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## Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization, Evolutionary Computation

Citations: | 8 - 3 self |

### Citations

1814 | A Fast Elitist Multi-Objective Genetic Algorithm: NSGA-II.
- Deb, Pratap, et al.
- 2000
(Show Context)
Citation Context ...07) published the first study constructing control maps across a range of problem dimensions for the recombination and mutation operators for the Non-dominated Sorting Genetic Algorithm II (NSGA-II) (=-=Deb et al., 2000-=-) by sampling points on a grid from parameter space. They demonstrated that the parameterization sweet-spot migrates as the number of objectives increases. This result suggests that default parameteri... |

845 | Evolutionary Algorithms for Solving Multiobjective Problems, - Coello, Veldhuizen, et al. - 2002 |

633 | Genetic algorithm for multiobjective optimization: formulation, discussion and generalization. Paper presented at the fifth international conference on genetic algorithms, - Fonseca, Fleming - 1993 |

627 | Comparison of multiobjective evolutionary algorithms: Empirical results.
- Zitzler, Deb, et al.
- 2000
(Show Context)
Citation Context ...courage diversity by restricting the number of objective vectors permitted in a region of objective space. The success of several state-of-the-art MOEAs has been attributed to the use of -dominance (=-=Deb et al., 2003-=-; Sierra and Coello Coello, 2005; Kollat and Reed, 2006; Hadka and Reed, 2011). To date, the complex dynamics of MOEAs when solving many-objective optimization problems has limited the analytical asse... |

284 | The compact genetic algorithm,”
- Harik, Lobo, et al.
- 1998
(Show Context)
Citation Context ...lex interactions between their operators and their parameterization, which has limited the analysis of generalized MOEA behavior. Most studies to date only examine one or two parameters in isolation (=-=Harik and Lobo, 1999-=-). However, recent advances in sensitivity analysis have introduced techniques for computing all parameter effects and their multivariate interactions more reliably and with fewer parametric assumptio... |

232 | Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms. I: A Unified Formulation. - Fonseca, Fleming - 1998 |

179 |
Sizing populations for serial and parallel genetic algorithms,
- Goldberg
- 1989
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Citation Context ...c structure in its implementation. -NSGA-II -NSGA-II (Kollat and Reed, 2006) is another popular MOEA that combines NSGA-II, an -dominance archive, adaptive population sizing and time continuation (=-=Goldberg, 1989-=-b; Srivastava, 2002). -NSGA-II has been applied successfully to a broad array of real-world many-objective problems (Kollat and Reed, 2006, 2007; Kasprzyk et al., 2009; Ferringer et al., 2009; Kasprz... |

148 | Scalable Test Problems for Evolutionary Multiobjective Optimization,
- Deb, Thiele, et al.
- 2005
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Citation Context ...e, the complex dynamics of MOEAs when solving many-objective optimization problems has limited the analytical assessment of their strengths and weaknesses. Alternatively, with the advent of the DTLZ (=-=Deb et al., 2001-=-),WFG (Huband et al., 2006) and CEC 2009 (Zhang et al., 2009b) test problem suites, the systematic study of objective scaling through numerical experimentation has provided important insights into MOE... |

141 | Multiobjective optimization using the niched pareto genetic algorithm.
- Horn, Nafpliotis
- 1993
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Citation Context ...Genetic Algorithm (MOGA) by Fonseca and Fleming (1993). In the following years, several popular MOEAs with Pareto-based selection were published, including the Niched-Pareto Genetic Algorithm (NPGA) (=-=Horn and Nafpliotis, 1993-=-) and the Non-dominated Sorting Genetic Algorithm (NSGA) (Srinivas and Deb, 1993). Between 1993 and 2003, several first-generation MOEAs were introduced demonstrating important design concepts such as... |

112 | Scalable multi-objective optimization test problems, in:
- Deb, Thiele, et al.
- 2002
(Show Context)
Citation Context ...s study. Algorithm Class Reference Borg MOEA Adaptive multi-operator (Hadka and Reed, 2011, This Issue) -NSGA-II Pareto front approximation (Kollat and Reed, 2006) -MOEA Pareto front approximation (=-=Deb et al., 2002-=-) IBEA Indicator-based (Zitzler and Künzli, 2004) OMOPSO Particle swarm optimization Sierra and Coello Coello (2005) GDE3 Differential evolution Kukkonen and Lampinen (2005) MOEA/D Aggregate function... |

