator of the quality of a set of $n$ non-dominated points in $d>2$ dimensions. It improves upon the existing HSO (Hypervolume by Slicing Objectives) algorithm by pruning the recursion tree to avoid repeated dominance checks and the recalculation of partial hypervolumes. Additionally, it incorporates a recent result for the three-dimensional special case. The proposed algorithm achieves $O(n^{d-2} \log n)$ time and linear space complexity in the worst-case, but experimental results show that the pruning techniques used may reduce the time complexity exponent even further.} } @article{BeuFonLopPaqVah09:tec, author = { Nicola Beume and Carlos M. Fonseca and Manuel L{\'o}pez-Ib{\'a}{\~n}ez 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}, abstract = {The goal of multi-objective optimization is to find a set of best compromise solutions for typically conflicting objectives. Due to the complex nature of most real-life problems, only an approximation to such an optimal set can be obtained within reasonable (computing) time. To compare such approximations, and thereby the performance of multi-objective optimizers providing them, unary quality measures are usually applied. Among these, the \emph{hypervolume indicator} (or \emph{S-metric}) is of particular relevance due to its favorable properties. Moreover, this indicator has been successfully integrated into stochastic optimizers, such as evolutionary algorithms, where it serves as a guidance criterion for finding good approximations to the Pareto front. Recent results show that computing the hypervolume indicator can be seen as solving a specialized version of Klee's Measure Problem. In general, Klee's Measure Problem can be solved with $\mathcal{O}(n \log n + n^{d/2}\log n)$ comparisons for an input instance of size $n$ in $d$ dimensions; as of this writing, it is unknown whether a lower bound higher than $\Omega(n \log n)$ can be proven. In this article, we derive a lower bound of $\Omega(n\log n)$ for the complexity of computing the hypervolume indicator in any number of dimensions $d>1$ by reducing the so-called \textsc{UniformGap} problem to it. For the three dimensional case, we also present a matching upper bound of $\mathcal{O}(n\log n)$ comparisons that is obtained by extending an algorithm for finding the maxima of a point set.} } @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, amonth = apr, 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}{\~n}ez 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} }