Performance assessment of multiobjective optimizers: an analysis and review

By Eckart Zitzler, Lothar Thiele, Marco Laumanns, Carlos M. Fonseca, Viviane Grunert da Fonseca. IEEE Transactions on Evolutionary Computation, 2003

4,242 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e839b9802348606a71a35b6354c6d9def58d7d49

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In Artificial Intelligence

1. Yaochu Jin
2. Xing-yi Zhang
3. Ran Cheng
4. Ye Tian
5. Xin Yao
6. Hisao Ishibuchi
7. Kalyanmoy Deb
8. Gary G. Yen

In Computational Theory and Mathematics

1. Yaochu Jin
2. Xing-yi Zhang
3. Ye Tian
4. Ran Cheng
5. Xin Yao
6. Hisao Ishibuchi
7. Gary G. Yen
8. Kalyanmoy Deb

Citations in the corpus

• Indicator-Based Selection in Multiobjective Search (2004, background): “For instance, the binary additive -indicator I + [18] gives the minimum distance by which a Pareto set approximation needs to or can be translated in each dimension in objective space such that another approximation is weakly dominated.”
• Covariance Matrix Adaptation for Multi-objective Optimization (2007, methodology): “We concisely define the performance measures used, for a detailed description of the methods we refer to the literature (Knowles and Corne, 2002; Zitzler et al., 2003; Knowles et al., 2005).”
• Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, background): “• Knee-driven inverted generational distance (KIGD): where d ( ν i , G ) means the Euclidean distance between reference point ν i in Q and the solution closest to this reference point in G .”
• The irace package: Iterated racing for automatic algorithm configuration (2016, background): “6 ) and the (cid:6) - measure [95] , assign a numerical value to a set of nondominated solutions, thus allowing the application of standard automatic con-figuration methods [58,91] .”
• A review of multiobjective test problems and a scalable test problem toolkit (2006, methodology): “The quality of numerous measures has recently been rigorously analyzed by several authors [17]–[19] and there are useful statistical techniques available (for example, randomization testing [12], [20] or in the case of attainment functions [16], [21]).”
• A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables (2016, methodology): “In the following experimental studies, the inverted generational distance (IGD) metric and I + metric, which are comprehensive indexes of convergence and uniformity [46], are used.”
• Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions (2014, methodology): “(2008) and Deb and Jain (2002), between a set of non-dominated solutions and the nearest solution on the Pareto set, and decreases when a non-dominated point far from the true Pareto front is added to a non-dominated set; (v) the Maximum Pareto Front Error (Van Veldhuizen, 1999), which measures them”
• Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II (2009, methodology): “The inverted generational distance (IGD) [47] is used in assessing the performance of the algorithms in our experimental studies.”
• An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints (2014, background): “For this purpose, the performance metrics (such as hyper-volume measure [7] or other metrics [3], [8]) are either computationally too expensive or may not be meaningful.”
• An Evolutionary Algorithm for Large-Scale Sparse Multiobjective Optimization Problems (2020, methodology): “The inverted generational distance (IGD) [72] is adopted to measure each obtained solution set.”
• Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, methodology): “Performance comparisons between algorithms are made according to a rigorous nonparametric statistical framework, drawing on recommendations in [44].”
• An exact epsilon-constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits (2009, background): “The last column I in both Tables is the -indicator metric reported in [31].”
• Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming (2009, methodology): “The process of updating the archive at each generation employs the concept of Pareto optimality in a set of selected optimization objectives (see [14], [15], and Fig.”
• ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems (2006, methodology): “Many such performance indicators7 exist in the literature but it has been shown in some recent works [38], [39], [ 61 ] that several of these are not consistent with the partial ordering of approximation sets that follows logically from the basic principles of Pareto optimization.”