Covariance Matrix Adaptation for Multi-objective Optimization

By Christian Igel, Nikolaus Hansen, Stefan Roth. Evolutionary Computation, 2007

863 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/368053ca18c627a31245b6b425847ddbd70b47ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yaochu Jin
2. Shengxiang Yang
3. Xin Yao
4. Ran Cheng
5. Xing-yi Zhang
6. Ye Tian
7. Qingfu Zhang
8. Kalyanmoy Deb

In Computational Theory and Mathematics

1. Yaochu Jin
2. Shengxiang Yang
3. Xin Yao
4. Ran Cheng
5. Xing-yi Zhang
6. Ye Tian
7. Qingfu Zhang
8. Gary G. Yen

Citations in the corpus

• Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point (2009, background): “In recent years, search algorithms based on the hypervolume indicator [27], a set measure reflecting the volume enclosed by a Pareto front approximation and a reference set, have become increasingly popular, e.g., [16, 9, 14].”
• An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition (2015, methodology): “During the last decades, indicator-based EMO approach (see [25]–[27]) was regarded as a promising method for many-objective optimization.”
• Multi-objective reinforcement learning using sets of pareto dominating policies (2014, background): “Yet, particular multi-objective algorithms also use indicators in their internal workings to steer the search process (Beume et al., 2007; Igel et al., 2007).”
• PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] (2017, neutral): “mo-CmA [69] 2007 mulTi-obJECTivE CovARiAnCE mATRiX AdAPTATion”
• Backtracking Search Optimization Algorithm for numerical optimization problems (2013, background): “The problem-based pairwise statistical comparisons for the solutions obtained in Test 2 (see Table 9) show that the algorithms closest to BSA in terms of problem-solving success are in the order of JDE, CLPSO, CMAES, SADE, ABC and PSO.”
• Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies (2024, neutral): “The hypervolume indicator was also proposed as a selection criterion in MO-CMA-ES [46, 83].”
• Evolution Strategies (2018, background): “We mention here constraint handling [48, 49], fitness surrogates [50], multi-objective variants [51, 52], and exploitation of fitness values [53].”
• A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “Nowadays, some hypervolume-based MOEAs have been well-established, such as indicator-based evolutionary algorithm [44], S metric selection evolutionary algorithm [45], and multiobjective covariance matrix adaptation evolution strategy [46].”
• Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection (2008, methodology): “The SBX and polynomial mutation has been adopted in many MOEA papers (Zitzler et al., 2002; Deb et al., 2002a; Deb and Jain, 2002; Khare et al., 2003; Igel et al., 2007).”
• Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers (2016, methodology): “There have been a few well-established indicator-based MOEAs [30]–[32] available in the literature that employ the HV as the selection criterion.”
• Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization (2014, methodology): “Recently, the indicator hypervolume [82] has been found to be promising in balancing convergence and diversity, leading to the popularity of several hypervolume-based algorithms, such as the S metric selection EMO algorithm (SMS-EMOA) [5] and multiobjective covariance matrix adaptation evolution str”
• HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, neutral): “Most hypervolume-based algorithms first perform a nondominated sorting and then rank solutions within a particular front according to the hypervolume loss that results from the removal of a specific solution (Knowles and Corne, 2003; Emmerich et al., 2005; Igel et al., 2007; Bader et al., 2008).”
• Evolutionary optimization of growing neural gas parameters for object categorization and recognition (2010, methodology): “) selection schemes described in [18], is used to select these individuals from the parent and the offspring population, based on a fitness value assigned to each of them during a fitness assessment.”
• A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization (2009, background): “Notable exceptions include the estimation-of-distribution algorithms (EDAs) [67] that sought to learn the interrelation through joint probability distribution models and the covariance matrix adaptation evolution strategies (CMA-ES) [46], which has been recently extended to MO optimization [27].”
• Parameter Control in Evolutionary Algorithms: Trends and Challenges (2015, methodology): “Based on this, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and its variants [101], [99], [98], [95], [102], [26], [14], [118] have become very successful numeric optimizers.”