107 | On metrics for comparing non-dominated sets. In: - Knowles, Corne - 2002 |

90 |
Chaotic Dynamics: An Introduction,
- Baker, Gollub
- 1990
(Show Context)
Citation Context ...ction of parameter sets within a radius r of each other. The growth of C(r) with respect to r reflects dimensionality since higher dimensional spaces permit more opportunities for points to be close (=-=Baker and Gollub, 1990-=-). As shown in Figure 2, rather than computing (9) directly, it is recommended to instead compute the slope where the correlation dimension estimate ln(C(r))/ ln(r) is relatively constant (this region... |

57 | Performance scaling of multi-objective evolutionary algorithms. In: - Khare, Yao, et al. - 2003 |

52 |
Sensitivity measures, Anova-like techniques and the use of bootstrap, in:
- Archer, Saltelli, et al.
- 1997
(Show Context)
Citation Context ...to terms of increasing dimension: f = f0 + ∑ i fi + ∑ i<j fij + ∑ i<j<k fijk + · · ·+ fijk...n, (15) where each individual term is a function only over the inputs in its index (Saltelli et al., 2008; =-=Archier et al., 1997-=-). For example, fi = fi(Xi) and fij = fij(Xi, Xj). Sobol’ proved that the individual terms can be computed using conditional expectations, such as f0 = E(Y ), (16) fi = E(Y |Xi)− f0, (17) fij = E(Y |X... |

50 |
Thierens D.: A balance between proximity and diversity in multiobjective evolutionary algorithms.
- Bosman
- 2003
(Show Context)
Citation Context ...equired to determine if one approximation set is preferred over another must be at least the number of objectives in the problem2. Because different MOEAs tend to perform better in different metrics (=-=Bosman and Thierens, 2003-=-), Deb and Jain (2002) suggest only using metrics for the two main 2Binary indicators alleviate this and other issues, but are more difficult to handle and would hinder comparability between studies. ... |

50 | A review of multiobjective test problems and a scalable test problem toolkit.
- Huband, Hingston, et al.
- 2006
(Show Context)
Citation Context ... of MOEAs when solving many-objective optimization problems has limited the analytical assessment of their strengths and weaknesses. Alternatively, with the advent of the DTLZ (Deb et al., 2001),WFG (=-=Huband et al., 2006-=-) and CEC 2009 (Zhang et al., 2009b) test problem suites, the systematic study of objective scaling through numerical experimentation has provided important insights into MOEA scalability for increasi... |

33 | Techniques for highly multiobjective optimisation: Some nondominated points are better than others,
- Corne, Knowles
- 2007
(Show Context)
Citation Context ...04), and preference order ranking (di Pierro et al., 2007). Classical methods of ranking non-dominated objective vectors, such as average ranking, have also been shown to provide competitive results (=-=Corne and Knowles, 2007-=-). Teytaud (2006, 2007) shows that for large numbers of objectives (i.e., ≥ 10), the rule for selecting candidate solutions may not be more effective than random search. However, some modern MOEAs hav... |

32 |
The paretoenvelope based selection algorithm for multi-objective optimization
- Corne, Knowles, et al.
- 2000
(Show Context)
Citation Context ...eneration algorithms in addition to those already mentioned include the Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele, 1999), the Pareto-Envelope based Selection Algorithm (PESA) (=-=Corne and Knowles, 2000-=-) and the Pareto Archived Evolution Strategy (PAES) (Knowles and Corne, 1999). Most of these MOEAs have since been revised to incorporate more efficient algorithms and improved design concepts. For a ... |

27 |
Many-objective optimization: An engineering design perspective,” in
- Fleming, Purshouse, et al.
- 2005
(Show Context)
Citation Context ...used predominately to solve two or three objective problems, there are growing demands for addressing higher dimensional problems yielding a growing research community in many-objective optimization (=-=Fleming et al., 2005-=-; Adra and Fleming, 2009). Many-objective optimization involves the simultaneous optimization of four or more objectives. Several researchers have examined how problemdifficulty is impacted by adding ... |

21 | An investigation on preference order ranking scheme for multiobjective evolutionary optimization,” - Pierro, Soon-Thiam, et al. - 2007 |

