The balance between proximity and diversity in multiobjective evolutionary algorithms

By Peter A. N. Bosman, Dirk Thierens. IEEE Transactions on Evolutionary Computation, 2003

1,057 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/cd1bb593696b58db29cbb897c12ca9694db42b26

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. Xing-yi Zhang
3. Ran Cheng
4. Ye Tian
5. Gary G. Yen
6. Xin Yao
7. Yanan Sun
8. Shengxiang Yang

In Computational Theory and Mathematics

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

Citations in the corpus

• An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition (2015, methodology): “1) Inverted Generational Distance (IGD) Metric [69]: Let P∗ be a set of points uniformly sampled over the true EF, and S be the set of solutions obtained by an EMO algorithm.”
• Modified Distance Calculation in Generational Distance and Inverted Generational Distance (2015, methodology): “The IGD indicator with the Euclidean distance was used in [2], [13] in 2003 without referring to it as IGD.”
• Improved Regularity Model-Based EDA for Many-Objective Optimization (2018, methodology): “Specifically, the IGD values and the HV values of the evolution trajectory results generated by 10- and 15-objective DTLZ2 test problems over 200 generations are illustrated in Figs.”
• A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling (2015, background): “the decision and objective space [28], [43], [44], which is unique to MOPs.”
• Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, background): “These allow visual inspection of performance in terms of the dual aims of proximity to and diversity across the global tradeoff surface [36].”
• Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition (2014, background): “a) Inverted generational distance (IGD) metric [51]: Let P∗ be a set of uniformly distributed Pareto optimal solutions in the objective space.”
• Stable Matching-Based Selection in Evolutionary Multiobjective Optimization (2014, background): “1) Inverted Generational Distance (IGD) metric [33]: Let P∗ be a set of points uniformly sampled along the PF, and S be the set of solutions obtained by some given MOEA.”
• Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization (2014, methodology): “Naturally, density estimation plays a fundamental role in the evolutionary process of multiobjective optimization for an algorithm to obtain a representative and diverse subset of the Pareto front [6], [53].”
• A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization (2018, methodology): “Inverted generational distance (IGD) [3] used as the performance measure to compare different algorithms.”
• Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons (2019, methodology): “Remark 3: In particular, if all the members in P are evenly distributed on the true PF, the values of IGD, MS, and GD will be zero, one, and zero, respectively.”
• On the Evolutionary Optimization of Many Conflicting Objectives (2007, background): “[18] and for regions of high-performance configurations (sweet-”
• Two-Archive Evolutionary Algorithm for Constrained Multiobjective Optimization (2017, background): “The comparison results of IGD and HV values are given in Table 1 and Table 2 respectively.”
• Towards a New Evolutionary Computation - Advances in the Estimation of Distribution Algorithms (2006, methodology): “2 It is well known that GP search space is significantly constrained [5], and that the bloat control is difficult [11].”
• A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization (2009, background): “There have been significant contributions made to the field of evolutionary multiobjective optimization (EMOO) in the past two decades, as a result of intense research examining topics such as fitness assignment [15], [16], diversity preservation [13], [35], and elitism [3], [39], [57].”
• An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions (2017, methodology): “5.2 Performance Metric To measure the performance of MOEA/D-IEpsilon, C-MOEA/D, MOEA/D-CDP, MOEA/D-SR and MOEA/D-Epsilon, two commonly used metrics–the inverted generation distance (IGD) (Bosman and Thierens (2003)) and the hypervolume (Zitzler and Thiele (1999)) are adopted.”
• A Grid-Based Evolutionary Algorithm for Many-Objective Optimization (2013, positive): “To study the sensitivity of the proposed algorithm to div, we repeat the experiments carried out in the previous section for div ∈ [5, 50] with a step size 1.”
• Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II (2009, methodology): “Since using Pareto dominance alone could discourage the diversity of search, some techniques such as fitness sharing and crowding have often been used as compensation in these MOEAs [5], [9], [11], [28].”
• Indicator-Based Selection in Multiobjective Search (2004, background): “Furthermore, there are also practical problems related to this issue as discussed in [1].”