19 |
Introduction to Linear Regression and
- Edwards
- 1976
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Citation Context ...fied, as shown in Figure 2. Let R = {r : rmin ≤ r ≤ rmax} be the sampled values of r within some bounds. The linearity of ln(C(r)) versus ln(r) is determined by computing the correlation coefficient (=-=Edwards, 1993-=-) ρ = n ( ∑ xy)− (∑x) (∑ y)√ n ( ∑ x2)− (∑ x)2√n (∑ y2)− (∑ y)2 , (12) 10 Evolutionary Computation Volume x, Number x Diagnostic Assessment of MOEAs ln(r) ln(C(r)) Saturation as radius encompasses ent... |

14 | Evolutionary many-objective optimisation: many once or one many?," - Hughes - 2005 |

13 | Searching for Pareto-optimal solutions through dimensionality reduction for certain largedimensionalmulti-objective optimization problem,” - Deb, Saxena - 2006 |

12 | Multi-objective optimisation based on relation favour
- Drechsler, Drechsler, et al.
- 2001
(Show Context)
Citation Context ...ion to provide more stringent dominance criteria. The preferability relation by Fonseca and Fleming (1998) is one of the first such contributions. Latter contributions include the relation preferred (=-=Drechsler et al., 2001-=-)1, -preferred (Sülflow et al., 2007), k-optimality and its fuzzy counterpart (Farina and Amato, 2004), and preference order ranking (di Pierro et al., 2007). Classical methods of ranking non-domina... |

12 | Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework”,
- Hadka, Reed
- 2013
(Show Context)
Citation Context ...d in a region of objective space. The success of several state-of-the-art MOEAs has been attributed to the use of -dominance (Deb et al., 2003; Sierra and Coello Coello, 2005; Kollat and Reed, 2006; =-=Hadka and Reed, 2011-=-). To date, the complex dynamics of MOEAs when solving many-objective optimization problems has limited the analytical assessment of their strengths and weaknesses. Alternatively, with the advent of t... |

11 |
A fuzzy definition of optimality for many-criteria optimization problems,”
- Farina, Amato
- 2004
(Show Context)
Citation Context ...98) is one of the first such contributions. Latter contributions include the relation preferred (Drechsler et al., 2001)1, -preferred (Sülflow et al., 2007), k-optimality and its fuzzy counterpart (=-=Farina and Amato, 2004-=-), and preference order ranking (di Pierro et al., 2007). Classical methods of ranking non-dominated objective vectors, such as average ranking, have also been shown to provide competitive results (Co... |

11 | Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems - Ishibuchi, Tsukamoto, et al. - 2008 |

10 |
Genetic Algorithms in Search, Optimization andMachine Learning
- Goldberg
- 1989
(Show Context)
Citation Context ...c structure in its implementation. -NSGA-II -NSGA-II (Kollat and Reed, 2006) is another popular MOEA that combines NSGA-II, an -dominance archive, adaptive population sizing and time continuation (=-=Goldberg, 1989-=-b; Srivastava, 2002). -NSGA-II has been applied successfully to a broad array of real-world many-objective problems (Kollat and Reed, 2006, 2007; Kasprzyk et al., 2009; Ferringer et al., 2009; Kasprz... |

9 | Improving the performance and scalability of differential evolution
- Iorio, Li
- 2008
(Show Context)
Citation Context ...nt operators— they produce offspring independent of the orientation of the fitness landscape— which is important for problems with high degrees of conditional dependence among its decision variables (=-=Iorio and Li, 2008-=-). GDE3 was a strong competitor in the CEC 2009 competition (Zhang and Suganthan, 2009). OMOPSO OMOPSO (Sierra and Coello Coello, 2005) is one of the most successful multiobjective particle swarm opti... |

8 | Managing population and drought risks using many-objective water portfolio planning under uncertainty.” Water Resour
- Kasprzyk, Reed, et al.
- 2009
(Show Context)
Citation Context ...pulation sizing and time continuation (Goldberg, 1989b; Srivastava, 2002). -NSGA-II has been applied successfully to a broad array of real-world many-objective problems (Kollat and Reed, 2006, 2007; =-=Kasprzyk et al., 2009-=-; Ferringer et al., 2009; Kasprzyk et al., 2011; Kollat et al., 2011). In addition, many of its components influenced the design of the Borg MOEA (Hadka and Reed, 2011, This Issue). Borg MOEA Given th... |

5 | Many-Objective Evolutionary Algorithms and Applications to Water Resources Engineering - Pierro - 2006 |

5 | Evolutionary Multi-Objective Optimization in Uncertain Environments: Issues and Algorithms - Goh, Tan - 2009 |

4 |
Indicatorbased Evolutionary Algorithm with Hypervolume Approximation by Achievement Scalarizing Functions
- Ishibuchi, Tsukamoto, et al.
(Show Context)
Citation Context ...(CEC 2009) competition (Zhang and Suganthan, 2009). IBEA Indicator-based methods replace the Pareto dominance relation with an indicator function intended to guide search towards regions of interest (=-=Ishibuchi et al., 2010-=-). IBEA uses the hypervolume measure, which avoids active diversity maintenance by not using an explicit diversity-preserving mechanism. Diversity is instead promoted through the hypervolume measure i... |

4 |
Many-objective de Novo water supply portfolio planning under deep uncertainty. Environ
- Kasprzyk, Reed, et al.
- 2012
(Show Context)
Citation Context ..., 1989b; Srivastava, 2002). -NSGA-II has been applied successfully to a broad array of real-world many-objective problems (Kollat and Reed, 2006, 2007; Kasprzyk et al., 2009; Ferringer et al., 2009; =-=Kasprzyk et al., 2011-=-; Kollat et al., 2011). In addition, many of its components influenced the design of the Borg MOEA (Hadka and Reed, 2011, This Issue). Borg MOEA Given the variety of fitness landscapes and the complex... |

3 |
P.J.: A Diversity Management Operator for Evolutionary Many-Objective Optimisation
- Adra, Fleming
- 2009
(Show Context)
Citation Context ...solve two or three objective problems, there are growing demands for addressing higher dimensional problems yielding a growing research community in many-objective optimization (Fleming et al., 2005; =-=Adra and Fleming, 2009-=-). Many-objective optimization involves the simultaneous optimization of four or more objectives. Several researchers have examined how problemdifficulty is impacted by adding additional objectives to... |

3 |
Many-objective reconfiguration of operational satellite constellations with the large-cluster epsilon Non-dominated Sorting Genetic Algorithm-II
- Ferringer, Spencer, et al.
- 2009
(Show Context)
Citation Context ...e continuation (Goldberg, 1989b; Srivastava, 2002). -NSGA-II has been applied successfully to a broad array of real-world many-objective problems (Kollat and Reed, 2006, 2007; Kasprzyk et al., 2009; =-=Ferringer et al., 2009-=-; Kasprzyk et al., 2011; Kollat et al., 2011). In addition, many of its components influenced the design of the Borg MOEA (Hadka and Reed, 2011, This Issue). Borg MOEA Given the variety of fitness lan... |

3 |
Behavior of evolutionary many-objective optimization
- Ishibuchi, Tsukamoto, et al.
- 2008
(Show Context)
Citation Context ...r selecting candidate solutions may not be more effective than random search. However, some modern MOEAs have the potential for significant search failures on problems with as few as four objectives (=-=Ishibuchi et al., 2008-=-a). At present, it is largely unknown if the dominance relations independently or jointly with search operators control failure modes for many-objective optimization. Also, the multivariate impacts of... |

2 | additional objectives make a problem harder - Do |

1 | 26 Evolutionary Computation Volume x, Number x Diagnostic Assessment of MOEAs Deb - K, Jain - 2002 |

1 |
Evolutionary Computation Volume x, Number x 27 D.Hadka and P.Reed
- Grassberger, Procaccia
- 1983
(Show Context)
Citation Context ... in the distribution of the parameters in Pα. Controllable algorithms are those which exhibit sweet spots, or regions in parameter space with high attainment probabilities. The correlation dimension (=-=Grassberger and Procaccia, 1983-=-) of Pα is our measure of controllability. Hence, controllability is computed by Controllability = lim r→0 ln(C(r)) ln(r) , (9) where C(r) = 1 N(N − 1) N∑ i,j=1 i6=j H(r − |pi − pj |) (10) with pi, pj... |